Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP384_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:37:47 AM UTC 2026

% Result   : Theorem 53.19s 13.58s
% Output   : Refutation 56.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  652
% Syntax   : Number of formulae    : 1306 ( 437 unt;   0 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  :    0 (   0   >;   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$d_decl',type,
    'inj_on$d': 'A_update_b_update_fun_a_update_a_update_fun_fun$' > 'A_update_b_update_fun_set$' > $o ).

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

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

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

thf('uus$_decl',type,
    'uus$': 'A_update_a_update_bool_fun_fun$' ).

thf('uvb$_decl',type,
    'uvb$': 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' ).

thf('rel_fun$au_decl',type,
    'rel_fun$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$aa_decl',type,
    'register_tensor$aa': 'B_update_a_update_fun$' > 'A_update_b_update_fun$' > 'B_a_prod_update_a_b_prod_update_fun$' ).

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

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

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

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

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

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

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

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

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

thf('uuq$_decl',type,
    'uuq$': 'C_update_c_update_bool_fun_fun$' ).

thf('fun_app$bx_decl',type,
    'fun_app$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$at_decl',type,
    'comp$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$am_decl',type,
    'map_fun$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$_decl',type,
    'member$': 'A_update$' > 'A_update_set$' > $o ).

thf('comp$ar_decl',type,
    'comp$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$e_decl',type,
    'image$e': 'B_update_b_update_fun$' > 'B_update_set_b_update_set_fun$' ).

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

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

thf('rel_fun$h_decl',type,
    'rel_fun$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$j_decl',type,
    'comp$j': 'B_update_b_update_fun$' > 'B_update_b_update_fun_b_update_b_update_fun_fun$' ).

thf('rel_fun$be_decl',type,
    'rel_fun$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$_decl',type,
    'uug$': 'B_update_a_update_fun$' > 'B_update_c_a_prod_update_fun$' ).

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

thf('rel_fun$z_decl',type,
    'rel_fun$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$aj_decl',type,
    'fun_app$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$f_decl',type,
    'register_tensor$f': 'A_update_a_update_fun$' > 'C_update_c_update_fun$' > 'A_c_prod_update_a_c_prod_update_fun$' ).

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

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

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

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

thf('comp$bh_decl',type,
    'comp$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$s_decl',type,
    'compatible$s': 'A_update_a_c_prod_update_fun$' > 'B_update_a_c_prod_update_fun$' > $o ).

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

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

thf('f$_decl',type,
    'f$': 'B_update_a_update_fun$' ).

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

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

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

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

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

thf('comp$bk_decl',type,
    'comp$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$b_decl',type,
    'id$b': 'A_update_a_update_fun$' ).

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

thf('fun_app$o_decl',type,
    'fun_app$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$bf_decl',type,
    'rel_fun$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$ba_decl',type,
    'rel_fun$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$b_decl',type,
    'iso_tuple_update_accessor_eq_assist$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$_decl',type,
    'uua$': 'C_update$' > 'A_update_c_update_fun$' ).

thf('fun_app$cc_decl',type,
    'fun_app$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$_decl',type,
    'fun_app$': 'A_update_b_update_fun_bool_fun$' > 'A_update_b_update_fun$' > $o ).

thf('rel_fun$al_decl',type,
    'rel_fun$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$u_decl',type,
    'id$u': 'C_update_set_c_update_set_fun$' ).

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

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

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

thf('map_fun$v_decl',type,
    'map_fun$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$b_decl',type,
    'rel_fun$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$k_decl',type,
    'id$k': 'A_a_prod_update_a_a_prod_update_fun$' ).

thf('comp$n_decl',type,
    'comp$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$w_decl',type,
    'fun_app$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$af_decl',type,
    'rel_fun$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$g_decl',type,
    'fun_app$g': 'A_update_c_update_fun$' > 'A_update$' > 'C_update$' ).

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

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

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

thf('rel_fun$bs_decl',type,
    'rel_fun$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$ac_decl',type,
    'map_fun$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$_decl',type,
    'the_inv_into$': 'C_update_set$' > 'C_update_a_update_fun$' > 'A_update_c_update_fun$' ).

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

thf('uur$_decl',type,
    'uur$': 'B_update_b_update_bool_fun_fun$' ).

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

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

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

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

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

thf('comp$o_decl',type,
    'comp$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$c_decl',type,
    'fcomp$c': 'C_update_a_update_fun$' > 'A_update_b_update_fun$' > 'C_update_b_update_fun$' ).

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

thf('rel_fun$bi_decl',type,
    'rel_fun$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$ab_decl',type,
    'comp$ab': 'A_update_c_update_fun$' > 'A_update_a_update_fun$' > 'A_update_c_update_fun$' ).

thf('grp$g_decl',type,
    'grp$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$d_decl',type,
    'iso_register$d': 'C_update_c_update_fun$' > $o ).

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

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

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

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

thf('fun_app$r_decl',type,
    'fun_app$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$b_decl',type,
    'grp$b': 'A_update_set$' > 'A_update_a_update_fun$' > 'A_update_a_update_bool_fun_fun$' ).

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

thf('map_fun$ar_decl',type,
    'map_fun$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$l_decl',type,
    'register_pair$l': 'A_update_a_update_fun$' > 'B_update_a_update_fun$' > 'A_b_prod_update_a_update_fun$' ).

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

thf('fun_app$ak_decl',type,
    'fun_app$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$m_decl',type,
    'inj_on$m': 'B_update_b_update_fun$' > 'B_update_set$' > $o ).

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

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

thf('uva$_decl',type,
    'uva$': 'A_update_c_update_fun_a_update_c_update_fun_bool_fun_fun$' ).

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

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

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

thf('rel_fun$bv_decl',type,
    'rel_fun$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$am_decl',type,
    'rel_fun$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$m_decl',type,
    'rel_fun$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$s_decl',type,
    'map_fun$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$h_decl',type,
    'inj_on$h': 'B_update_a_update_fun_b_update_b_update_fun_fun$' > 'B_update_a_update_fun_set$' > $o ).

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

thf('rel_fun$bh_decl',type,
    'rel_fun$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$am_decl',type,
    'fun_app$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$f_decl',type,
    'type_definition$f': 'A_update_b_update_fun$' > 'B_update_a_update_fun$' > 'B_update_set$' > $o ).

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

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

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

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

thf('rel_fun$bl_decl',type,
    'rel_fun$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$bo_decl',type,
    'fun_app$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$f_decl',type,
    'map_fun$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$o_decl',type,
    'map_fun$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$o_decl',type,
    'rel_fun$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$ad_decl',type,
    'map_fun$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$f_decl',type,
    'id$f': 'B_c_prod_update_b_c_prod_update_fun$' ).

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

thf('map_fun$g_decl',type,
    'map_fun$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$c_decl',type,
    'map_fun$c': 'A_update_b_update_fun$' > 'A_update_c_update_fun$' > 'B_update_a_update_fun_a_update_c_update_fun_fun$' ).

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

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

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

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

thf('fun_app$ce_decl',type,
    'fun_app$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$_decl',type,
    'uun$': 'A_update_c_update_fun$' > 'A_update_c_update_fun$' > 'A_update_bool_fun$' ).

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

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

thf('comp$q_decl',type,
    'comp$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$bt_decl',type,
    'rel_fun$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$f_decl',type,
    'image$f': 'A_update_a_update_fun$' > 'A_update_set_a_update_set_fun$' ).

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

thf('fun_app$bl_decl',type,
    'fun_app$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$a_decl',type,
    'iso_tuple_update_accessor_eq_assist$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$a_decl',type,
    'collect$a': 'C_update_a_update_fun_bool_fun$' > 'C_update_a_update_fun_set$' ).

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

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

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

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

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

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

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

thf('comp$bl_decl',type,
    'comp$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$p_decl',type,
    'register_pair$p': 'C_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_c_prod_update_a_update_fun$' ).

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

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

thf('grp$i_decl',type,
    'grp$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$_decl',type,
    'image$': 'A_update_b_update_fun$' > 'A_update_set$' > 'B_update_set$' ).

thf('comp$aq_decl',type,
    'comp$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$y_decl',type,
    'rel_fun$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$ay_decl',type,
    'fun_app$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$bb_decl',type,
    'rel_fun$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$l_decl',type,
    'id$l': 'C_update_c_update_fun_c_update_c_update_fun_fun$' ).

thf('map_fun$h_decl',type,
    'map_fun$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$bj_decl',type,
    'rel_fun$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$au_decl',type,
    'map_fun$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$z_decl',type,
    'register_tensor$z': 'C_update_b_update_fun$' > 'A_update_a_update_fun$' > 'C_a_prod_update_b_a_prod_update_fun$' ).

thf('rel_fun$bc_decl',type,
    'rel_fun$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$ae_decl',type,
    'fun_app$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$bm_decl',type,
    'rel_fun$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$g_decl',type,
    'image$g': 'B_update_c_update_fun$' > 'B_update_set$' > 'C_update_set$' ).

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

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

thf('grp$d_decl',type,
    'grp$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$i_decl',type,
    'rel_fun$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$bc_decl',type,
    'fun_app$bc': 'A_update_c_update_fun_a_update_b_update_fun_fun$' > 'A_update_c_update_fun$' > 'A_update_b_update_fun$' ).

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

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

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

thf('fun_app$bp_decl',type,
    'fun_app$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$s_decl',type,
    'register_pair$s': 'B_update_c_update_fun$' > 'C_update_c_update_fun$' > 'B_c_prod_update_c_update_fun$' ).

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

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

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

thf('fun_app$bk_decl',type,
    'fun_app$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$u_decl',type,
    'fun_app$u': 'A_update_b_update_fun$' > 'A_update$' > 'B_update$' ).

thf('rel_fun$j_decl',type,
    'rel_fun$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$bd_decl',type,
    'rel_fun$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$d_decl',type,
    'id$d': 'C_b_prod_update_c_b_prod_update_fun$' ).

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

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

thf('rel_fun$a_decl',type,
    'rel_fun$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$a_decl',type,
    'fun_app$a': 'C_update_a_update_fun_bool_fun$' > 'C_update_a_update_fun$' > $o ).

thf('map_fun$aq_decl',type,
    'map_fun$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$at_decl',type,
    'rel_fun$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$_decl',type,
    'comp_update$': 'C_update$' > 'C_update_c_update_fun$' ).

thf('pred_DEADID$_decl',type,
    'pred_DEADID$': 'C_update_bool_fun$' ).

thf('rel_fun$q_decl',type,
    'rel_fun$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$ao_decl',type,
    'rel_fun$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$c_decl',type,
    'register$c': 'A_update_b_update_fun$' > $o ).

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

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

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

thf('rel_fun$ab_decl',type,
    'rel_fun$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$j_decl',type,
    'compatible$j': 'C_update_b_update_fun$' > 'B_update_b_update_fun$' > $o ).

thf('comp$bi_decl',type,
    'comp$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$n_decl',type,
    'register_tensor$n': 'C_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_c_prod_update_a_a_prod_update_fun$' ).

thf('map_fun$aa_decl',type,
    'map_fun$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$ap_decl',type,
    'comp$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$_decl',type,
    'uuk$': 'A_update_bool_fun$' ).

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

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

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

thf('rel_fun$br_decl',type,
    'rel_fun$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$aw_decl',type,
    'rel_fun$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$g_decl',type,
    'the_inv_into$g': 'C_update_set$' > 'C_update_b_update_fun$' > 'B_update_c_update_fun$' ).

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

thf('map_fun$af_decl',type,
    'map_fun$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$ae_decl',type,
    'rel_fun$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$_decl',type,
    'uum$': 'C_update_bool_fun$' ).

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

thf('rel_fun$x_decl',type,
    'rel_fun$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$d_decl',type,
    'rel_fun$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$d_decl',type,
    'comp$d': 'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$' ).

thf('rel_fun$bx_decl',type,
    'rel_fun$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$b_decl',type,
    'the_inv_into$b': 'A_update_set$' > 'A_update_b_update_fun$' > 'B_update_a_update_fun$' ).

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

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

thf('map_fun$i_decl',type,
    'map_fun$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$aq_decl',type,
    'fun_app$aq': 'B_a_prod_update_a_c_prod_update_fun$' > 'B_a_prod_update$' > 'A_c_prod_update$' ).

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

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

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

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

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

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

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

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

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

thf('map_fun$al_decl',type,
    'map_fun$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$ak_decl',type,
    'map_fun$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$aj_decl',type,
    'comp$aj': 'B_update_c_update_fun$' > 'A_update_b_update_fun$' > 'A_update_c_update_fun$' ).

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

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

thf('rel_fun$an_decl',type,
    'rel_fun$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$_decl',type,
    'iso_tuple_surjective_proof_assist$': 'C_update$' > 'C_update$' > 'C_update_c_update_fun$' > $o ).

thf('map_fun$aw_decl',type,
    'map_fun$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$b_decl',type,
    'inj_on$b': 'B_update_a_update_fun$' > 'B_update_set$' > $o ).

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

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

thf('rel_fun$az_decl',type,
    'rel_fun$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$u_decl',type,
    'map_fun$u': 'C_update_c_update_fun$' > 'B_update_b_update_fun$' > 'C_update_b_update_fun_c_update_b_update_fun_fun$' ).

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

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

thf('rel_fun$bw_decl',type,
    'rel_fun$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$x_decl',type,
    'fun_app$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$ab_decl',type,
    'map_fun$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$q_decl',type,
    'fun_app$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$ap_decl',type,
    'rel_fun$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$bd_decl',type,
    'comp$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$i_decl',type,
    'comp$i': 'B_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_update_b_update_fun$' ).

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

thf('id$_decl',type,
    'id$': 'C_update_c_update_fun$' ).

thf('comp$s_decl',type,
    'comp$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$_decl',type,
    'uul$': 'B_update_a_update_fun$' > 'B_update_a_update_fun$' > 'B_update_bool_fun$' ).

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

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

thf('rel_fun$g_decl',type,
    'rel_fun$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$a_decl',type,
    'relcompp$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$bu_decl',type,
    'fun_app$bu': 'B_update_set_b_update_fun$' > 'B_update_set$' > 'B_update$' ).

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

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

thf('rel_fun$ar_decl',type,
    'rel_fun$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$a_decl',type,
    'id$a': 'B_update_b_update_fun$' ).

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

thf('rel_fun$c_decl',type,
    'rel_fun$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$d_decl',type,
    'image$d': 'C_update_c_update_fun$' > 'C_update_set_c_update_set_fun$' ).

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

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

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

thf('rel_fun$ag_decl',type,
    'rel_fun$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$a_decl',type,
    'image$a': 'C_update_a_update_fun$' > 'C_update_set$' > 'A_update_set$' ).

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

thf('map_fun$ae_decl',type,
    'map_fun$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$h_decl',type,
    'type_definition$h': 'B_update_a_update_fun$' > 'A_update_b_update_fun$' > 'A_update_set$' > $o ).

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

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

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

thf('rel_fun$p_decl',type,
    'rel_fun$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$t_decl',type,
    'rel_fun$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$am_decl',type,
    'comp$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$b_decl',type,
    'iso_register$b': 'A_update_c_update_fun$' > $o ).

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

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

thf('rel_fun$bq_decl',type,
    'rel_fun$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$f_decl',type,
    'compatible$f': 'B_update_a_update_fun$' > 'A_update_a_update_fun$' > $o ).

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

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

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

thf('rel_fun$ac_decl',type,
    'rel_fun$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$an_decl',type,
    'fun_app$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$a_decl',type,
    'comp_update$a': 'A_update$' > 'A_update_a_update_fun$' ).

thf('rel_fun$e_decl',type,
    'rel_fun$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$l_decl',type,
    'rel_fun$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$bo_decl',type,
    'comp$bo': 'C_update_bool_fun$' > 'A_update_c_update_fun$' > 'A_update_bool_fun$' ).

thf('uuo$_decl',type,
    'uuo$': 'B_update_bool_fun$' ).

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

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

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

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

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

thf('rel_fun$v_decl',type,
    'rel_fun$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$l_decl',type,
    'register_tensor$l': 'B_update_a_update_fun$' > 'B_update_a_update_fun$' > 'B_b_prod_update_a_a_prod_update_fun$' ).

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

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

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

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

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

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

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

thf('map_fun$p_decl',type,
    'map_fun$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$ad_decl',type,
    'fun_app$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$e_decl',type,
    'register_tensor$e': 'B_update_b_update_fun$' > 'A_update_a_update_fun$' > 'B_a_prod_update_b_a_prod_update_fun$' ).

thf('fun_app$ac_decl',type,
    'fun_app$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$ah_decl',type,
    'rel_fun$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$j_decl',type,
    'register_pair$j': 'C_update_b_update_fun$' > 'A_update_b_update_fun$' > 'C_a_prod_update_b_update_fun$' ).

thf('relcompp$b_decl',type,
    'relcompp$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$m_decl',type,
    'fun_app$m': 'A_update_bool_fun$' > 'A_update$' > $o ).

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

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

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

thf('rel_fun$aj_decl',type,
    'rel_fun$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$h_decl',type,
    'image$h': 'C_update_b_update_fun$' > 'C_update_set$' > 'B_update_set$' ).

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

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

thf('comp$ao_decl',type,
    'comp$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$bo_decl',type,
    'rel_fun$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$ag_decl',type,
    'map_fun$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$j_decl',type,
    'map_fun$j': 'A_update_a_update_fun$' > 'B_update_b_update_fun$' > 'A_update_b_update_fun_a_update_b_update_fun_fun$' ).

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

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

thf('comp$ak_decl',type,
    'comp$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$e_decl',type,
    'type_definition$e': 'A_update_a_update_fun$' > 'A_update_a_update_fun$' > 'A_update_set$' > $o ).

thf('rel_fun$ak_decl',type,
    'rel_fun$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$h_decl',type,
    'comp$h': 'C_update_c_update_fun$' > 'B_update_c_update_fun$' > 'B_update_c_update_fun$' ).

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

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

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

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

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

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

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

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

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

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

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

thf('rel_fun$bu_decl',type,
    'rel_fun$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$as_decl',type,
    'rel_fun$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$bq_decl',type,
    'fun_app$bq': 'A_update_set_a_update_set_fun$' > 'A_update_set$' > 'A_update_set$' ).

thf('rel_fun$by_decl',type,
    'rel_fun$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$a_decl',type,
    'conversep$a': 'B_update_b_update_bool_fun_fun$' > 'B_update_b_update_bool_fun_fun$' ).

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

thf('rel_fun$bg_decl',type,
    'rel_fun$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$h_decl',type,
    'register_pair$h': 'C_update_c_update_fun$' > 'A_update_c_update_fun$' > 'C_a_prod_update_c_update_fun$' ).

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

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

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

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

thf('map_fun$ao_decl',type,
    'map_fun$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$k_decl',type,
    'compatible$k': 'B_update_b_update_fun$' > 'C_update_b_update_fun$' > $o ).

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

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

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

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

thf('comp$bf_decl',type,
    'comp$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$q_decl',type,
    'compatible$q': 'A_update_a_update_fun$' > 'A_update_a_update_fun$' > $o ).

thf('map_fun$an_decl',type,
    'map_fun$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$d_decl',type,
    'register$d': 'A_a_prod_update_c_c_prod_update_fun$' > $o ).

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

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

thf('comp$l_decl',type,
    'comp$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$b_decl',type,
    'collect$b': 'B_update_a_update_fun_bool_fun$' > 'B_update_a_update_fun_set$' ).

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

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

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

thf('rel_fun$bk_decl',type,
    'rel_fun$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$f_decl',type,
    'rel_fun$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$s_decl',type,
    'rel_fun$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$bg_decl',type,
    'fun_app$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$g_decl',type,
    'iso_tuple_update_accessor_cong_assist$g': 'A_update_a_update_fun_c_update_c_update_fun_fun$' > 'C_update_a_update_fun$' > $o ).

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

thf('rel_fun$bn_decl',type,
    'rel_fun$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$g_decl',type,
    'comp$g': 'C_update_c_update_fun$' > 'C_update_c_update_fun_c_update_c_update_fun_fun$' ).

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

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

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

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

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

thf('top$_decl',type,
    'top$': 'A_update_set$' ).

thf('comp$r_decl',type,
    'comp$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$a_decl',type,
    'compatible$a': 'A_update_c_update_fun$' > 'A_update_c_update_fun$' > $o ).

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

thf('map_fun$n_decl',type,
    'map_fun$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$u_decl',type,
    'rel_fun$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$a_decl',type,
    'the_inv_into$a': 'B_update_set$' > 'B_update_a_update_fun$' > 'A_update_b_update_fun$' ).

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

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

thf('map_fun$ai_decl',type,
    'map_fun$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$f_decl',type,
    'iso_register$f': 'C_update_b_update_fun$' > $o ).

thf('map_fun$as_decl',type,
    'map_fun$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$c_decl',type,
    'iso_register$c': 'B_update_a_update_fun$' > $o ).

thf('comp$m_decl',type,
    'comp$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$as_decl',type,
    'comp$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$bm_decl',type,
    'fun_app$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$_decl',type,
    'inv_into$': 'B_update_set$' > 'B_update_a_update_fun$' > 'A_update_b_update_fun$' ).

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

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

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

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

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

thf('rel_fun$_decl',type,
    'rel_fun$': '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$v_decl',type,
    'id$v': 'B_update_set_b_update_set_fun$' ).

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

thf('rel_fun$bp_decl',type,
    'rel_fun$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$y_decl',type,
    'comp$y': 'B_update_a_update_fun$' > 'B_update_b_update_fun$' > 'B_update_a_update_fun$' ).

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

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

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

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

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

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

thf('rel_fun$ai_decl',type,
    'rel_fun$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$bm_decl',type,
    'comp$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$bb_decl',type,
    'fun_app$bb': 'B_update_a_update_fun_a_update_b_update_fun_fun$' > 'B_update_a_update_fun$' > 'A_update_b_update_fun$' ).

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

thf('map_fun$x_decl',type,
    'map_fun$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$l_decl',type,
    'map_fun$l': 'A_update_c_update_fun$' > 'A_update_b_update_fun$' > 'C_update_a_update_fun_a_update_b_update_fun_fun$' ).

thf('comp$t_decl',type,
    'comp$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$c_decl',type,
    'grp$c': 'B_update_set$' > 'B_update_a_update_fun$' > 'B_update_a_update_bool_fun_fun$' ).

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

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

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

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

thf('rel_fun$ay_decl',type,
    'rel_fun$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$aa_decl',type,
    'comp$aa': 'A_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_update_a_update_fun$' ).

thf('fun_app$bi_decl',type,
    'fun_app$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$av_decl',type,
    'rel_fun$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$f_decl',type,
    'pred_fun$f': 'C_update_bool_fun$' > 'B_update_bool_fun$' > 'C_update_b_update_fun$' > $o ).

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

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

thf('rel_fun$aa_decl',type,
    'rel_fun$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$b_decl',type,
    'pred_DEADID$b': 'A_update_bool_fun$' ).

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

thf('fun_app$bd_decl',type,
    'fun_app$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$a_decl',type,
    'tensor_update$a': 'A_update$' > 'A_update$' > 'A_a_prod_update$' ).

thf('fun_app$y_decl',type,
    'fun_app$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$n_decl',type,
    'rel_fun$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$z_decl',type,
    'comp$z': 'C_update_a_update_fun$' > 'C_update_c_update_fun$' > 'C_update_a_update_fun$' ).

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

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

thf('fun_app$bn_decl',type,
    'fun_app$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$av_decl',type,
    'fun_app$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$cb_decl',type,
    'fun_app$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$i_decl',type,
    'compatible$i': 'C_update_b_update_fun$' > 'C_update_b_update_fun$' > $o ).

thf('comp$al_decl',type,
    'comp$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$e_decl',type,
    'top$e': 'B_update_a_update_fun_set$' ).

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

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

thf('rel_fun$k_decl',type,
    'rel_fun$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$b_decl',type,
    'id_update$b': 'B_update$' ).

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

thf('fun_app$bz_decl',type,
    'fun_app$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$g_decl',type,
    'type_definition$g': 'C_update_a_update_fun$' > 'A_update_c_update_fun$' > 'A_update_set$' > $o ).

thf('map_fun$ah_decl',type,
    'map_fun$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$aj_decl',type,
    'map_fun$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$cd_decl',type,
    'fun_app$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$t_decl',type,
    'compatible$t': 'B_update_c_a_prod_update_fun$' > 'A_update_c_a_prod_update_fun$' > $o ).

thf('rel_fun$w_decl',type,
    'rel_fun$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$ax_decl',type,
    'rel_fun$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$c_decl',type,
    'compatible$c': 'B_update_a_update_fun$' > 'C_update_a_update_fun$' > $o ).

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

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

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

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

thf('grp$j_decl',type,
    'grp$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$b_decl',type,
    'type_definition$b': 'A_update_c_update_fun$' > 'C_update_a_update_fun$' > 'C_update_set$' > $o ).

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

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

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

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

thf('map_fun$at_decl',type,
    'map_fun$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$k_decl',type,
    'register$k': 'B_update_b_update_fun$' > $o ).

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

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

thf('comp$u_decl',type,
    'comp$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$b_decl',type,
    'iso_tuple_surjective_proof_assist$b': 'A_update$' > 'A_update$' > 'A_update_a_update_fun$' > $o ).

thf('map_fun$r_decl',type,
    'map_fun$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$ax_decl',type,
    'fun_app$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$a_decl',type,
    'type_definition$a': 'B_update_c_update_fun$' > 'C_update_b_update_fun$' > 'C_update_set$' > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf('uuz$_decl',type,
    'uuz$': 'B_update_a_update_fun_b_update_a_update_fun_bool_fun_fun$' ).

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

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

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

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

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

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

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

thf('comp$an_decl',type,
    'comp$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$_decl',type,
    'register_tensor$': '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$_decl',type,
    'iso_tuple_update_accessor_eq_assist$': '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$b_decl',type,
    'fun_app$b': 'B_update_a_update_fun_bool_fun$' > 'B_update_a_update_fun$' > $o ).

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

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

thf('map_fun$w_decl',type,
    'map_fun$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$cf_decl',type,
    'fun_app$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$ad_decl',type,
    'rel_fun$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$c_decl',type,
    'image$c': 'A_update_c_update_fun$' > 'A_update_set$' > 'C_update_set$' ).

thf('comp$bg_decl',type,
    'comp$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$x_decl',type,
    'register_tensor$x': 'A_update_b_update_fun$' > 'B_update_a_update_fun$' > 'A_b_prod_update_b_a_prod_update_fun$' ).

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

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

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

thf('rel_fun$r_decl',type,
    'rel_fun$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$_decl',type,
    'collect$': 'A_update_b_update_fun_bool_fun$' > 'A_update_b_update_fun_set$' ).

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

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

thf('g$_decl',type,
    'g$': 'A_update_c_update_fun$' ).

thf('fun_app$af_decl',type,
    'fun_app$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$i_decl',type,
    'id$i': 'A_c_prod_update_a_c_prod_update_fun$' ).

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

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

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

thf('grp$f_decl',type,
    'grp$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$bj_decl',type,
    'comp$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$l_decl',type,
    'fun_app$l': 'B_update_b_update_bool_fun_fun$' > 'B_update$' > 'B_update_bool_fun$' ).

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

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

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

thf('rel_fun$aq_decl',type,
    'rel_fun$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$c_decl',type,
    'the_inv_into$c': 'A_update_set$' > 'A_update_a_update_fun_a_update_a_update_fun_fun$' ).

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

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

thf('comp$p_decl',type,
    'comp$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$d_decl',type,
    'inv_into$d': 'C_update_set$' > 'C_update_c_update_fun_c_update_c_update_fun_fun$' ).

thf('map_fun$e_decl',type,
    'map_fun$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$f_decl',type,
    'inj_on$f': 'B_update_a_update_fun_b_update_c_update_fun_fun$' > 'B_update_a_update_fun_set$' > $o ).

thf('comp$be_decl',type,
    'comp$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$au_decl',type,
    'fun_app$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$k_decl',type,
    'inj_on$k': 'B_update_c_update_fun$' > 'B_update_set$' > $o ).

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

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

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

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

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

thf(538,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ah' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom142) ).

thf(2630,plain,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ah' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(48,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$a' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$o' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$d' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).

thf(809,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$a' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$o' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(368,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ 'preregister$f' ) )
     => ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'preregister$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).

thf(2031,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ 'preregister$f' ) )
     => ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'preregister$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(378,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
      = ( C @ ( B @ 'comp$ac' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).

thf(2072,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
      = ( C @ ( B @ 'comp$ac' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).

thf(2263,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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$y' ) )
          = F )
        & ( ( B @ ( A @ 'comp$w' ) )
          = ( D @ ( C @ 'comp$x' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).

thf(909,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$y' ) )
          = F )
        & ( ( B @ ( A @ 'comp$w' ) )
          = ( D @ ( C @ 'comp$x' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(313,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$m' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).

thf(1840,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$m' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ae' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( G @ ( E @ ( B @ 'comp$ae' ) @ 'comp$z' ) @ ( A @ ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).

thf(2787,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ae' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( G @ ( E @ ( B @ 'comp$ae' ) @ 'comp$z' ) @ ( A @ ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(509,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$a' ) )
     => ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$' ) )
      <=> ( B @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).

thf(2544,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$a' ) )
     => ( ( ( B @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) )
         => ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$' ) ) )
        & ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$' ) )
         => ( B @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = ( D @ ( C @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).

thf(2331,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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = ( D @ ( C @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

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$'] : ( 'comp$b' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$v' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$u' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$s' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).

thf(2612,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$'] : ( 'comp$b' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$v' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$u' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$s' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(218,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ! [E: 'A_update$'] :
              ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
              = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$d' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).

thf(1469,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$'] :
              ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
              = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$d' ) ) )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

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$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$i' ) @ ( A @ ( C @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).

thf(1168,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$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$i' ) @ ( A @ ( C @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(442,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$u' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).

thf(2295,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$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$u' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(444,axiom,
    ( ( 'g$a' @ ( 'g$' @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
    = 'id$' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).

thf(2306,plain,
    ( ( 'g$a' @ ( 'g$' @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
    = 'id$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(34,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$c' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$' ) @ 'fun_app$au' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).

thf(760,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$c' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$' ) @ 'fun_app$au' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(456,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register_pair$s' ) )
        = ( C @ ( B @ 'register_pair$f' ) @ ( A @ 'comp$ba' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).

thf(2341,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register_pair$s' ) )
        = ( C @ ( B @ 'register_pair$f' ) @ ( A @ 'comp$ba' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(492,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
      = ( C @ ( B @ 'comp$ae' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).

thf(2480,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
      = ( C @ ( B @ 'comp$ae' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(123,axiom,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'uum$' @ 'fun_app$i' ) )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).

thf(1083,plain,
    ! [A: 'C_update$'] : ( A @ ( 'uum$' @ 'fun_app$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(352,axiom,
    ( ( 'id$a' @ ( 'id$a' @ 'register_tensor$d' ) )
    = 'id$g' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).

thf(1982,plain,
    ( ( 'id$a' @ ( 'id$a' @ 'register_tensor$d' ) )
    = 'id$g' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(7,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( B @ 'register$l' )
        & ( A @ 'register$l' ) )
     => ( A @ 'iso_register$h' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom101) ).

thf(666,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( B @ 'register$l' )
        & ( A @ 'register$l' ) )
     => ( A @ 'iso_register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(306,axiom,
    ! [A: 'B_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$by' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom653) ).

thf(1818,plain,
    ! [A: 'B_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$by' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(170,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_update$d' ) @ ( B @ ( A @ 'register_tensor$j' ) @ 'fun_app$ap' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'tensor_update$c' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).

thf(1295,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_update$d' ) @ ( B @ ( A @ 'register_tensor$j' ) @ 'fun_app$ap' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'tensor_update$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(318,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).

thf(1855,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(154,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) )
     => ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).

thf(1211,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) )
     => ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(143,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).

thf(1158,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(13,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uuh$' @ 'fun_app$h' ) )
      = ( 'id_update$a' @ ( B @ ( A @ 'fun_app$g' ) @ 'tensor_update$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).

thf(683,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uuh$' @ 'fun_app$h' ) )
      = ( 'id_update$a' @ ( B @ ( A @ 'fun_app$g' ) @ 'tensor_update$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

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$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$i' ) @ ( A @ ( C @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).

thf(1882,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$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$i' ) @ ( A @ ( C @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(467,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_b_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$g' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$av' ) @ 'fun_app$bo' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).

thf(2395,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_b_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$g' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$av' ) @ 'fun_app$bo' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$u' ) @ ( H @ ( C @ 'fun_app$u' ) @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ! [H: 'B_update$',I: 'B_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( H @ ( H @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( I @ ( H @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
           => ( I @ ( B @ 'fun_app$d' ) @ ( H @ ( B @ 'fun_app$d' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( G @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).

thf(1618,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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$u' ) @ ( H @ ( C @ 'fun_app$u' ) @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ! [H: 'B_update$',I: 'B_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( H @ ( H @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( I @ ( H @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
           => ( I @ ( B @ 'fun_app$d' ) @ ( H @ ( B @ 'fun_app$d' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( G @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

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$'] : ( 'comp$b' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$v' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$u' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$s' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom613) ).

thf(2527,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$'] : ( 'comp$b' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$v' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$u' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$s' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(343,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
    <=> ( ? [B: 'A_update_c_update_fun$'] :
            ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
              = 'id$' )
            & ( ( B @ ( A @ 'comp$k' ) )
              = 'id$b' )
            & ( B @ 'register$' ) )
        & ( A @ 'register$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).

thf(1939,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( ( ? [B: 'A_update_c_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$k' ) )
                = 'id$b' )
              & ( B @ 'register$' ) )
          & ( A @ 'register$b' ) )
       => ( A @ 'iso_register$' ) )
      & ( ( A @ 'iso_register$' )
       => ( ? [B: 'A_update_c_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$k' ) )
                = 'id$b' )
              & ( B @ 'register$' ) )
          & ( A @ 'register$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(652,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
    <=> ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).

thf(3012,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
       => ( 'top$a' @ ( A @ 'inj_on$a' ) ) )
      & ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
       => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(387,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
      = ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).

thf(2114,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
      = ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(235,axiom,
    ( ( 'id$a' @ 'image$e' )
    = 'id$v' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).

thf(1533,plain,
    ( ( 'id$a' @ 'image$e' )
    = 'id$v' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(11,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$bd' ) )
      = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$b' ) ) ),
    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$',D: 'A_update_b_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$bd' ) )
      = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(210,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).

thf(1437,plain,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ae' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$i' ) )
        = ( D @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom116) ).

thf(2117,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ae' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$i' ) )
        = ( D @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(385,axiom,
    ! [A: 'C_update_bool_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( 'uuo$' @ 'pred_fun$e' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).

thf(2104,plain,
    ! [A: 'C_update_bool_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
       => ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( 'uuo$' @ 'pred_fun$e' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( 'uuo$' @ 'pred_fun$e' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(421,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'inj_on$a' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).

thf(2231,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'inj_on$a' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(120,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( ( 'top$' @ ( A @ 'image$c' ) )
        = 'top$a' )
    <=> ( ( A @ ( 'top$' @ 'inv_into$c' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).

thf(1068,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( 'top$' @ 'inv_into$c' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
       => ( ( 'top$' @ ( A @ 'image$c' ) )
          = 'top$a' ) )
      & ( ( ( 'top$' @ ( A @ 'image$c' ) )
          = 'top$a' )
       => ( ( A @ ( 'top$' @ 'inv_into$c' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(590,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ 'the_inv_into$g' ) @ 'fun_app$ah' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'the_inv_into$b' ) @ ( B @ ( C @ 'the_inv_into$' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom603) ).

thf(2808,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ 'the_inv_into$g' ) @ 'fun_app$ah' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'the_inv_into$b' ) @ ( B @ ( C @ 'the_inv_into$' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$z' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( G @ ( E @ ( B @ 'comp$z' ) @ 'comp$z' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).

thf(1522,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$z' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( G @ ( E @ ( B @ 'comp$z' ) @ 'comp$z' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(547,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$b' @ ( 'uur$' @ ( A @ 'rel_fun$bg' ) @ ( 'uus$' @ ( A @ 'rel_fun$ah' ) @ 'rel_fun$bf' ) @ ( 'uvb$' @ 'rel_fun$be' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom644) ).

thf(2671,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$b' @ ( 'uur$' @ ( A @ 'rel_fun$bg' ) @ ( 'uus$' @ ( A @ 'rel_fun$ah' ) @ 'rel_fun$bf' ) @ ( 'uvb$' @ 'rel_fun$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(549,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( 'uuq$' @ 'rel_fun$aq' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom622) ).

thf(2676,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( 'uuq$' @ 'rel_fun$aq' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(438,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) )
     => ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).

thf(2282,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) )
     => ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(253,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$a' ) )
     => ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$c' ) )
      <=> ( B @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).

thf(1591,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$a' ) )
     => ( ( ( B @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) )
         => ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$c' ) ) )
        & ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$c' ) )
         => ( B @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(280,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
    <=> ( ! [C: 'B_update$',D: 'B_update$'] :
            ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).

thf(1705,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ! [C: 'B_update$',D: 'B_update$'] :
              ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
              = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$a' ) )
       => ( B @ ( A @ 'compatible$' ) ) )
      & ( ( B @ ( A @ 'compatible$' ) )
       => ( ! [C: 'B_update$',D: 'B_update$'] :
              ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
              = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(205,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$c' ) )
        & ( B @ ( A @ 'inj_on$a' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).

thf(1426,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) @ ( C @ 'inj_on$c' ) )
        & ( B @ ( A @ 'inj_on$a' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(255,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'compatible$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).

thf(1608,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'compatible$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(140,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ! [E: 'B_update$',F: 'B_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$d' ) )
                = ( F @ ( D @ 'fun_app$d' ) ) )
              & ( 'top$' @ ( B @ 'image$' ) @ ( F @ 'member$a' ) )
              & ( 'top$' @ ( A @ 'image$' ) @ ( E @ 'member$a' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).

thf(1137,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 @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ! [E: 'B_update$',F: 'B_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$d' ) )
                = ( F @ ( D @ 'fun_app$d' ) ) )
              & ( 'top$' @ ( B @ 'image$' ) @ ( F @ 'member$a' ) )
              & ( 'top$' @ ( A @ 'image$' ) @ ( E @ 'member$a' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(629,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$a' @ 'the_inv_into$' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( B @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).

thf(2933,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$a' @ 'the_inv_into$' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( B @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ah' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).

thf(1919,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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ah' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(72,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).

thf(913,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(263,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( A @ ( 'top$' @ 'inv_into$b' ) @ 'iso_register$c' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).

thf(1640,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( A @ ( 'top$' @ 'inv_into$b' ) @ 'iso_register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(601,axiom,
    'g$a' @ 'iso_register$',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).

thf(2844,plain,
    'g$a' @ 'iso_register$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(8,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'bijection$b' )
     => ( ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).

thf(670,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'bijection$b' )
     => ( ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) )
        = ( D @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).

thf(1164,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) )
        = ( D @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(358,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).

thf(1999,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(45,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ 'register$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).

thf(797,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ 'register$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(490,axiom,
    ( ( 'id$' @ ( 'id$b' @ 'map_fun$e' ) )
    = 'id$s' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).

thf(2476,plain,
    ( ( 'id$' @ ( 'id$b' @ 'map_fun$e' ) )
    = 'id$s' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(537,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).

thf(2627,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(400,axiom,
    ( ( 'id$' @ ( 'id$a' @ 'map_fun$v' ) )
    = 'id$q' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).

thf(2168,plain,
    ( ( 'id$' @ ( 'id$a' @ 'map_fun$v' ) )
    = 'id$q' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(162,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' )
     => ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).

thf(1260,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' )
     => ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(68,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( D @ ( C @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).

thf(898,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( D @ ( C @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(416,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_c_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$h' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$aw' ) @ 'fun_app$bp' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).

thf(2216,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_c_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$h' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$aw' ) @ 'fun_app$bp' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

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$'] : ( 'comp$a' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$am' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom617) ).

thf(2723,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$'] : ( 'comp$a' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$am' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(298,axiom,
    ! [A: 'B_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uub$' @ 'fun_app$u' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).

thf(1782,plain,
    ! [A: 'B_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uub$' @ 'fun_app$u' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(41,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$c' ) ) )
     => ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).

thf(782,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$c' ) ) )
     => ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

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$'] : ( 'comp$c' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ad' ) @ ( A @ ( C @ 'rel_fun$ac' ) @ 'rel_fun$ab' ) @ ( B @ ( A @ 'rel_fun$aa' ) @ 'rel_fun$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom615) ).

thf(885,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$'] : ( 'comp$c' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ad' ) @ ( A @ ( C @ 'rel_fun$ac' ) @ 'rel_fun$ab' ) @ ( B @ ( A @ 'rel_fun$aa' ) @ 'rel_fun$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(332,axiom,
    'id$b' @ 'iso_register$h',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).

thf(1904,plain,
    'id$b' @ 'iso_register$h',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(470,axiom,
    ( ( 'id$' @ 'image$d' )
    = 'id$u' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).

thf(2405,plain,
    ( ( 'id$' @ 'image$d' )
    = 'id$u' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(615,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$a' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$ag' ) @ 'comp$v' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).

thf(2886,plain,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$a' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$ag' ) @ 'comp$v' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(187,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$i' ) @ 'fun_app$cf' ) @ 'fun_app$ca' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom656) ).

thf(1359,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$i' ) @ 'fun_app$cf' ) @ 'fun_app$ca' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = ( G @ ( E @ ( B @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) @ 'comp$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).

thf(2400,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = ( G @ ( E @ ( B @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) @ 'comp$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(376,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$a' @ ( B @ ( 'uur$' @ 'rel_fun$az' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$ay' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ax' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom624) ).

thf(2067,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$a' @ ( B @ ( 'uur$' @ 'rel_fun$az' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$ay' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ax' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ 'comp$y' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).

thf(1287,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ 'comp$y' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(268,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bm' ) @ 'fun_app$cc' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom652) ).

thf(1660,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bm' ) @ 'fun_app$cc' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(42,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) )
      = ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).

thf(785,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) )
      = ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(163,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( B @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).

thf(1264,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( B @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(618,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$ab' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).

thf(2897,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$ab' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(391,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ 'comp$aj' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).

thf(2126,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ 'comp$aj' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(517,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$b' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$y' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'comp$t' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).

thf(2571,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$b' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$y' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'comp$t' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(544,axiom,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A @ 'bijection$' )
     => ( ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).

thf(2654,plain,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A @ 'bijection$' )
     => ( ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$z' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).

thf(1628,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$z' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( F @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).

thf(2603,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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( F @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(624,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$p' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$u' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).

thf(2916,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$p' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(514,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$g' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).

thf(2562,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$g' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(495,axiom,
    ( ( 'f$a' @ ( 'f$' @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
    = 'id$b' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).

thf(2488,plain,
    ( ( 'f$a' @ ( 'f$' @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
    = 'id$b' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(239,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'compatible$q' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).

thf(1545,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'compatible$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(561,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$q' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'comp$bk' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$r' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).

thf(2713,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$q' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'comp$bk' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$r' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(125,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).

thf(1087,plain,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(176,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'C_update$'] :
            ( ( B @ ( E @ 'member$b' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
              = ( E @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).

thf(1319,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'C_update$'] :
            ( ( B @ ( E @ 'member$b' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
              = ( E @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( E @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( 'uuq$' @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).

thf(1479,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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( E @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( 'uuq$' @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(37,axiom,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( ( B @ ( 'pred_DEADID$b' @ 'fun_app$m' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
        = ( B @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).

thf(770,plain,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( ( B @ ( 'pred_DEADID$b' @ 'fun_app$m' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
        = ( B @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(63,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$',C: 'B_update$'] :
      ( ( A @ 'register$a' )
     => ( ( C @ ( A @ 'fun_app$d' ) @ ( B @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).

thf(881,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$',C: 'B_update$'] :
      ( ( A @ 'register$a' )
     => ( ( C @ ( A @ 'fun_app$d' ) @ ( B @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(339,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$' ) )
      = ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).

thf(1931,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$' ) )
      = ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

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$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ai' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).

thf(1773,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$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ai' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(645,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$a' @ ( A @ 'image$a' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$u' ) )
            = ( D @ ( C @ 'fun_app$u' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).

thf(2989,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$a' @ ( A @ 'image$a' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$u' ) )
            = ( D @ ( C @ 'fun_app$u' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(325,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).

thf(1875,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(464,axiom,
    'id$' @ ( 'id$l' @ 'iso_tuple_update_accessor_cong_assist$' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).

thf(2388,plain,
    'id$' @ ( 'id$l' @ 'iso_tuple_update_accessor_cong_assist$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(462,axiom,
    ! [A: 'B_update_c_update_fun$'] :
      ( ( A @ 'iso_register$e' )
    <=> ( ? [B: 'C_update_b_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$v' ) )
              = 'id$a' )
            & ( ( B @ ( A @ 'comp$' ) )
              = 'id$' )
            & ( B @ 'register$j' ) )
        & ( A @ 'register$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).

thf(2373,plain,
    ! [A: 'B_update_c_update_fun$'] :
      ( ( ( ? [B: 'C_update_b_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$v' ) )
                = 'id$a' )
              & ( ( B @ ( A @ 'comp$' ) )
                = 'id$' )
              & ( B @ 'register$j' ) )
          & ( A @ 'register$i' ) )
       => ( A @ 'iso_register$e' ) )
      & ( ( A @ 'iso_register$e' )
       => ( ? [B: 'C_update_b_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$v' ) )
                = 'id$a' )
              & ( ( B @ ( A @ 'comp$' ) )
                = 'id$' )
              & ( B @ 'register$j' ) )
          & ( A @ 'register$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(183,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$e' @ ( 'uur$' @ ( A @ 'rel_fun$bm' ) @ ( 'uus$' @ ( A @ 'rel_fun$f' ) @ 'rel_fun$bl' ) @ ( 'uvb$' @ 'rel_fun$bk' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom647) ).

thf(1347,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$e' @ ( 'uur$' @ ( A @ 'rel_fun$bm' ) @ ( 'uus$' @ ( A @ 'rel_fun$f' ) @ 'rel_fun$bl' ) @ ( 'uvb$' @ 'rel_fun$bk' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(133,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).

thf(1115,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ 'comp$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).

thf(2635,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ 'comp$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(418,axiom,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bx' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom660) ).

thf(2222,plain,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(533,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$b' @ ( B @ ( 'uuq$' @ 'rel_fun$bd' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$bc' ) @ ( B @ ( A @ 'rel_fun$bb' ) @ 'rel_fun$ba' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).

thf(2616,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$b' @ ( B @ ( 'uuq$' @ 'rel_fun$bd' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$bc' ) @ ( B @ ( A @ 'rel_fun$bb' ) @ 'rel_fun$ba' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(585,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
      = ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$ab' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).

thf(2794,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
      = ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$ab' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(430,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) )
     => ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).

thf(2259,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) )
     => ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(613,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$z' ) @ 'comp$k' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).

thf(2880,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C = 'id$' )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$z' ) @ 'comp$k' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(80,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$a' @ ( A @ 'image$a' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$g' ) )
            = ( D @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).

thf(937,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$a' @ ( A @ 'image$a' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$g' ) )
            = ( D @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(512,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'compatible$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).

thf(2555,plain,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'compatible$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$ae' ) @ 'comp$k' ) )
          = ( E @ ( I @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) @ ( A @ ( H @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$f' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).

thf(2335,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$ae' ) @ 'comp$k' ) )
          = ( E @ ( I @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) @ ( A @ ( H @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$f' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(167,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( ! [E: 'B_update$'] :
              ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$u' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).

thf(1283,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$'] :
              ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$u' ) ) )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(132,axiom,
    ! [A: 'A_update_set$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'uux$' @ 'fun_app$a' ) )
    <=> ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

thf(1109,plain,
    ! [A: 'A_update_set$',B: 'C_update_a_update_fun$'] :
      ( ( ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$a' ) )
       => ( B @ ( A @ 'uux$' @ 'fun_app$a' ) ) )
      & ( ( B @ ( A @ 'uux$' @ 'fun_app$a' ) )
       => ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(260,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'preregister$d' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).

thf(1632,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'preregister$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$g' ) @ ( H @ ( C @ 'fun_app$g' ) @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
        & ! [H: 'C_update$',I: 'C_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( H @ ( H @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( I @ ( H @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
           => ( I @ ( B @ 'fun_app$ag' ) @ ( H @ ( B @ 'fun_app$ag' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( G @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).

thf(2451,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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$g' ) @ ( H @ ( C @ 'fun_app$g' ) @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
        & ! [H: 'C_update$',I: 'C_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( H @ ( H @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( I @ ( H @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
           => ( I @ ( B @ 'fun_app$ag' ) @ ( H @ ( B @ 'fun_app$ag' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( G @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(423,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
      = ( C @ ( B @ ( A @ 'comp$ah' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).

thf(2236,plain,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
      = ( C @ ( B @ ( A @ 'comp$ah' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(319,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) )
     => ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).

thf(1858,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) )
     => ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(321,axiom,
    ( ( 'id$b' @ ( 'id$b' @ 'register_tensor$h' ) )
    = 'id$k' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).

thf(1864,plain,
    ( ( 'id$b' @ ( 'id$b' @ 'register_tensor$h' ) )
    = 'id$k' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(309,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$a' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$r' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$r' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$c' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).

thf(1828,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$a' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$r' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$r' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(627,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).

thf(2925,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ah' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom122) ).

thf(2291,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ah' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$h' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(194,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A = 'id$b' )
     => ( ( A @ ( 'top$' @ 'grp$b' ) @ ( A @ ( 'top$' @ 'grp$b' ) @ 'conversep$b' @ 'relcompp$' ) )
        = ( A @ ( 'top$' @ 'grp$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).

thf(1383,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A = 'id$b' )
     => ( ( A @ ( 'top$' @ 'grp$b' ) @ ( A @ ( 'top$' @ 'grp$b' ) @ 'conversep$b' @ 'relcompp$' ) )
        = ( A @ ( 'top$' @ 'grp$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$l' ) @ 'fun_app$bf' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$be' ) )
      = ( E @ ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$m' ) @ 'fun_app$bg' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).

thf(1843,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$l' ) @ 'fun_app$bf' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$be' ) )
      = ( E @ ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$m' ) @ 'fun_app$bg' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(480,axiom,
    ! [A: 'C_update$',B: 'C_update_c_update_fun$',C: 'C_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$z' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$' @ ( 'id$l' @ 'iso_tuple_update_accessor_eq_assist$' ) ) ) @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).

thf(2437,plain,
    ! [A: 'C_update$',B: 'C_update_c_update_fun$',C: 'C_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$z' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$' @ ( 'id$l' @ 'iso_tuple_update_accessor_eq_assist$' ) ) ) @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(607,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( ! [E: 'B_update$'] :
              ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$g' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
          = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).

thf(2861,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$'] :
              ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$g' ) ) )
        & ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
          = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(330,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$w' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( C @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).

thf(1896,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$w' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( C @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(27,axiom,
    'id$a' @ 'register$k',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).

thf(734,plain,
    'id$a' @ 'register$k',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(359,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$j' ) @ 'register$e' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).

thf(2002,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$j' ) @ 'register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(182,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) )
     => ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).

thf(1345,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) )
     => ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(208,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( 'top$a' @ ( B @ 'inj_on$a' ) )
        & ( 'top$' @ ( A @ 'inj_on$c' ) ) )
     => ( 'top$a' @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).

thf(1433,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( 'top$a' @ ( B @ 'inj_on$a' ) )
        & ( 'top$' @ ( A @ 'inj_on$c' ) ) )
     => ( 'top$a' @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(573,axiom,
    'f$a' @ 'iso_register$a',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).

thf(2750,plain,
    'f$a' @ 'iso_register$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(151,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$a' ) )
      = ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).

thf(1201,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$a' ) )
      = ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(563,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$a' @ ( 'uuq$' @ ( A @ 'rel_fun$aw' ) @ ( 'uus$' @ ( A @ 'rel_fun$f' ) @ 'rel_fun$av' ) @ ( 'uva$' @ 'rel_fun$au' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom643) ).

thf(2718,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$a' @ ( 'uuq$' @ ( A @ 'rel_fun$aw' ) @ ( 'uus$' @ ( A @ 'rel_fun$f' ) @ 'rel_fun$av' ) @ ( 'uva$' @ 'rel_fun$au' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(246,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) )
      = ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).

thf(1564,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) )
      = ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(91,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$d' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).

thf(981,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(36,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$' )
     => ( ( C @ ( A @ 'fun_app$g' ) @ ( B @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
        = ( C @ ( B @ 'comp_update$a' @ 'fun_app$ab' ) @ ( A @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).

thf(766,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$' )
     => ( ( C @ ( A @ 'fun_app$g' ) @ ( B @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
        = ( C @ ( B @ 'comp_update$a' @ 'fun_app$ab' ) @ ( A @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(534,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$c' ) )
      = ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).

thf(2618,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$c' ) )
      = ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(599,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$b' @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$g' ) )
            = ( D @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).

thf(2833,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$b' @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$g' ) )
            = ( D @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(437,axiom,
    'f$' @ 'register$a',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).

thf(2281,plain,
    'f$' @ 'register$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(213,axiom,
    ( ( 'top$b' @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) )
    = 'top$b' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).

thf(1447,plain,
    ( ( 'top$b' @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) )
    = 'top$b' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$g' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$aq' ) @ ( F @ ( B @ 'map_fun$ap' ) @ 'map_fun$ao' ) @ ( I @ ( E @ 'map_fun$e' ) @ 'map_fun$an' ) ) )
        = 'comp$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).

thf(2483,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$g' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$aq' ) @ ( F @ ( B @ 'map_fun$ap' ) @ 'map_fun$ao' ) @ ( I @ ( E @ 'map_fun$e' ) @ 'map_fun$an' ) ) )
        = 'comp$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
        = ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).

thf(2424,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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
        = ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(38,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uup$' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).

thf(774,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uup$' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

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$',F: 'A_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$d' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( F @ ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).

thf(1104,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$',F: 'A_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$d' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( F @ ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(279,axiom,
    ! [A: 'B_update_set$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( ~ ( A @ ( B @ 'image$b' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) @ 'fun_app$u' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$b' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) @ 'fun_app$u' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$a' ) @ 'fun_app$u' ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).

thf(1697,plain,
    ! [A: 'B_update_set$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( ~ ( A @ ( B @ 'image$b' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) @ 'fun_app$u' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$b' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuv$' ) ) @ 'fun_app$u' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$a' ) @ 'fun_app$u' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(522,axiom,
    ( 'uuq$'
    = ( 'id$' @ ( 'top$a' @ 'grp$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).

thf(2586,plain,
    ( 'uuq$'
    = ( 'id$' @ ( 'top$a' @ 'grp$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(643,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( B @ 'register$h' )
        & ( A @ 'register$h' ) )
     => ( A @ 'iso_register$d' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).

thf(2982,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( B @ 'register$h' )
        & ( A @ 'register$h' ) )
     => ( A @ 'iso_register$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(614,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( 'top$d' @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'inj_on$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).

thf(2884,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( 'top$d' @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'inj_on$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(266,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'comp$bc' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).

thf(1651,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'comp$bc' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(362,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$d' @ ( 'uuq$' @ ( A @ 'rel_fun$ai' ) @ ( 'uus$' @ ( A @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( 'uva$' @ 'rel_fun$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom640) ).

thf(2011,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$d' @ ( 'uuq$' @ ( A @ 'rel_fun$ai' ) @ ( 'uus$' @ ( A @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( 'uva$' @ 'rel_fun$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(153,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$z' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( C @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).

thf(1206,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$z' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
        = ( C @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$d' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$d' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$n' ) @ ( F @ ( B @ 'map_fun$l' ) @ 'map_fun$ab' ) @ ( I @ ( E @ 'map_fun$d' ) @ 'map_fun$aa' ) ) )
        = 'comp$d' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).

thf(1691,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$d' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$d' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$n' ) @ ( F @ ( B @ 'map_fun$l' ) @ 'map_fun$ab' ) @ ( I @ ( E @ 'map_fun$d' ) @ 'map_fun$aa' ) ) )
        = 'comp$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(76,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$d' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$j' @ 'fun_app$an' ) @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).

thf(925,plain,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$d' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$j' @ 'fun_app$an' ) @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(460,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_c_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom151) ).

thf(2364,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_c_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

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$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).

thf(1338,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$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(373,axiom,
    ( ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
        ( ( ( ( 'g$a' @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
            = 'id$' )
          & ( ( B @ ( 'g$a' @ 'comp$k' ) )
            = 'id$b' )
          & ( ( 'f$a' @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
            = 'id$b' )
          & ( ( A @ ( 'f$a' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
            = 'id$a' )
          & ( B @ 'register$' )
          & ( A @ 'register$a' ) )
       => $false )
   => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).

thf(2047,plain,
    ~ ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
        ~ ( ( ( 'g$a' @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
            = 'id$' )
          & ( ( B @ ( 'g$a' @ 'comp$k' ) )
            = 'id$b' )
          & ( ( 'f$a' @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
            = 'id$b' )
          & ( ( A @ ( 'f$a' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
            = 'id$a' )
          & ( B @ 'register$' )
          & ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(535,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ai' ) @ 'fun_app$bx' ) @ 'fun_app$bw' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom657) ).

thf(2621,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ai' ) @ 'fun_app$bx' ) @ 'fun_app$bw' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ac' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
        = ( G @ ( E @ ( B @ 'comp$ac' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ 'comp$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).

thf(2574,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ac' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
        = ( G @ ( E @ ( B @ 'comp$ac' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ 'comp$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(5,axiom,
    ( ( 'id$a' @ ( 'id$a' @ 'map_fun$w' ) )
    = 'id$m' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).

thf(661,plain,
    ( ( 'id$a' @ ( 'id$a' @ 'map_fun$w' ) )
    = 'id$m' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(620,axiom,
    ( ( 'top$a' @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) )
    = 'top$a' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).

thf(2905,plain,
    ( ( 'top$a' @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) )
    = 'top$a' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(23,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'iso_register$h' )
    <=> ( ? [B: 'A_update_a_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
              = 'id$b' )
            & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
              = 'id$b' )
            & ( B @ 'register$l' ) )
        & ( A @ 'register$l' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92) ).

thf(714,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( ( ? [B: 'A_update_a_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
                = 'id$b' )
              & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
                = 'id$b' )
              & ( B @ 'register$l' ) )
          & ( A @ 'register$l' ) )
       => ( A @ 'iso_register$h' ) )
      & ( ( A @ 'iso_register$h' )
       => ( ? [B: 'A_update_a_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
                = 'id$b' )
              & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
                = 'id$b' )
              & ( B @ 'register$l' ) )
          & ( A @ 'register$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).

thf(2061,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(579,axiom,
    ( ( 'id$b' @ ( 'id$' @ 'map_fun$m' ) )
    = 'id$p' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).

thf(2773,plain,
    ( ( 'id$b' @ ( 'id$' @ 'map_fun$m' ) )
    = 'id$p' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(262,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'B_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'register_tensor$l' ) @ 'fun_app$ar' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'tensor_update$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).

thf(1636,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'B_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'register_tensor$l' ) @ 'fun_app$ar' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'tensor_update$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(113,axiom,
    'id$b' @ 'preregister$b',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).

thf(1047,plain,
    'id$b' @ 'preregister$b',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

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$'] : ( 'comp$d' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$n' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$l' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$j' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom611) ).

thf(1730,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$'] : ( 'comp$d' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$n' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$l' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(558,axiom,
    ! [A: 'B_update_b_update_fun_c_update_c_update_fun_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$e' ) )
     => ( ( 'id$a' @ ( A @ 'fun_app$bp' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).

thf(2705,plain,
    ! [A: 'B_update_b_update_fun_c_update_c_update_fun_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$e' ) )
     => ( ( 'id$a' @ ( A @ 'fun_app$bp' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(67,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( C @ ( 'id$b' @ 'comp$f' @ 'fun_app$al' ) ) )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( D @ ( C @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).

thf(894,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( C @ ( 'id$b' @ 'comp$f' @ 'fun_app$al' ) ) )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( D @ ( C @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(477,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$e' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$ap' ) )
        = ( D @ ( B @ 'comp$ai' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$j' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).

thf(2428,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$e' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$ap' ) )
        = ( D @ ( B @ 'comp$ai' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(589,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$g' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$n' ) )
        = ( C @ ( B @ 'register_pair$o' ) @ ( A @ 'comp$av' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).

thf(2805,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$g' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$n' ) )
        = ( C @ ( B @ 'register_pair$o' ) @ ( A @ 'comp$av' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(39,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ ( 'top$a' @ 'inv_into$a' ) @ 'iso_register$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).

thf(778,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ ( 'top$a' @ 'inv_into$a' ) @ 'iso_register$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'fun_app$bh' ) )
      = ( E @ ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$p' ) @ 'fun_app$am' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).

thf(1519,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'fun_app$bh' ) )
      = ( E @ ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$p' ) @ 'fun_app$am' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ai' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
        = ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).

thf(2277,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ai' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
        = ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(59,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$d' ) )
      = ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).

thf(862,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$d' ) )
      = ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(248,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( C @ ( 'id$' @ 'comp$g' @ 'fun_app$am' ) ) )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).

thf(1570,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( C @ ( 'id$' @ 'comp$g' @ 'fun_app$am' ) ) )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(270,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).

thf(1666,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

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$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$aq' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom618) ).

thf(2969,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$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$aq' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(630,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aj' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$af' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom146) ).

thf(2937,plain,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aj' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$af' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(529,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
      = ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).

thf(2606,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
      = ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(43,axiom,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( 'uuo$' @ 'pred_fun$g' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).

thf(788,plain,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
       => ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( 'uuo$' @ 'pred_fun$g' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( 'uuo$' @ 'pred_fun$g' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

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$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).

thf(2986,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$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(364,axiom,
    ! [A: 'B_update_b_update_fun_a_update_a_update_fun_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$f' ) )
     => ( ( 'id$a' @ ( A @ 'fun_app$au' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).

thf(2015,plain,
    ! [A: 'B_update_b_update_fun_a_update_a_update_fun_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$f' ) )
     => ( ( 'id$a' @ ( A @ 'fun_app$au' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(244,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$k' ) )
     => ( A @ ( B @ 'comp$y' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).

thf(1560,plain,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$k' ) )
     => ( A @ ( B @ 'comp$y' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(481,axiom,
    ( ( 'g$' @ ( 'g$a' @ 'comp$k' ) )
    = 'id$b' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).

thf(2441,plain,
    ( ( 'g$' @ ( 'g$a' @ 'comp$k' ) )
    = 'id$b' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(548,axiom,
    ! [A: 'C_update$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'uua$' @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).

thf(2673,plain,
    ! [A: 'C_update$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'uua$' @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(195,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( B @ 'register$l' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ 'comp$ad' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom199) ).

thf(1387,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( B @ 'register$l' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ 'comp$ad' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(284,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).

thf(1723,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).

thf(2890,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(25,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uuk$' @ 'fun_app$m' ) )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).

thf(729,plain,
    ! [A: 'A_update$'] : ( A @ ( 'uuk$' @ 'fun_app$m' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(73,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) )
     => ( C @ ( B @ 'inj_on$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).

thf(916,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) )
     => ( C @ ( B @ 'inj_on$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$g' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$g' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$av' ) @ ( F @ ( B @ 'map_fun$ap' ) @ 'map_fun$au' ) @ ( I @ ( E @ 'map_fun$g' ) @ 'map_fun$at' ) ) )
        = 'comp$e' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).

thf(1032,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$g' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$g' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$av' ) @ ( F @ ( B @ 'map_fun$ap' ) @ 'map_fun$au' ) @ ( I @ ( E @ 'map_fun$g' ) @ 'map_fun$at' ) ) )
        = 'comp$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(349,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ ( 'uva$' @ 'fun_app$q' ) @ 'fun_app$p' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).

thf(1968,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uva$' @ 'fun_app$q' ) @ 'fun_app$p' ) ) )
      & ( ( B @ ( A @ ( 'uva$' @ 'fun_app$q' ) @ 'fun_app$p' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(33,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).

thf(757,plain,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(457,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ac' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).

thf(2344,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ac' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(22,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( B @ 'register$k' )
        & ( A @ 'register$k' ) )
     => ( A @ 'iso_register$g' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).

thf(710,plain,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
          = 'id$a' )
        & ( B @ 'register$k' )
        & ( A @ 'register$k' ) )
     => ( A @ 'iso_register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(100,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$e' @ ( B @ ( 'uur$' @ 'rel_fun$bm' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$bl' ) @ ( B @ ( A @ 'rel_fun$h' ) @ 'rel_fun$bk' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).

thf(1012,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$e' @ ( B @ ( 'uur$' @ 'rel_fun$bm' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$bl' ) @ ( B @ ( A @ 'rel_fun$h' ) @ 'rel_fun$bk' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ae' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( G @ ( E @ ( B @ 'comp$ae' ) @ 'comp$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).

thf(2958,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ae' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( G @ ( E @ ( B @ 'comp$ae' ) @ 'comp$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(204,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).

thf(1423,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$d' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$ae' ) @ ( F @ ( B @ 'map_fun$h' ) @ 'map_fun$ad' ) @ ( I @ ( E @ 'map_fun$d' ) @ 'map_fun$ac' ) ) )
        = 'comp$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).

thf(2464,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$d' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$ae' ) @ ( F @ ( B @ 'map_fun$h' ) @ 'map_fun$ad' ) @ ( I @ ( E @ 'map_fun$d' ) @ 'map_fun$ac' ) ) )
        = 'comp$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(342,axiom,
    'id$a' @ 'preregister$a',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).

thf(1938,plain,
    'id$a' @ 'preregister$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(577,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'C_update_set$'] :
      ( ( B @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) )
      = ( B @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).

thf(2758,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'C_update_set$'] :
      ( ( B @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) )
      = ( B @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(242,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( 'uuq$' @ 'rel_fun$ai' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom621) ).

thf(1555,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( 'uuq$' @ 'rel_fun$ai' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(594,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$m' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$q' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).

thf(2820,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$m' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(610,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$' ) )
          = 'top$b' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = 'top$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).

thf(2872,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$' ) )
          = 'top$b' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = 'top$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$aa' ) )
        = ( C @ ( E @ 'fun_app$ab' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).

thf(1951,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$aa' ) )
        = ( C @ ( E @ 'fun_app$ab' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(411,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( 'top$' @ 'inv_into$c' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).

thf(2200,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( 'top$' @ 'inv_into$c' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( F @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).

thf(2609,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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( F @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(312,axiom,
    ! [A: 'B_update$',B: 'B_update_b_update_fun$',C: 'B_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$aa' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$a' @ ( 'id$m' @ 'iso_tuple_update_accessor_eq_assist$a' ) ) ) @ 'fun_app$l' ) @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).

thf(1836,plain,
    ! [A: 'B_update$',B: 'B_update_b_update_fun$',C: 'B_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$aa' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$a' @ ( 'id$m' @ 'iso_tuple_update_accessor_eq_assist$a' ) ) ) @ 'fun_app$l' ) @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(405,axiom,
    ( ( 'id$' @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) )
    = 'id$' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).

thf(2181,plain,
    ( ( 'id$' @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) )
    = 'id$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
        = ( D @ ( C @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).

thf(1079,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$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
        = ( D @ ( C @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

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$'] : ( 'comp$e' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$y' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$x' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$w' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).

thf(1027,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$'] : ( 'comp$e' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$y' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$x' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$w' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(451,axiom,
    ( ( 'id$' @ ( 'id$' @ 'register_tensor$' ) )
    = 'id$c' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).

thf(2327,plain,
    ( ( 'id$' @ ( 'id$' @ 'register_tensor$' ) )
    = 'id$c' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(150,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ! [D: 'B_update$'] :
          ( ( 'top$' @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
         => ( ( D @ ( B @ 'fun_app$d' ) )
            = ( D @ ( C @ 'fun_app$d' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).

thf(1195,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ! [D: 'B_update$'] :
          ( ( 'top$' @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
         => ( ( D @ ( B @ 'fun_app$d' ) )
            = ( D @ ( C @ 'fun_app$d' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(200,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ad' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).

thf(1407,plain,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ad' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(261,axiom,
    ( ( 'id$b' @ ( 'id$a' @ 'map_fun$x' ) )
    = 'id$r' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).

thf(1634,plain,
    ( ( 'id$b' @ ( 'id$a' @ 'map_fun$x' ) )
    = 'id$r' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(197,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) )
      = ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).

thf(1392,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) )
      = ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(341,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'uuo$' @ 'fun_app$k' ) )
    <=> $true ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).

thf(1936,plain,
    ! [A: 'B_update$'] : ( A @ ( 'uuo$' @ 'fun_app$k' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(398,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$g' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).

thf(2157,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$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$g' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

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$'] : ( 'comp$e' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$y' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$x' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$w' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).

thf(1017,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$'] : ( 'comp$e' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$y' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$x' ) @ ( B @ ( A @ 'rel_fun$t' ) @ 'rel_fun$w' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(559,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register$j' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).

thf(2709,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register$j' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(501,axiom,
    ! [A: 'C_update_c_update_fun_c_update_c_update_fun_fun$',B: 'C_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$am' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).

thf(2509,plain,
    ! [A: 'C_update_c_update_fun_c_update_c_update_fun_fun$',B: 'C_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$am' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(326,axiom,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( ( B @ ( 'pred_DEADID$a' @ 'fun_app$k' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
        = ( B @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).

thf(1878,plain,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( ( B @ ( 'pred_DEADID$a' @ 'fun_app$k' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$a' @ 'fun_app$aa' ) )
        = ( B @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(606,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
      = ( C @ ( B @ 'comp$z' ) @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).

thf(2858,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
      = ( C @ ( B @ 'comp$z' ) @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(134,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$' ) )
     => ( ( B @ ( A @ 'image$' ) @ ( C @ 'inj_on$b' ) )
      <=> ( B @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).

thf(1118,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$' ) )
     => ( ( ( B @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) )
         => ( B @ ( A @ 'image$' ) @ ( C @ 'inj_on$b' ) ) )
        & ( ( B @ ( A @ 'image$' ) @ ( C @ 'inj_on$b' ) )
         => ( B @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(16,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_b_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$a' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$w' ) @ 'fun_app$an' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).

thf(697,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'B_update_b_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$a' ) ) )
     => ( ( 'id$a' @ ( B @ ( C @ 'map_fun$w' ) @ 'fun_app$an' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

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$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ai' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom616) ).

thf(1234,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$'] : ( 'comp$d' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ai' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ag' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(238,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$e' ) @ ( B @ ( A @ 'register_tensor$k' ) @ 'fun_app$aq' ) )
        = ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'tensor_update$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).

thf(1541,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$e' ) @ ( B @ ( A @ 'register_tensor$k' ) @ 'fun_app$aq' ) )
        = ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'tensor_update$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$af' ) @ 'comp$' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$ae' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).

thf(1567,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$af' ) @ 'comp$' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$ae' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(188,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$' ) )
          = 'top$b' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = 'top$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).

thf(1361,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$' ) )
          = 'top$b' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = 'top$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(597,axiom,
    'g$' @ 'register$',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).

thf(2830,plain,
    'g$' @ 'register$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).

thf(2868,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(14,axiom,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A @ 'bijection$a' )
     => ( ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).

thf(686,plain,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A @ 'bijection$a' )
     => ( ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(651,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ai' ) @ 'fun_app$bx' ) @ 'fun_app$bw' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom648) ).

thf(3010,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ai' ) @ 'fun_app$bx' ) @ 'fun_app$bw' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).

thf(1584,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(371,axiom,
    ! [A: 'C_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uua$' @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).

thf(2038,plain,
    ! [A: 'C_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uua$' @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(111,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ah' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).

thf(1039,plain,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ah' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(587,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( B @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'compatible$n' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom249) ).

thf(2798,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( B @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'compatible$n' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(276,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( ( 'top$b' @ ( A @ 'image$b' ) )
        = 'top$' )
    <=> ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).

thf(1683,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
       => ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' ) )
      & ( ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' )
       => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(648,axiom,
    ( ( 'id$' @ 'vimage$' )
    = 'id$u' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom666) ).

thf(3000,plain,
    ( ( 'id$' @ 'vimage$' )
    = 'id$u' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(450,axiom,
    ! [A: 'C_update_c_update_fun_a_update_a_update_fun_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$d' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$bi' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).

thf(2323,plain,
    ! [A: 'C_update_c_update_fun_a_update_a_update_fun_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$d' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$bi' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(169,axiom,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( 'id$b' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$b' ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).

thf(1292,plain,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( 'id$b' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$b' ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(78,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$k' ) @ 'register$f' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).

thf(933,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$k' ) @ 'register$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(304,axiom,
    ( ( 'id$a' @ ( 'id$b' @ 'map_fun$j' ) )
    = 'id$t' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).

thf(1810,plain,
    ( ( 'id$a' @ ( 'id$b' @ 'map_fun$j' ) )
    = 'id$t' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(402,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).

thf(2172,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(155,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$' @ 'the_inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( B @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).

thf(1214,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$' @ 'the_inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( B @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(458,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aj' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).

thf(2349,plain,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aj' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(53,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ac' ) @ ( B @ ( A @ 'register_pair$o' ) @ 'comp$at' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ 'comp$k' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom243) ).

thf(837,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ac' ) @ ( B @ ( A @ 'register_pair$o' ) @ 'comp$at' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ 'comp$k' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(439,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) )
      = ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).

thf(2285,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) )
      = ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(95,axiom,
    ( 'uur$'
    = ( 'id$a' @ ( 'top$b' @ 'grp$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).

thf(997,plain,
    ( 'uur$'
    = ( 'id$a' @ ( 'top$b' @ 'grp$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(252,axiom,
    ! [A: 'B_update$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'uub$' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).

thf(1588,plain,
    ! [A: 'B_update$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'uub$' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(18,axiom,
    ( ( 'id$a' @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) )
    = 'id$a' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).

thf(701,plain,
    ( ( 'id$a' @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) )
    = 'id$a' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(602,axiom,
    'id$' @ ( 'id$' @ ( 'uuq$' @ 'quotient3$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).

thf(2845,plain,
    'id$' @ ( 'id$' @ ( 'uuq$' @ 'quotient3$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(353,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).

thf(1984,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(317,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$h' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$c' ) )
        = ( C @ ( B @ 'register_pair$p' ) @ ( A @ 'comp$ay' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).

thf(1852,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$h' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$c' ) )
        = ( C @ ( B @ 'register_pair$p' ) @ ( A @ 'comp$ay' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(281,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ ( 'top$' @ 'inv_into$c' ) @ 'iso_register$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).

thf(1715,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ ( 'top$' @ 'inv_into$c' ) @ 'iso_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$p' ) @ ( F @ ( B @ 'map_fun$m' ) @ 'map_fun$am' ) @ ( I @ ( E @ 'map_fun$e' ) @ 'map_fun$al' ) ) )
        = 'comp$d' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).

thf(1979,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$p' ) @ ( F @ ( B @ 'map_fun$m' ) @ 'map_fun$am' ) @ ( I @ ( E @ 'map_fun$e' ) @ 'map_fun$al' ) ) )
        = 'comp$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(142,axiom,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( B @ ( A @ ( 'uur$' @ 'fun_app$l' ) @ 'fun_app$k' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).

thf(1150,plain,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uur$' @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
      & ( ( B @ ( A @ ( 'uur$' @ 'fun_app$l' ) @ 'fun_app$k' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(504,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).

thf(2519,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(234,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
      = ( 'top$' @ ( B @ 'image$' ) @ ( A @ 'image$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).

thf(1530,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
      = ( 'top$' @ ( B @ 'image$' ) @ ( A @ 'image$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(216,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
    <=> ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).

thf(1456,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
       => ( 'top$b' @ ( A @ 'inj_on$b' ) ) )
      & ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
       => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(619,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ai' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).

thf(2900,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ai' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(310,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).

thf(1831,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

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$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
     => ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).

thf(1131,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$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
     => ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(1,conjecture,
    ( ( 'g$a' @ ( 'f$a' @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( 'f$' @ ( 'g$' @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
    = 'id$' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture29) ).

thf(2,negated_conjecture,
    ( ( 'g$a' @ ( 'f$a' @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( 'f$' @ ( 'g$' @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
   != 'id$' ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(654,plain,
    ( ( 'g$a' @ ( 'f$a' @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( 'f$' @ ( 'g$' @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
   != 'id$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(241,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$b' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).

thf(1552,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$b' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(604,axiom,
    ( ( 'id$' @ ( 'id$' @ 'map_fun$p' ) )
    = 'id$l' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).

thf(2851,plain,
    ( ( 'id$' @ ( 'id$' @ 'map_fun$p' ) )
    = 'id$l' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(515,axiom,
    ( ( 'id$a' @ ( 'id$' @ 'register_tensor$a' ) )
    = 'id$d' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).

thf(2566,plain,
    ( ( 'id$a' @ ( 'id$' @ 'register_tensor$a' ) )
    = 'id$d' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(301,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$',D: 'A_update$'] :
      ( ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
        & ( C @ ( B @ 'inj_on$' ) )
        & ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ 'inv_into$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$' ) @ 'inv_into$' ) @ ( B @ ( C @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).

thf(1799,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$',D: 'A_update$'] :
      ( ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
        & ( C @ ( B @ 'inj_on$' ) )
        & ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ 'inv_into$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$' ) @ 'inv_into$' ) @ ( B @ ( C @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(395,axiom,
    ( ( 'f$' @ ( 'f$a' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
    = 'id$a' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).

thf(2140,plain,
    ( ( 'f$' @ ( 'f$a' @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
    = 'id$a' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(576,axiom,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bx' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom651) ).

thf(2756,plain,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(178,axiom,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$h' ) @ ( 'uur$' @ 'rel_fun$d' ) )
      = ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ ( A @ 'uuy$' @ 'collect$b' @ 'grp$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom609) ).

thf(1333,plain,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$h' ) @ ( 'uur$' @ 'rel_fun$d' ) )
      = ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ ( A @ 'uuy$' @ 'collect$b' @ 'grp$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(355,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$e' ) ) )
     => ( ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).

thf(1991,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$e' ) ) )
     => ( ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$d' ) @ 'fun_app$ax' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'fun_app$bb' ) )
      = ( E @ ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$i' ) @ 'fun_app$bc' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).

thf(2203,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$d' ) @ 'fun_app$ax' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'fun_app$bb' ) )
      = ( E @ ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$i' ) @ 'fun_app$bc' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(75,axiom,
    ! [A: 'A_update$',B: 'A_update_a_update_fun$',C: 'A_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$ab' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$b' @ ( 'id$n' @ 'iso_tuple_update_accessor_eq_assist$b' ) ) ) @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).

thf(921,plain,
    ! [A: 'A_update$',B: 'A_update_a_update_fun$',C: 'A_update$'] :
      ( ( A
        = ( C @ ( B @ 'fun_app$ab' ) ) )
     => ( C @ ( A @ ( B @ ( C @ ( 'id$b' @ ( 'id$n' @ 'iso_tuple_update_accessor_eq_assist$b' ) ) ) @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(147,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'comp$c' @ ( 'comp$c' @ ( 'uus$' @ ( A @ 'rel_fun$i' ) @ ( 'uur$' @ ( A @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( 'uuz$' @ 'rel_fun$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom639) ).

thf(1170,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'comp$c' @ ( 'comp$c' @ ( 'uus$' @ ( A @ 'rel_fun$i' ) @ ( 'uur$' @ ( A @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( 'uuz$' @ 'rel_fun$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

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$'] : ( 'comp$a' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$r' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$p' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$o' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).

thf(2995,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$'] : ( 'comp$a' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$r' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$p' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$o' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(508,axiom,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( A = B )
    <=> ? [C: 'C_update$'] :
          ( ( ( C @ ( 'id$' @ 'fun_app$z' ) )
            = B )
          & ( ( C @ ( 'id$' @ 'fun_app$z' ) )
            = A )
          & ( 'top$a' @ ( C @ 'member$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).

thf(2529,plain,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( ? [C: 'C_update$'] :
            ( ( ( C @ ( 'id$' @ 'fun_app$z' ) )
              = B )
            & ( ( C @ ( 'id$' @ 'fun_app$z' ) )
              = A )
            & ( 'top$a' @ ( C @ 'member$b' ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ? [C: 'C_update$'] :
            ( ( ( C @ ( 'id$' @ 'fun_app$z' ) )
              = B )
            & ( ( C @ ( 'id$' @ 'fun_app$z' ) )
              = A )
            & ( 'top$a' @ ( C @ 'member$b' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(287,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( C @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).

thf(1732,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( C @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(622,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$d' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'comp$bg' ) )
      = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).

thf(2909,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$d' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'comp$bg' ) )
      = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$q' ) @ 'fun_app$bj' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'fun_app$bh' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$r' ) @ 'fun_app$bk' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).

thf(2702,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$q' ) @ 'fun_app$bj' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'fun_app$bh' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$r' ) @ 'fun_app$bk' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(578,axiom,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'iso_register$f' )
    <=> ( ? [B: 'B_update_c_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$' ) )
              = 'id$' )
            & ( ( B @ ( A @ 'comp$v' ) )
              = 'id$a' )
            & ( B @ 'register$i' ) )
        & ( A @ 'register$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom90) ).

thf(2761,plain,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( ( ? [B: 'B_update_c_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$v' ) )
                = 'id$a' )
              & ( B @ 'register$i' ) )
          & ( A @ 'register$j' ) )
       => ( A @ 'iso_register$f' ) )
      & ( ( A @ 'iso_register$f' )
       => ( ? [B: 'B_update_c_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$v' ) )
                = 'id$a' )
              & ( B @ 'register$i' ) )
          & ( A @ 'register$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(315,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'B_update_set$'] :
      ( ( B @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) )
      = ( B @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).

thf(1846,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'B_update_set$'] :
      ( ( B @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) )
      = ( B @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(115,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bm' ) @ 'fun_app$cc' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom661) ).

thf(1054,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$bm' ) @ 'fun_app$cc' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(637,axiom,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$h' ) @ ( 'uuq$' @ 'rel_fun$c' ) )
      = ( B @ ( 'comp$b' @ 'fun_app$y' ) @ ( A @ 'uux$' @ 'collect$a' @ 'grp$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom608) ).

thf(2963,plain,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$h' ) @ ( 'uuq$' @ 'rel_fun$c' ) )
      = ( B @ ( 'comp$b' @ 'fun_app$y' ) @ ( A @ 'uux$' @ 'collect$a' @ 'grp$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(109,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( A @ 'register$c' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).

thf(1035,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( A @ 'register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(44,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_pair$r' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$ax' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).

thf(794,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_pair$r' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$ax' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(455,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_c_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$p' ) @ 'fun_app$am' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom373) ).

thf(2338,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_c_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$p' ) @ 'fun_app$am' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(389,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$e' @ ( B @ ( 'uur$' @ 'rel_fun$bj' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$bi' ) @ ( B @ ( A @ 'rel_fun$bb' ) @ 'rel_fun$bh' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).

thf(2121,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$e' @ ( B @ ( 'uur$' @ 'rel_fun$bj' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$bi' ) @ ( B @ ( A @ 'rel_fun$bb' ) @ 'rel_fun$bh' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(292,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'inj_on$b' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).

thf(1764,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'inj_on$b' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(275,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$e' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$a' ) @ 'fun_app$av' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).

thf(1680,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$e' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$a' ) @ 'fun_app$av' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$g' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$z' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).

thf(2033,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$g' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$z' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(521,axiom,
    'id$' @ 'iso_register$d',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).

thf(2585,plain,
    'id$' @ 'iso_register$d',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(15,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ ( 'uuz$' @ 'fun_app$o' ) @ 'fun_app$b' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).

thf(689,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uuz$' @ 'fun_app$o' ) @ 'fun_app$b' ) ) )
      & ( ( B @ ( A @ ( 'uuz$' @ 'fun_app$o' ) @ 'fun_app$b' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(617,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$f' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'comp$bf' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).

thf(2894,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$f' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'comp$bf' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(139,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( 'top$c' @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'inj_on$d' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).

thf(1135,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( 'top$c' @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'inj_on$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(265,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'B_update_set$'] :
      ( ( B @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) )
      = ( B @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom579) ).

thf(1648,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'B_update_set$'] :
      ( ( B @ ( 'id$a' @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) )
      = ( B @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(87,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ 'the_inv_into$d' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'the_inv_into$e' ) @ ( B @ ( C @ 'the_inv_into$' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom601) ).

thf(965,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ 'the_inv_into$d' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'the_inv_into$e' ) @ ( B @ ( C @ 'the_inv_into$' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(285,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$m' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ak' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).

thf(1727,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$m' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ak' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(228,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$al' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$c' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).

thf(1510,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$al' ) )
        = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(172,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ! [E: 'B_update$'] :
            ( ( 'top$' @ ( B @ 'image$' ) @ ( E @ 'member$a' ) )
           => ( ( E @ ( C @ 'fun_app$d' ) )
              = ( E @ ( D @ 'fun_app$d' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).

thf(1301,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$'] :
            ( ( 'top$' @ ( B @ 'image$' ) @ ( E @ 'member$a' ) )
           => ( ( E @ ( C @ 'fun_app$d' ) )
              = ( E @ ( D @ 'fun_app$d' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(569,axiom,
    ! [A: 'C_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ad' ) @ 'fun_app$cb' ) @ 'fun_app$ca' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom659) ).

thf(2734,plain,
    ! [A: 'C_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ad' ) @ 'fun_app$cb' ) @ 'fun_app$ca' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(51,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).

thf(819,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( F @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).

thf(1916,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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( F @ ( E @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(328,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
    <=> ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).

thf(1884,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ! [C: 'A_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
              = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
          & ( B @ 'register$' )
          & ( A @ 'register$' ) )
       => ( B @ ( A @ 'compatible$a' ) ) )
      & ( ( B @ ( A @ 'compatible$a' ) )
       => ( ! [C: 'A_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
              = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
          & ( B @ 'register$' )
          & ( A @ 'register$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(196,axiom,
    ! [A: 'A_update$',B: 'B_update$'] :
      ( ( B @ ( A @ 'uu$' @ 'fun_app$d' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).

thf(1389,plain,
    ! [A: 'A_update$',B: 'B_update$'] :
      ( ( B @ ( A @ 'uu$' @ 'fun_app$d' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).

thf(2568,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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(236,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( B @ 'register$h' )
        & ( A @ 'register$' ) )
     => ( A @ ( B @ 'comp$ah' ) @ 'register$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).

thf(1535,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_c_update_fun$'] :
      ( ( ( B @ 'register$h' )
        & ( A @ 'register$' ) )
     => ( A @ ( B @ 'comp$ah' ) @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(562,axiom,
    ! [A: 'C_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ad' ) @ 'fun_app$cb' ) @ 'fun_app$ca' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom650) ).

thf(2716,plain,
    ! [A: 'C_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$ad' ) @ 'fun_app$cb' ) @ 'fun_app$ca' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(348,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$',D: 'A_update$'] :
      ( ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
        & ( C @ ( B @ 'inj_on$' ) )
        & ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ 'the_inv_into$c' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$' ) @ 'the_inv_into$a' ) @ ( B @ ( C @ 'the_inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom600) ).

thf(1965,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$',D: 'A_update$'] :
      ( ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
        & ( C @ ( B @ 'inj_on$' ) )
        & ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ 'the_inv_into$c' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$' ) @ 'the_inv_into$a' ) @ ( B @ ( C @ 'the_inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(593,axiom,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( 'id$' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$' ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).

thf(2817,plain,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( 'id$' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$' ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(135,axiom,
    'id$a' @ 'iso_register$g',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).

thf(1124,plain,
    'id$a' @ 'iso_register$g',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(55,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ ( 'uvb$' @ 'fun_app$r' ) @ 'fun_app$' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).

thf(843,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uvb$' @ 'fun_app$r' ) @ 'fun_app$' ) ) )
      & ( ( B @ ( A @ ( 'uvb$' @ 'fun_app$r' ) @ 'fun_app$' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = ( D @ ( C @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).

thf(1125,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = ( D @ ( C @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(506,axiom,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$at' ) @ 'fun_app$bz' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom649) ).

thf(2525,plain,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$at' ) @ 'fun_app$bz' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(545,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
          = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$u' ) )
                = ( F @ ( D @ 'fun_app$u' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).

thf(2657,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 @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
          = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$u' ) )
                = ( F @ ( D @ 'fun_app$u' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(466,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$a' @ ( B @ ( 'uur$' @ 'rel_fun$aw' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$av' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$au' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom623) ).

thf(2393,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'C_update_c_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$a' @ ( B @ ( 'uur$' @ 'rel_fun$aw' ) @ ( A @ ( 'uur$' @ 'rel_fun$f' ) @ 'rel_fun$av' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$au' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(291,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
    <=> ( ? [B: 'B_update_a_update_fun$'] :
            ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
              = 'id$b' )
            & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
              = 'id$a' )
            & ( B @ 'register$a' ) )
        & ( A @ 'register$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).

thf(1752,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( ( ? [B: 'B_update_a_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
                = 'id$b' )
              & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
                = 'id$a' )
              & ( B @ 'register$a' ) )
          & ( A @ 'register$c' ) )
       => ( A @ 'iso_register$a' ) )
      & ( ( A @ 'iso_register$a' )
       => ( ? [B: 'B_update_a_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
                = 'id$b' )
              & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
                = 'id$a' )
              & ( B @ 'register$a' ) )
          & ( A @ 'register$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(84,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
      = ( C @ ( B @ 'comp$w' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).

thf(958,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
      = ( C @ ( B @ 'comp$w' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(199,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$k' ) )
          = 'id$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$b' ) )
     => ( A @ 'iso_register$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).

thf(1403,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$k' ) )
          = 'id$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$b' ) )
     => ( A @ 'iso_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(300,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$k' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( B @ 'register$b' )
        & ( A @ 'register$' ) )
     => ( A @ 'iso_register$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).

thf(1795,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$k' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( B @ 'register$b' )
        & ( A @ 'register$' ) )
     => ( A @ 'iso_register$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(468,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$b' @ ( B @ ( 'uuq$' @ 'rel_fun$bg' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$bf' ) @ ( B @ ( A @ 'rel_fun$h' ) @ 'rel_fun$be' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).

thf(2398,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'B_update_b_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$b' @ ( B @ ( 'uuq$' @ 'rel_fun$bg' ) @ ( A @ ( 'uuq$' @ 'rel_fun$ah' ) @ 'rel_fun$bf' ) @ ( B @ ( A @ 'rel_fun$h' ) @ 'rel_fun$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(158,axiom,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( B @ ( A @ ( 'uus$' @ 'fun_app$n' ) @ 'fun_app$m' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).

thf(1226,plain,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uus$' @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
      & ( ( B @ ( A @ ( 'uus$' @ 'fun_app$n' ) @ 'fun_app$m' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(224,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$u' ) )
                = ( F @ ( D @ 'fun_app$u' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).

thf(1488,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 @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$u' ) )
                = ( F @ ( D @ 'fun_app$u' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(596,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$h' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$e' ) )
        = ( C @ ( B @ 'register_pair$p' ) @ ( A @ 'comp$au' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).

thf(2827,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$h' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$e' ) )
        = ( C @ ( B @ 'register_pair$p' ) @ ( A @ 'comp$au' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(393,axiom,
    ! [A: 'C_update$',B: 'C_update_set$',C: 'C_update_a_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( C @ 'inj_on$a' ) )
        & ( B @ ( A @ 'member$b' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uuu$' ) ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( A @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom595) ).

thf(2134,plain,
    ! [A: 'C_update$',B: 'C_update_set$',C: 'C_update_a_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( C @ 'inj_on$a' ) )
        & ( B @ ( A @ 'member$b' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uuu$' ) ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) )
        = ( A @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(206,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
      = ( C @ ( B @ 'comp$z' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).

thf(1428,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$g' @ 'fun_app$am' ) )
      = ( C @ ( B @ 'comp$z' ) @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(271,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$c' ) @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).

thf(1669,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$c' ) @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(445,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
      = ( C @ ( B @ ( A @ 'comp$x' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).

thf(2308,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
      = ( C @ ( B @ ( A @ 'comp$x' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(174,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).

thf(1312,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
        = ( D @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).

thf(3002,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
        = ( D @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

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$'] :
      ( ( ( E @ ( D @ ( 'uur$' @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( E @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( 'uus$' @ 'relcompp$' ) @ ( A @ 'relcompp$' ) @ 'quotient3$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).

thf(1997,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$'] :
      ( ( ( E @ ( D @ ( 'uur$' @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( E @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( 'uus$' @ 'relcompp$' ) @ ( A @ 'relcompp$' ) @ 'quotient3$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(126,axiom,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$b' @ ( 'top$' @ 'grp$b' ) @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).

thf(1090,plain,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$b' @ ( 'top$' @ 'grp$b' ) @ 'fun_app$n' ) @ 'fun_app$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$z' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( G @ ( E @ ( B @ 'comp$z' ) @ 'comp$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).

thf(2557,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$z' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$b' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
        = ( G @ ( E @ ( B @ 'comp$z' ) @ 'comp$ac' ) @ ( A @ ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$ah' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(157,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) )
     => ( C @ ( B @ 'inj_on$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).

thf(1224,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) )
     => ( C @ ( B @ 'inj_on$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
          = ( E @ ( I @ ( B @ 'comp$x' ) @ 'comp$w' ) @ ( A @ ( H @ ( D @ 'comp$ad' ) @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$' @ ( F @ ( E @ 'type_definition$e' ) ) )
        & ( 'top$' @ ( D @ ( C @ 'type_definition$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$d' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).

thf(1356,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
          = ( E @ ( I @ ( B @ 'comp$x' ) @ 'comp$w' ) @ ( A @ ( H @ ( D @ 'comp$ad' ) @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$' @ ( F @ ( E @ 'type_definition$e' ) ) )
        & ( 'top$' @ ( D @ ( C @ 'type_definition$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$d' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(273,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$d' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'comp$be' ) )
      = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$e' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).

thf(1675,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$d' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'comp$be' ) )
      = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(117,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).

thf(1058,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(131,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( 'top$b' @ ( B @ 'inj_on$b' ) )
        & ( 'top$' @ ( A @ 'inj_on$' ) ) )
     => ( 'top$b' @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).

thf(1107,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( 'top$b' @ ( B @ 'inj_on$b' ) )
        & ( 'top$' @ ( A @ 'inj_on$' ) ) )
     => ( 'top$b' @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(217,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom153) ).

thf(1464,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(82,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( 'top$b' @ ( B @ 'image$b' ) )
          = 'top$' )
        & ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$b' ) )
     => ( ( 'top$' @ ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
        = 'top$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).

thf(947,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( 'top$b' @ ( B @ 'image$b' ) )
          = 'top$' )
        & ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$b' ) )
     => ( ( 'top$' @ ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) )
        = 'top$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(90,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$i' ) @ 'fun_app$cf' ) @ 'fun_app$ca' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom665) ).

thf(979,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$i' ) @ 'fun_app$cf' ) @ 'fun_app$ca' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(446,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$as' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$n' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).

thf(2311,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$as' ) )
        = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

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

thf(2478,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$c' ) )
        & ( B @ ( A @ 'inj_on$b' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(420,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) )
     => ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).

thf(2229,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) )
     => ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

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$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$aq' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).

thf(2084,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$'] : ( 'comp$b' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$aq' ) @ ( A @ ( C @ 'rel_fun$ah' ) @ 'rel_fun$ap' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(249,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$k' ) )
    <=> ( ( C @ ( A @ 'fun_app$d' ) )
        = ( C @ ( B @ 'fun_app$d' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).

thf(1574,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( ( ( C @ ( A @ 'fun_app$d' ) )
          = ( C @ ( B @ 'fun_app$d' ) ) )
       => ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$k' ) ) )
      & ( ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$k' ) )
       => ( ( C @ ( A @ 'fun_app$d' ) )
          = ( C @ ( B @ 'fun_app$d' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

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

thf(1048,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$b' @ ( A @ 'image$b' ) @ ( D @ 'member$' ) )
         => ( ( D @ ( B @ 'fun_app$u' ) )
            = ( D @ ( C @ 'fun_app$u' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(429,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( 'top$b' @ ( B @ 'inj_on$b' ) )
        & ( 'top$' @ ( A @ 'inj_on$c' ) ) )
     => ( 'top$b' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).

thf(2257,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( 'top$b' @ ( B @ 'inj_on$b' ) )
        & ( 'top$' @ ( A @ 'inj_on$c' ) ) )
     => ( 'top$b' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(600,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$z' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
        = ( C @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).

thf(2839,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$z' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
        = ( C @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(410,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$a' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$r' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$n' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$s' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).

thf(2197,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$a' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$r' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$n' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$s' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( E @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( 'uur$' @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$h' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).

thf(2065,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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( E @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( 'uur$' @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(473,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$d' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$n' ) @ 'fun_app$bh' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).

thf(2415,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$d' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$n' ) @ 'fun_app$bh' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(329,axiom,
    ( ( 'id$a' @ ( 'id$b' @ 'register_tensor$g' ) )
    = 'id$j' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).

thf(1894,plain,
    ( ( 'id$a' @ ( 'id$b' @ 'register_tensor$g' ) )
    = 'id$j' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(184,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( ( D @ ( C @ 'register_tensor$x' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'comp$aq' ) )
        = ( D @ ( B @ 'comp$ad' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$l' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom240) ).

thf(1349,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( ( D @ ( C @ 'register_tensor$x' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'comp$aq' ) )
        = ( D @ ( B @ 'comp$ad' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ah' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).

thf(2097,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ah' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(635,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
      = ( C @ ( B @ ( A @ 'comp$ai' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).

thf(2955,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
      = ( C @ ( B @ ( A @ 'comp$ai' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(426,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'B_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
              = ( E @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).

thf(2246,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'B_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
              = ( E @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(29,axiom,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A @ 'iso_register$g' )
    <=> ( ? [B: 'B_update_b_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
              = 'id$a' )
            & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
              = 'id$a' )
            & ( B @ 'register$k' ) )
        & ( A @ 'register$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).

thf(737,plain,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( ( ? [B: 'B_update_b_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
                = 'id$a' )
              & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
                = 'id$a' )
              & ( B @ 'register$k' ) )
          & ( A @ 'register$k' ) )
       => ( A @ 'iso_register$g' ) )
      & ( ( A @ 'iso_register$g' )
       => ( ? [B: 'B_update_b_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$j' @ 'fun_app$an' ) )
                = 'id$a' )
              & ( ( B @ ( A @ 'comp$j' @ 'fun_app$an' ) )
                = 'id$a' )
              & ( B @ 'register$k' ) )
          & ( A @ 'register$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( F @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).

thf(2945,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$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( F @ ( E @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(66,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( ! [E: 'C_update$'] :
              ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$g' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).

thf(890,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$'] :
              ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$g' ) ) )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = ( D @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(367,axiom,
    ! [A: 'C_update_bool_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( 'uum$' @ 'pred_fun$d' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uum$' @ 'pred_fun$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).

thf(2025,plain,
    ! [A: 'C_update_bool_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
       => ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( 'uum$' @ 'pred_fun$d' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( 'uum$' @ 'pred_fun$d' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bo' ) @ ( 'uum$' @ 'pred_fun$a' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(572,axiom,
    ! [A: 'C_update_c_update_fun$'] :
      ( ! [B: 'C_update$'] :
          ( ( B @ ( A @ 'fun_app$z' ) )
          = B )
    <=> ( A = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).

thf(2742,plain,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( ( A = 'id$' )
       => ! [B: 'C_update$'] :
            ( ( B @ ( A @ 'fun_app$z' ) )
            = B ) )
      & ( ! [B: 'C_update$'] :
            ( ( B @ ( A @ 'fun_app$z' ) )
            = B )
       => ( A = 'id$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(447,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).

thf(2314,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$aj' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(50,axiom,
    ! [A: 'C_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uua$' @ 'fun_app$g' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).

thf(816,plain,
    ! [A: 'C_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uua$' @ 'fun_app$g' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(433,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( C @ ( 'id$a' @ 'comp$i' ) ) )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).

thf(2267,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( C @ ( 'id$a' @ 'comp$i' ) ) )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( E @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( 'uuq$' @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).

thf(2261,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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( E @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( 'uuq$' @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(17,axiom,
    'id$b' @ 'register$l',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).

thf(700,plain,
    'id$b' @ 'register$l',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = ( D @ ( C @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).

thf(2647,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = ( D @ ( C @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

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$'] : ( 'comp$a' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$am' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom636) ).

thf(2553,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$'] : ( 'comp$a' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$am' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( B @ ( A @ 'rel_fun$af' ) @ 'rel_fun$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(628,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).

thf(2928,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(485,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
      = ( C @ ( B @ ( A @ 'comp$ai' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).

thf(2461,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ 'comp$v' ) )
      = ( C @ ( B @ ( A @ 'comp$ai' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(452,axiom,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$a' @ ( 'uuq$' @ ( A @ 'rel_fun$bq' ) @ ( 'uus$' @ ( A @ 'rel_fun$bp' ) @ 'rel_fun$bo' ) @ ( 'uva$' @ 'rel_fun$bn' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom642) ).

thf(2329,plain,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$d' @ ( 'comp$a' @ ( 'uuq$' @ ( A @ 'rel_fun$bq' ) @ ( 'uus$' @ ( A @ 'rel_fun$bp' ) @ 'rel_fun$bo' ) @ ( 'uva$' @ 'rel_fun$bn' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(307,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'compatible$l' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).

thf(1820,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'compatible$l' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(58,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( C @ ( 'id$a' @ 'comp$j' @ 'fun_app$an' ) ) )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).

thf(858,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( C @ ( 'id$a' @ 'comp$j' @ 'fun_app$an' ) ) )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(243,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$c' ) )
          = 'top$a' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = 'top$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).

thf(1557,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$c' ) )
          = 'top$a' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = 'top$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(46,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( ( 'top$' @ ( A @ 'image$' ) )
        = 'top$b' )
    <=> ( ( A @ ( 'top$' @ 'inv_into$b' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).

thf(799,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( 'top$' @ 'inv_into$b' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
       => ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$b' ) )
      & ( ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$b' )
       => ( ( A @ ( 'top$' @ 'inv_into$b' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(334,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).

thf(1909,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$av' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$au' ) )
      = ( E @ ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$b' ) @ 'fun_app$al' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).

thf(726,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$av' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$au' ) )
      = ( E @ ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$b' ) @ 'fun_app$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(626,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) )
     => ( C @ ( B @ 'inj_on$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).

thf(2923,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) )
     => ( C @ ( B @ 'inj_on$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(177,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$u' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).

thf(1325,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$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$u' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(107,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).

thf(1029,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = ( D @ ( C @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).

thf(3006,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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
        = ( D @ ( C @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ab' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$aa' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).

thf(943,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ab' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$aa' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

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$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$d' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).

thf(1022,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$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$d' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( C @ ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$z' ) @ 'comp$k' ) )
          = ( E @ ( I @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) @ ( A @ ( H @ ( D @ 'comp$k' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$b' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).

thf(2252,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$z' ) @ 'comp$k' ) )
          = ( E @ ( I @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) @ ( A @ ( H @ ( D @ 'comp$k' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$b' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(566,axiom,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id$' @ 'fun_app$z' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).

thf(2725,plain,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id$' @ 'fun_app$z' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(415,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uun$' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).

thf(2212,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uun$' ) @ ( 'uuo$' @ 'pred_fun$b' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(61,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).

thf(868,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(382,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
          = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$g' ) )
                = ( F @ ( D @ 'fun_app$g' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).

thf(2086,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 @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
          = ( B @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$g' ) )
                = ( F @ ( D @ 'fun_app$g' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(40,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( A @ ( 'top$b' @ 'inv_into$' ) @ 'iso_register$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).

thf(780,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( A @ ( 'top$b' @ 'inv_into$' ) @ 'iso_register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(461,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_c_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( C @ ( 'id$' @ 'comp$h' ) ) )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).

thf(2369,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_c_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( C @ ( 'id$' @ 'comp$h' ) ) )
     => ( ( D @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( D @ ( C @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(440,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register_pair$t' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$bb' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).

thf(2288,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register_pair$t' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$bb' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(586,axiom,
    'id$' @ 'register$h',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).

thf(2797,plain,
    'id$' @ 'register$h',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(366,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$d' ) )
        = 'id_update$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).

thf(2022,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$d' ) )
        = 'id_update$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(384,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).

thf(2101,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$c' ) @ ( A @ 'fun_app$bt' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(189,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).

thf(1364,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(443,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$c' ) )
          = 'top$a' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = 'top$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).

thf(2303,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( 'top$' @ ( B @ 'image$c' ) )
          = 'top$a' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = 'top$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(56,axiom,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A = 'id$a' )
     => ( ( A @ ( 'top$b' @ 'grp$a' ) @ ( A @ ( 'top$b' @ 'grp$a' ) @ 'conversep$a' @ 'relcompp$b' ) )
        = ( A @ ( 'top$b' @ 'grp$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).

thf(851,plain,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A = 'id$a' )
     => ( ( A @ ( 'top$b' @ 'grp$a' ) @ ( A @ ( 'top$b' @ 'grp$a' ) @ 'conversep$a' @ 'relcompp$b' ) )
        = ( A @ ( 'top$b' @ 'grp$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ 'comp$w' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).

thf(1805,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$f' @ 'fun_app$al' ) )
        = ( G @ ( E @ ( B @ 'comp$w' ) @ 'comp$w' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(377,axiom,
    ! [A: 'B_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uub$' @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).

thf(2069,plain,
    ! [A: 'B_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uub$' @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(245,axiom,
    ! [A: 'B_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$by' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom662) ).

thf(1562,plain,
    ! [A: 'B_update_a_update_bool_fun_fun$'] : ( 'id$b' @ ( 'id$a' @ ( A @ ( A @ 'rel_fun$by' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(92,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( A @ 'iso_register$c' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).

thf(983,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( A @ 'iso_register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(379,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$b' ) )
     => ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$c' ) )
      <=> ( B @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).

thf(2075,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$b' ) )
     => ( ( ( B @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) )
         => ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$c' ) ) )
        & ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$c' ) )
         => ( B @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'inj_on$k' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(474,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).

thf(2418,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(112,axiom,
    ! [A: 'A_update_set_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$b' ) @ ( A @ 'fun_app$bv' ) )
      = ( D @ ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).

thf(1044,plain,
    ! [A: 'A_update_set_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$b' ) @ ( A @ 'fun_app$bv' ) )
      = ( D @ ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$f' ) @ 'fun_app$az' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'fun_app$aw' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$g' ) @ 'fun_app$ba' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).

thf(2550,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$f' ) @ 'fun_app$az' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'fun_app$aw' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$g' ) @ 'fun_app$ba' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(425,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( B @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'compatible$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).

thf(2244,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$g' ) ) )
     => ( B @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'compatible$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(209,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'preregister$c' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).

thf(1435,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'preregister$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(296,axiom,
    ! [A: 'B_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'uuw$' @ 'fun_app$' ) )
    <=> ( A @ ( 'top$' @ ( B @ 'image$' ) @ 'less_eq$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).

thf(1775,plain,
    ! [A: 'B_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( ( A @ ( 'top$' @ ( B @ 'image$' ) @ 'less_eq$' ) )
       => ( B @ ( A @ 'uuw$' @ 'fun_app$' ) ) )
      & ( ( B @ ( A @ 'uuw$' @ 'fun_app$' ) )
       => ( A @ ( 'top$' @ ( B @ 'image$' ) @ 'less_eq$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(524,axiom,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$at' ) @ 'fun_app$bz' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom658) ).

thf(2592,plain,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$' @ ( A @ ( A @ 'rel_fun$at' ) @ 'fun_app$bz' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(278,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
      = ( C @ ( B @ ( A @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).

thf(1694,plain,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
      = ( C @ ( B @ ( A @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(554,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).

thf(2693,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$f' ) @ 'fun_app$az' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'fun_app$bb' ) )
      = ( E @ ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$j' ) @ 'fun_app$bd' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).

thf(1076,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$f' ) @ 'fun_app$az' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'fun_app$bb' ) )
      = ( E @ ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$j' ) @ 'fun_app$bd' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(424,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ac' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
        = ( C @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).

thf(2239,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ac' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$v' ) )
        = ( C @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(10,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).

thf(675,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(634,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) )
     => ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).

thf(2952,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) )
     => ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(324,axiom,
    ! [A: 'A_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$y' ) @ 'fun_app$ce' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom664) ).

thf(1873,plain,
    ! [A: 'A_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$y' ) @ 'fun_app$ce' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(49,axiom,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$a' @ ( 'top$b' @ 'grp$a' ) @ 'fun_app$l' ) @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).

thf(812,plain,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$a' @ ( 'top$b' @ 'grp$a' ) @ 'fun_app$l' ) @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(30,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'bijection$b' )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).

thf(749,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'bijection$b' )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$e' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$d' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$s' ) @ ( F @ ( B @ 'map_fun$l' ) @ 'map_fun$ag' ) @ ( I @ ( E @ 'map_fun$f' ) @ 'map_fun$af' ) ) )
        = 'comp$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).

thf(2684,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$e' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$d' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$s' ) @ ( F @ ( B @ 'map_fun$l' ) @ 'map_fun$ag' ) @ ( I @ ( E @ 'map_fun$f' ) @ 'map_fun$af' ) ) )
        = 'comp$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(603,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ae' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
        = ( C @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).

thf(2846,plain,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ae' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
        = ( C @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(32,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uue$' @ 'fun_app$t' ) )
      = ( B @ ( A @ 'fun_app$g' ) @ ( 'id_update$a' @ 'tensor_update$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).

thf(754,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uue$' @ 'fun_app$t' ) )
      = ( B @ ( A @ 'fun_app$g' ) @ ( 'id_update$a' @ 'tensor_update$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(88,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$ao' ) )
        = ( D @ ( B @ 'comp$ah' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$h' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).

thf(968,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$ao' ) )
        = ( D @ ( B @ 'comp$ah' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(520,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom592) ).

thf(2582,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(269,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uul$' ) @ ( 'uuk$' @ 'pred_fun$' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).

thf(1662,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uul$' ) @ ( 'uuk$' @ 'pred_fun$' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( B @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(532,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register$i' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).

thf(2614,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'register$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(448,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ 'the_inv_into$f' ) @ 'fun_app$ai' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'the_inv_into$e' ) @ ( B @ ( C @ 'the_inv_into$a' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).

thf(2318,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ 'the_inv_into$f' ) @ 'fun_app$ai' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'the_inv_into$e' ) @ ( B @ ( C @ 'the_inv_into$a' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(434,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$e' )
        & ( A @ 'preregister$f' ) )
     => ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'preregister$h' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).

thf(2271,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$e' )
        & ( A @ 'preregister$f' ) )
     => ( A @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'preregister$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(12,axiom,
    ! [A: 'A_update_set_a_update_fun$',B: 'A_update_set$'] :
      ( ( B @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) )
      = ( B @ ( A @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).

thf(680,plain,
    ! [A: 'A_update_set_a_update_fun$',B: 'A_update_set$'] :
      ( ( B @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) )
      = ( B @ ( A @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(6,axiom,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A @ 'bijection$a' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).

thf(663,plain,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( A @ 'bijection$a' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$e' @ 'fun_app$an' ) @ 'comp$j' @ 'fun_app$an' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ai' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$i' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).

thf(2471,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ai' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$i' ) @ 'fun_app$ai' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

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$',F: 'A_update_a_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( F @ 'comp$f' @ 'fun_app$al' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).

thf(1905,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$',F: 'A_update_a_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( F @ 'comp$f' @ 'fun_app$al' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(202,axiom,
    'id$b' @ ( 'id$b' @ ( 'uus$' @ 'quotient3$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).

thf(1420,plain,
    'id$b' @ ( 'id$b' @ ( 'uus$' @ 'quotient3$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(612,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( 'top$a' @ ( B @ 'inj_on$a' ) )
        & ( 'top$' @ ( A @ 'inj_on$' ) ) )
     => ( 'top$a' @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).

thf(2878,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( 'top$a' @ ( B @ 'inj_on$a' ) )
        & ( 'top$' @ ( A @ 'inj_on$' ) ) )
     => ( 'top$a' @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(499,axiom,
    ! [A: 'A_update_a_update_fun_c_update_c_update_fun_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$g' ) )
     => ( ( 'id$b' @ ( A @ 'fun_app$bh' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).

thf(2503,plain,
    ! [A: 'A_update_a_update_fun_c_update_c_update_fun_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$g' ) )
     => ( ( 'id$b' @ ( A @ 'fun_app$bh' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(526,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).

thf(2597,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(346,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' )
     => ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).

thf(1958,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' )
     => ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(631,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$ae' ) )
      = ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).

thf(2942,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$ae' ) )
      = ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(502,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( ! [E: 'C_update$'] :
              ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$u' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
          = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom157) ).

thf(2513,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$'] :
              ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
              = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$u' ) ) )
        & ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
          = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(240,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).

thf(1547,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
        = ( G @ ( E @ ( B @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) @ 'comp$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).

thf(1003,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$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$w' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) )
        = ( G @ ( E @ ( B @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( D @ ( F @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$aa' ) @ 'comp$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(57,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) )
     => ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).

thf(855,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) )
     => ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(230,axiom,
    ! [A: 'A_update$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'uu$' @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).

thf(1516,plain,
    ! [A: 'A_update$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'uu$' @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(105,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'uug$' @ ( A @ 'uuh$' @ 'compatible$v' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).

thf(1025,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'uug$' @ ( A @ 'uuh$' @ 'compatible$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(65,axiom,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( 'id$a' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$a' ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).

thf(887,plain,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( 'id$a' @ ( B @ ( A @ 'iso_tuple_surjective_proof_assist$a' ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(89,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$g' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).

thf(971,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$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$' ) )
           => ( ( E @ ( C @ 'fun_app$g' ) )
              = ( E @ ( D @ 'fun_app$g' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ai' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
        = ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).

thf(2588,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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ai' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
        = ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(550,axiom,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id$' @ 'fun_app$z' ) @ ( 'pred_DEADID$' @ 'fun_app$i' ) )
    <=> ( A @ ( 'pred_DEADID$' @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).

thf(2678,plain,
    ! [A: 'C_update$'] :
      ( ( ( A @ ( 'pred_DEADID$' @ 'fun_app$i' ) )
       => ( A @ ( 'id$' @ 'fun_app$z' ) @ ( 'pred_DEADID$' @ 'fun_app$i' ) ) )
      & ( ( A @ ( 'id$' @ 'fun_app$z' ) @ ( 'pred_DEADID$' @ 'fun_app$i' ) )
       => ( A @ ( 'pred_DEADID$' @ 'fun_app$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(403,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'compatible$o' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).

thf(2175,plain,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'compatible$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(471,axiom,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( ( B @ ( 'pred_DEADID$' @ 'fun_app$i' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$' @ 'fun_app$z' ) )
        = ( B @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).

thf(2407,plain,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( ( B @ ( 'pred_DEADID$' @ 'fun_app$i' ) )
        & ( A = B ) )
     => ( ( A @ ( 'id$' @ 'fun_app$z' ) )
        = ( B @ ( 'id$' @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(564,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
      = ( C @ ( B @ 'comp$ac' ) @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom168) ).

thf(2720,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) )
      = ( C @ ( B @ 'comp$ac' ) @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

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$'] : ( 'comp$a' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$r' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$p' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$o' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom612) ).

thf(2831,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$'] : ( 'comp$a' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$r' ) @ ( A @ ( C @ 'rel_fun$q' ) @ 'rel_fun$p' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$o' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(20,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).

thf(705,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' )
        & ( ( B @ ( A @ 'comp$f' @ 'fun_app$al' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$h' ) @ 'comp$af' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).

thf(2977,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$h' ) @ 'comp$af' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(225,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) )
        = ( C @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).

thf(1499,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) )
        = ( C @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(9,axiom,
    ( ( 'id$b' @ 'image$f' )
    = 'id$w' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).

thf(673,plain,
    ( ( 'id$b' @ 'image$f' )
    = 'id$w' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(399,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$o' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'comp$bl' ) )
      = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$t' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).

thf(2165,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$o' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'comp$bl' ) )
      = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$t' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(323,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' )
     => ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).

thf(1869,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' )
     => ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$g' ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(417,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$v' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$h' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).

thf(2219,plain,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$v' ) )
          = 'id$a' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$h' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(175,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$l' ) @ 'register$g' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).

thf(1317,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$l' ) @ 'register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(331,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
      = ( C @ ( B @ ( A @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom182) ).

thf(1901,plain,
    ! [A: 'C_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$g' @ 'fun_app$am' ) )
      = ( C @ ( B @ ( A @ 'comp$ah' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(124,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register$k' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).

thf(1085,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register$k' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(494,axiom,
    ( ( 'id$a' @ ( 'id$' @ 'map_fun$u' ) )
    = 'id$o' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).

thf(2486,plain,
    ( ( 'id$a' @ ( 'id$' @ 'map_fun$u' ) )
    = 'id$o' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(156,axiom,
    ! [A: 'A_update_bool_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( 'uuk$' @ 'pred_fun$c' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bn' ) @ ( 'uuk$' @ 'pred_fun$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).

thf(1218,plain,
    ! [A: 'A_update_bool_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bn' ) @ ( 'uuk$' @ 'pred_fun$' ) ) )
       => ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( 'uuk$' @ 'pred_fun$c' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( 'uuk$' @ 'pred_fun$c' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bn' ) @ ( 'uuk$' @ 'pred_fun$' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(179,axiom,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'A_update_a_update_bool_fun_fun$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( 'uus$' @ 'rel_fun$i' ) @ ( A @ ( 'uus$' @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).

thf(1336,plain,
    ! [A: 'B_update_b_update_bool_fun_fun$',B: 'A_update_a_update_bool_fun_fun$'] : ( 'comp$c' @ ( 'comp$c' @ ( B @ ( 'uus$' @ 'rel_fun$i' ) @ ( A @ ( 'uus$' @ 'rel_fun$h' ) @ 'rel_fun$g' ) @ ( B @ ( A @ 'rel_fun$f' ) @ 'rel_fun$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(354,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'B_update$'] :
      ( ( ! [E: 'B_update$',F: 'B_update$'] :
            ( ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( E @ ( A @ 'fun_app$d' ) @ ( F @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$at' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).

thf(1987,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$',D: 'B_update$'] :
      ( ( ! [E: 'B_update$',F: 'B_update$'] :
            ( ( F @ ( B @ 'fun_app$d' ) @ ( E @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( E @ ( A @ 'fun_app$d' ) @ ( F @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$at' ) )
        = ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

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

thf(2224,plain,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ae' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$i' ) )
        = ( C @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(54,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ 'inv_into$d' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'inv_into$c' ) @ ( B @ ( C @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).

thf(840,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( C @ 'inv_into$d' @ 'fun_app$am' ) @ 'fun_app$z' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'inv_into$c' ) @ ( B @ ( C @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

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$'] :
      ( ( ! [H: 'B_update$',I: 'B_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$l' ) @ 'fun_app$k' ) )
           => ( I @ ( C @ 'fun_app$d' ) @ ( H @ ( C @ 'fun_app$d' ) @ ( G @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ! [H: 'A_update$',I: 'A_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$n' ) @ 'fun_app$m' ) )
              & ( H @ ( H @ ( A @ 'fun_app$n' ) @ 'fun_app$m' ) )
              & ( I @ ( H @ ( G @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
           => ( I @ ( B @ 'fun_app$u' ) @ ( H @ ( B @ 'fun_app$u' ) @ ( D @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( F @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( G @ 'relcompp$' ) @ ( A @ 'relcompp$' ) @ 'quotient3$b' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).

thf(1785,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$'] :
      ( ( ! [H: 'B_update$',I: 'B_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$l' ) @ 'fun_app$k' ) )
           => ( I @ ( C @ 'fun_app$d' ) @ ( H @ ( C @ 'fun_app$d' ) @ ( G @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ! [H: 'A_update$',I: 'A_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$n' ) @ 'fun_app$m' ) )
              & ( H @ ( H @ ( A @ 'fun_app$n' ) @ 'fun_app$m' ) )
              & ( I @ ( H @ ( G @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
           => ( I @ ( B @ 'fun_app$u' ) @ ( H @ ( B @ 'fun_app$u' ) @ ( D @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( F @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( B @ ( E @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( G @ 'relcompp$' ) @ ( A @ 'relcompp$' ) @ 'quotient3$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$u' ) @ ( H @ ( C @ 'fun_app$u' ) @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ! [H: 'B_update$',I: 'B_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( H @ ( H @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( I @ ( H @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
           => ( I @ ( B @ 'fun_app$d' ) @ ( H @ ( B @ 'fun_app$d' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( G @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$h' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).

thf(2354,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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$u' ) @ ( H @ ( C @ 'fun_app$u' ) @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
        & ! [H: 'B_update$',I: 'B_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( H @ ( H @ ( A @ 'fun_app$l' ) @ 'fun_app$k' ) )
              & ( I @ ( H @ ( G @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
           => ( I @ ( B @ 'fun_app$d' ) @ ( H @ ( B @ 'fun_app$d' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( F @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( G @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(70,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'preregister$d' )
        & ( A @ 'preregister$e' ) )
     => ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'preregister$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).

thf(907,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'preregister$d' )
        & ( A @ 'preregister$e' ) )
     => ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'preregister$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(293,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$o' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'comp$bj' ) )
      = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$p' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).

thf(1766,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$o' ) @ ( B @ ( A @ 'map_fun$n' ) @ 'comp$bj' ) )
      = ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(316,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_pair$f' ) @ 'comp$an' ) )
        = ( D @ ( B @ 'comp$k' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).

thf(1849,plain,
    ! [A: 'B_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_pair$f' ) @ 'comp$an' ) )
        = ( D @ ( B @ 'comp$k' ) @ ( C @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(19,axiom,
    ! [A: 'A_update_set$'] : ( A @ ( 'id$b' @ 'inj_on$i' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).

thf(703,plain,
    ! [A: 'A_update_set$'] : ( A @ ( 'id$b' @ 'inj_on$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(519,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_pair$q' ) )
        = ( C @ ( B @ 'register_pair$f' ) @ ( A @ 'comp$aw' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).

thf(2579,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$c' ) )
     => ( ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_pair$q' ) )
        = ( C @ ( B @ 'register_pair$f' ) @ ( A @ 'comp$aw' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$q' ) @ 'fun_app$bj' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'fun_app$bl' ) )
      = ( E @ ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$u' ) @ 'fun_app$bn' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).

thf(1749,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$q' ) @ 'fun_app$bj' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'fun_app$bl' ) )
      = ( E @ ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$u' ) @ 'fun_app$bn' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(226,axiom,
    ! [A: 'A_update$',B: 'A_update_set$',C: 'A_update_b_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'member$' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uut$' ) ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( A @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).

thf(1504,plain,
    ! [A: 'A_update$',B: 'A_update_set$',C: 'A_update_b_update_fun$',D: 'A_update$'] :
      ( ( ( B @ ( C @ 'inj_on$' ) )
        & ( B @ ( A @ 'member$' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uut$' ) ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
        = ( A @ ( 'id$b' @ 'fun_app$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(127,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$k' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$c' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).

thf(1094,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$k' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$' @ 'inv_into$c' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(98,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register$h' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).

thf(1008,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(191,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'B_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
              = ( E @ ( A @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).

thf(1372,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'B_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
              = ( E @ ( A @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(165,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$m' ) )
    <=> ( ( C @ ( A @ 'fun_app$u' ) )
        = ( C @ ( B @ 'fun_app$u' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).

thf(1272,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( ( ( C @ ( A @ 'fun_app$u' ) )
          = ( C @ ( B @ 'fun_app$u' ) ) )
       => ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$m' ) ) )
      & ( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$m' ) )
       => ( ( C @ ( A @ 'fun_app$u' ) )
          = ( C @ ( B @ 'fun_app$u' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(340,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'uue$' @ ( A @ 'uuf$' @ 'compatible$w' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).

thf(1934,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'uue$' @ ( A @ 'uuf$' @ 'compatible$w' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ai' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom208) ).

thf(2948,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ai' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$ag' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) @ 'fun_app$z' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ah' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).

thf(2411,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$ah' ) @ ( A @ 'fun_app$ag' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'comp$h' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(498,axiom,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A @ 'bijection$' )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).

thf(2500,plain,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A @ 'bijection$' )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$d' @ 'fun_app$am' ) @ 'comp$g' @ 'fun_app$am' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(3,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_a_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$b' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$b' ) @ 'fun_app$al' ) )
        = 'id$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$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$b' ) ) )
     => ( ( 'id$b' @ ( B @ ( C @ 'map_fun$b' ) @ 'fun_app$al' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(302,axiom,
    ! [A: 'B_update_set$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'grp$c' ) @ ( 'uus$' @ 'rel_fun$' ) )
      = ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ ( A @ 'uuw$' @ 'collect$' @ 'grp$d' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom605) ).

thf(1802,plain,
    ! [A: 'B_update_set$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'grp$c' ) @ ( 'uus$' @ 'rel_fun$' ) )
      = ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ ( A @ 'uuw$' @ 'collect$' @ 'grp$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(345,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).

thf(1955,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(397,axiom,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A @ 'iso_register$d' )
    <=> ( ? [B: 'C_update_c_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
              = 'id$' )
            & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
              = 'id$' )
            & ( B @ 'register$h' ) )
        & ( A @ 'register$h' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).

thf(2145,plain,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( ( ? [B: 'C_update_c_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
                = 'id$' )
              & ( B @ 'register$h' ) )
          & ( A @ 'register$h' ) )
       => ( A @ 'iso_register$d' ) )
      & ( ( A @ 'iso_register$d' )
       => ( ? [B: 'C_update_c_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$g' @ 'fun_app$am' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$g' @ 'fun_app$am' ) )
                = 'id$' )
              & ( B @ 'register$h' ) )
          & ( A @ 'register$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(223,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ! [C: 'B_update$',D: 'B_update$'] :
            ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'register$n' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).

thf(1485,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ! [C: 'B_update$',D: 'B_update$'] :
            ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'register$n' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(560,axiom,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$d' @ ( 'uuq$' @ ( A @ 'rel_fun$am' ) @ ( 'uus$' @ ( A @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( 'uva$' @ 'rel_fun$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom641) ).

thf(2711,plain,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$a' @ ( 'comp$d' @ ( 'uuq$' @ ( A @ 'rel_fun$am' ) @ ( 'uus$' @ ( A @ 'rel_fun$al' ) @ 'rel_fun$ak' ) @ ( 'uva$' @ 'rel_fun$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$h' ) @ 'comp$' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$ae' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).

thf(2728,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$h' ) @ 'comp$' ) )
          = ( E @ ( I @ ( B @ 'comp$ad' ) @ 'comp$ae' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(282,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).

thf(1717,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$y' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(479,axiom,
    ! [A: 'A_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$n' ) @ 'fun_app$cd' ) @ 'fun_app$bw' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom663) ).

thf(2435,plain,
    ! [A: 'A_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$n' ) @ 'fun_app$cd' ) @ 'fun_app$bw' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(149,axiom,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( A = B )
    <=> ? [C: 'B_update$'] :
          ( ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
            = B )
          & ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
            = A )
          & ( 'top$b' @ ( C @ 'member$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).

thf(1180,plain,
    ! [A: 'B_update$',B: 'B_update$'] :
      ( ( ? [C: 'B_update$'] :
            ( ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
              = B )
            & ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
              = A )
            & ( 'top$b' @ ( C @ 'member$a' ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ? [C: 'B_update$'] :
            ( ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
              = B )
            & ( ( C @ ( 'id$a' @ 'fun_app$aa' ) )
              = A )
            & ( 'top$b' @ ( C @ 'member$a' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(555,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$ar' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$m' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom241) ).

thf(2696,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$ar' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( E @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( 'uur$' @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).

thf(1834,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$'] :
      ( ( ( E @ ( D @ ( 'uus$' @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$c' ) ) ) )
     => ( E @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( B @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( 'uur$' @ 'relcompp$b' ) @ ( A @ 'relcompp$b' ) @ 'quotient3$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(69,axiom,
    ! [A: 'A_update_a_update_fun_b_update_b_update_fun_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$h' ) )
     => ( ( 'id$b' @ ( A @ 'fun_app$av' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).

thf(903,plain,
    ! [A: 'A_update_a_update_fun_b_update_b_update_fun_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$h' ) )
     => ( ( 'id$b' @ ( A @ 'fun_app$av' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(409,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).

thf(2194,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
      = ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(608,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).

thf(2865,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(611,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$l' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$o' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).

thf(2875,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_tensor$m' ) @ 'comp$l' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$o' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(203,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$e' )
        & ( A @ 'preregister$d' ) )
     => ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'preregister$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).

thf(1421,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$e' )
        & ( A @ 'preregister$d' ) )
     => ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'preregister$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(363,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'uuh$' @ ( A @ 'uug$' @ 'compatible$t' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).

thf(2013,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'uuh$' @ ( A @ 'uug$' @ 'compatible$t' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(267,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$b' ) )
     => ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$' ) )
      <=> ( B @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).

thf(1654,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_set$',C: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'inj_on$b' ) )
     => ( ( ( B @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) )
         => ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$' ) ) )
        & ( ( B @ ( A @ 'image$b' ) @ ( C @ 'inj_on$' ) )
         => ( B @ ( A @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'inj_on$m' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(201,axiom,
    ! [A: 'C_update_set$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ~ ( A @ ( B @ 'image$a' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$g' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$a' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$g' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$' ) @ 'fun_app$g' ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).

thf(1412,plain,
    ! [A: 'C_update_set$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ~ ( A @ ( B @ 'image$a' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$g' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$a' ) @ ( D @ 'member$' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uuu$' ) ) @ 'fun_app$g' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$' ) @ 'fun_app$g' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(297,axiom,
    'id$a' @ ( 'id$a' @ ( 'uur$' @ 'quotient3$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).

thf(1781,plain,
    'id$a' @ ( 'id$a' @ ( 'uur$' @ 'quotient3$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$g' @ 'fun_app$am' ) @ 'comp$h' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$ac' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$a' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).

thf(2209,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$g' @ 'fun_app$am' ) @ 'comp$h' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$ac' ) @ ( A @ ( H @ ( D @ 'comp$ah' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$a' ) ) )
        & ( 'top$a' @ ( D @ ( C @ 'type_definition$' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$' ) @ 'comp$g' @ 'fun_app$am' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$z' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).

thf(2997,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$' ) @ 'comp$g' @ 'fun_app$am' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$z' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(496,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$c' ) @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).

thf(2490,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$c' ) @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ai' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(386,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$c' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$af' ) @ 'comp$' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).

thf(2110,plain,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$',C: 'B_update_b_update_fun$'] :
      ( ( ( C = 'id$a' )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$c' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$af' ) @ 'comp$' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(99,axiom,
    ( ( 'id$a' @ 'vimage$a' )
    = 'id$v' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom667) ).

thf(1010,plain,
    ( ( 'id$a' @ 'vimage$a' )
    = 'id$v' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(625,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).

thf(2919,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$g' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$ab' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(215,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$k' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$a' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).

thf(1453,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$k' ) )
          = 'id$b' ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$a' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$aj' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
        = ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).

thf(2643,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$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$aa' ) )
          = F )
        & ( ( B @ ( A @ 'comp$aj' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
        = ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$e' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$a' ) @ ( F @ ( B @ 'map_fun$h' ) @ 'map_fun$ai' ) @ ( I @ ( E @ 'map_fun$f' ) @ 'map_fun$ah' ) ) )
        = 'comp$e' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).

thf(1866,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$e' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$c' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$e' ) ) ) )
     => ( ( 'comp$c' @ ( H @ ( C @ 'map_fun$a' ) @ ( F @ ( B @ 'map_fun$h' ) @ 'map_fun$ai' ) @ ( I @ ( E @ 'map_fun$f' ) @ 'map_fun$ah' ) ) )
        = 'comp$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$aj' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$af' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom126) ).

thf(2775,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$aj' ) )
          = ( D @ ( C @ 'comp$ab' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$af' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(584,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'compatible$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).

thf(2792,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'compatible$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(621,axiom,
    ! [A: 'A_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$n' ) @ 'fun_app$cd' ) @ 'fun_app$bw' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom654) ).

thf(2907,plain,
    ! [A: 'A_update_c_update_bool_fun_fun$'] : ( 'id$' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$n' ) @ 'fun_app$cd' ) @ 'fun_app$bw' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ae' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
        = ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).

thf(2443,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ae' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$' ) )
        = ( D @ ( F @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

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$',F: 'A_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( E @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( F @ ( C @ 'comp$f' @ 'fun_app$al' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).

thf(1341,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$',F: 'A_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( E @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( F @ ( C @ 'comp$f' @ 'fun_app$al' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(605,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ai' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).

thf(2853,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ai' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ 'comp$ag' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(222,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$b' @ 'the_inv_into$a' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( B @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).

thf(1481,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( B @ ( A @ ( A @ ( 'top$b' @ 'the_inv_into$a' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( B @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(129,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) )
     => ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).

thf(1101,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ 'type_definition$h' ) ) )
     => ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).

thf(2823,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(289,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).

thf(1745,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C = 'id$b' )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( A @ ( C @ ( B @ 'comp$f' @ 'fun_app$al' ) @ 'comp$f' @ 'fun_app$al' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(640,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'C_update$'] :
            ( ( B @ ( E @ 'member$b' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
              = ( E @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).

thf(2971,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'C_update$'] :
            ( ( B @ ( E @ 'member$b' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
              = ( E @ ( A @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(478,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uup$' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).

thf(2431,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uup$' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( B @ ( D @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(308,axiom,
    ! [A: 'A_update_set$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'uuy$' @ 'fun_app$b' ) )
    <=> ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).

thf(1822,plain,
    ! [A: 'A_update_set$',B: 'B_update_a_update_fun$'] :
      ( ( ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$a' ) )
       => ( B @ ( A @ 'uuy$' @ 'fun_app$b' ) ) )
      & ( ( B @ ( A @ 'uuy$' @ 'fun_app$b' ) )
       => ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(392,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( B @ 'comp$ai' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).

thf(2130,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( 'top$a' @ ( A @ 'inj_on$a' ) )
     => ( ( A @ ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( B @ 'comp$ai' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(26,axiom,
    ! [A: 'A_update_set_a_update_fun$',B: 'A_update_set$'] :
      ( ( B @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) )
      = ( B @ ( A @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).

thf(731,plain,
    ! [A: 'A_update_set_a_update_fun$',B: 'A_update_set$'] :
      ( ( B @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) )
      = ( B @ ( A @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(94,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) @ ( C @ 'inj_on$b' ) )
        & ( B @ ( A @ 'inj_on$' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).

thf(995,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) @ ( C @ 'inj_on$b' ) )
        & ( B @ ( A @ 'inj_on$' ) ) )
     => ( B @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

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$'] : ( 'comp$c' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ad' ) @ ( A @ ( C @ 'rel_fun$ac' ) @ 'rel_fun$ab' ) @ ( B @ ( A @ 'rel_fun$aa' ) @ 'rel_fun$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).

thf(961,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$'] : ( 'comp$c' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$ad' ) @ ( A @ ( C @ 'rel_fun$ac' ) @ 'rel_fun$ab' ) @ ( B @ ( A @ 'rel_fun$aa' ) @ 'rel_fun$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$' ) @ 'comp$h' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$ac' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$a' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).

thf(2594,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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$' ) @ 'comp$h' ) )
          = ( E @ ( I @ ( B @ 'comp$aa' ) @ 'comp$ac' ) @ ( A @ ( H @ ( D @ 'comp$aj' ) @ 'comp$ab' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$a' ) ) )
        & ( 'top$b' @ ( D @ ( C @ 'type_definition$c' ) ) )
        & ( 'top$' @ ( B @ ( A @ 'type_definition$e' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(283,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'uuf$' @ ( A @ 'uue$' @ 'compatible$s' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).

thf(1721,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'uuf$' @ ( A @ 'uue$' @ 'compatible$s' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(86,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( 'top$' @ ( B @ 'inj_on$' ) )
        & ( 'top$b' @ ( A @ 'inj_on$b' ) ) )
     => ( 'top$' @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).

thf(963,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( 'top$' @ ( B @ 'inj_on$' ) )
        & ( 'top$b' @ ( A @ 'inj_on$b' ) ) )
     => ( 'top$' @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = ( D @ ( C @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).

thf(2273,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) )
        = ( D @ ( C @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
        = ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom113) ).

thf(2389,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$',F: 'A_update_c_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$ab' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$ad' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'comp$af' ) )
        = ( D @ ( F @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(220,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ 'inv_into$e' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'inv_into$b' ) @ ( B @ ( C @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).

thf(1476,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ 'inv_into$e' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'inv_into$b' ) @ ( B @ ( C @ 'inv_into$' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(118,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).

thf(1062,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_set$'] :
      ( ( D @ ( C @ 'image$b' ) @ ( B @ 'image$' ) @ ( A @ 'fun_app$bu' ) )
      = ( D @ ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'image$e' @ 'fun_app$bs' ) @ ( A @ 'fun_app$bu' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(227,axiom,
    ( ( 'id$b' @ ( 'id$a' @ 'register_tensor$e' ) )
    = 'id$h' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).

thf(1508,plain,
    ( ( 'id$b' @ ( 'id$a' @ 'register_tensor$e' ) )
    = 'id$h' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(591,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$v' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$' ) )
          = 'id$' )
        & ( B @ 'register$j' )
        & ( A @ 'register$i' ) )
     => ( A @ 'iso_register$e' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).

thf(2811,plain,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$v' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$' ) )
          = 'id$' )
        & ( B @ 'register$j' )
        & ( A @ 'register$i' ) )
     => ( A @ 'iso_register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).

thf(2004,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$',F: 'B_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$ad' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$w' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$j' @ 'fun_app$an' ) )
        = ( F @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$z' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
        = ( D @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom114) ).

thf(2447,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$w' ) )
          = F )
        & ( ( B @ ( A @ 'comp$z' ) )
          = ( D @ ( C @ 'comp$aa' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'comp$ag' ) )
        = ( D @ ( F @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( F @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).

thf(1861,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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( F @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( F @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).

thf(2081,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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
        = ( F @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(489,axiom,
    'id$' @ 'preregister$',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).

thf(2475,plain,
    'id$' @ 'preregister$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(406,axiom,
    ! [A: 'C_update_set_c_update_fun$',B: 'C_update_set$'] :
      ( ( B @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) )
      = ( B @ ( A @ 'fun_app$bt' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).

thf(2183,plain,
    ! [A: 'C_update_set_c_update_fun$',B: 'C_update_set$'] :
      ( ( B @ ( 'id$' @ 'image$d' @ 'fun_app$br' ) @ ( A @ 'fun_app$bt' ) )
      = ( B @ ( A @ 'fun_app$bt' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

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

thf(763,plain,
    ! [A: 'A_update_set$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'grp$e' ) @ ( 'uuq$' @ 'rel_fun$a' ) )
      = ( B @ ( 'comp$d' @ 'fun_app$af' ) @ ( A @ 'uux$' @ 'collect$a' @ 'grp$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$d' ) @ 'fun_app$ax' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'fun_app$aw' ) )
      = ( E @ ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$e' ) @ 'fun_app$ay' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).

thf(1513,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$d' ) @ 'fun_app$ax' ) @ ( B @ ( A @ 'map_fun$c' ) @ 'fun_app$aw' ) )
      = ( E @ ( D @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$e' ) @ 'fun_app$ay' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

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$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
     => ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).

thf(2623,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$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) )
     => ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(356,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$l' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$bi' ) )
      = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).

thf(1994,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$l' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$bi' ) )
      = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

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$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) )
     => ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$u' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).

thf(2912,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$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) )
     => ( ( E @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( E @ ( D @ 'fun_app$ag' ) @ ( C @ 'fun_app$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(372,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id$b' @ 'fun_app$ab' ) @ ( 'pred_DEADID$b' @ 'fun_app$m' ) )
    <=> ( A @ ( 'pred_DEADID$b' @ 'fun_app$m' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).

thf(2041,plain,
    ! [A: 'A_update$'] :
      ( ( ( A @ ( 'pred_DEADID$b' @ 'fun_app$m' ) )
       => ( A @ ( 'id$b' @ 'fun_app$ab' ) @ ( 'pred_DEADID$b' @ 'fun_app$m' ) ) )
      & ( ( A @ ( 'id$b' @ 'fun_app$ab' ) @ ( 'pred_DEADID$b' @ 'fun_app$m' ) )
       => ( A @ ( 'pred_DEADID$b' @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(211,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).

thf(1440,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ 'comp$ad' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

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$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) )
     => ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$u' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).

thf(929,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$'] :
      ( ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = ( D @ ( C @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) ) )
     => ( ( E @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( E @ ( D @ 'fun_app$d' ) @ ( C @ 'fun_app$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(370,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) )
     => ( C @ ( B @ 'inj_on$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).

thf(2036,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) )
     => ( C @ ( B @ 'inj_on$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(173,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).

thf(1309,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( C @ ( A @ 'fun_app$g' ) @ ( D @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(571,axiom,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id$' @ 'fun_app$z' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).

thf(2739,plain,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id$' @ 'fun_app$z' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(497,axiom,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( 'uum$' @ 'pred_fun$f' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uum$' @ 'pred_fun$a' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).

thf(2494,plain,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
       => ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( 'uum$' @ 'pred_fun$f' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( 'uum$' @ 'pred_fun$f' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bp' ) @ ( 'uum$' @ 'pred_fun$a' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(212,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$a' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$aa' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'comp$u' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).

thf(1444,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ 'register$a' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$aa' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'comp$u' ) )
        = ( D @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(581,axiom,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A = 'id$' )
     => ( ( A @ ( 'top$a' @ 'grp$' ) @ ( A @ ( 'top$a' @ 'grp$' ) @ 'conversep$' @ 'relcompp$a' ) )
        = ( A @ ( 'top$a' @ 'grp$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).

thf(2779,plain,
    ! [A: 'C_update_c_update_fun$'] :
      ( ( A = 'id$' )
     => ( ( A @ ( 'top$a' @ 'grp$' ) @ ( A @ ( 'top$a' @ 'grp$' ) @ 'conversep$' @ 'relcompp$a' ) )
        = ( A @ ( 'top$a' @ 'grp$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(365,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$q' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'comp$bm' ) )
      = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$u' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).

thf(2019,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_c_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$q' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'comp$bm' ) )
      = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(144,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$w' ) )
      = ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$x' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).

thf(1161,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$w' ) )
      = ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(257,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( A @ 'iso_register$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).

thf(1614,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
        & ( ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
          = 'id$a' )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( A @ 'iso_register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(475,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ 'inv_into$g' ) @ 'fun_app$ai' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'inv_into$c' ) @ ( B @ ( C @ 'inv_into$' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).

thf(2421,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'C_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) @ ( D @ 'member$b' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$c' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ 'inv_into$g' ) @ 'fun_app$ai' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'inv_into$c' ) @ ( B @ ( C @ 'inv_into$' ) @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(396,axiom,
    ! [A: 'A_update_set$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'grp$e' ) @ ( 'uur$' @ 'rel_fun$b' ) )
      = ( B @ ( 'comp$a' @ 'fun_app$w' ) @ ( A @ 'uuy$' @ 'collect$b' @ 'grp$g' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom607) ).

thf(2142,plain,
    ! [A: 'A_update_set$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'grp$e' ) @ ( 'uur$' @ 'rel_fun$b' ) )
      = ( B @ ( 'comp$a' @ 'fun_app$w' ) @ ( A @ 'uuy$' @ 'collect$b' @ 'grp$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(390,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
      = ( C @ ( B @ ( A @ 'comp$aj' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).

thf(2123,plain,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$' ) )
      = ( C @ ( B @ ( A @ 'comp$aj' ) @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(96,axiom,
    ! [A: 'B_update$',B: 'B_update_set$',C: 'B_update_a_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( C @ 'inj_on$b' ) )
        & ( B @ ( A @ 'member$a' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uuv$' ) ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( A @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596) ).

thf(999,plain,
    ! [A: 'B_update$',B: 'B_update_set$',C: 'B_update_a_update_fun$',D: 'B_update$'] :
      ( ( ( B @ ( C @ 'inj_on$b' ) )
        & ( B @ ( A @ 'member$a' ) ) )
     => ( ( A @ ( C @ ( D @ ( C @ ( B @ 'uuv$' ) ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( A @ ( 'id$a' @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(503,axiom,
    ( ( 'id$' @ ( 'id$b' @ 'register_tensor$f' ) )
    = 'id$i' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).

thf(2517,plain,
    ( ( 'id$' @ ( 'id$b' @ 'register_tensor$f' ) )
    = 'id$i' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(166,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).

thf(1280,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(428,axiom,
    ( ( 'id$' @ ( 'id$a' @ 'register_tensor$c' ) )
    = 'id$f' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).

thf(2255,plain,
    ( ( 'id$' @ ( 'id$a' @ 'register_tensor$c' ) )
    = 'id$f' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(422,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$a' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$s' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$w' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).

thf(2233,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$a' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$s' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'register_tensor$w' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(198,axiom,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( ~ ( A @ ( B @ 'image$' ) @ ( D @ 'member$a' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) @ 'fun_app$d' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$' ) @ ( D @ 'member$a' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) @ 'fun_app$d' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$b' ) @ 'fun_app$d' ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).

thf(1395,plain,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( ~ ( A @ ( B @ 'image$' ) @ ( D @ 'member$a' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) @ 'fun_app$d' ) )
          = C ) )
      & ( ( A @ ( B @ 'image$' ) @ ( D @ 'member$a' ) )
       => ( ( D @ ( C @ ( B @ ( A @ 'uut$' ) ) @ 'fun_app$d' ) )
          = ( D @ ( B @ ( A @ 'the_inv_into$b' ) @ 'fun_app$d' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(505,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ 'inv_into$h' ) @ 'fun_app$ah' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'inv_into$b' ) @ ( B @ ( C @ 'inv_into$a' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).

thf(2522,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$a' ) )
        & ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ 'inv_into$h' ) @ 'fun_app$ah' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$a' ) @ 'inv_into$b' ) @ ( B @ ( C @ 'inv_into$a' ) @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(193,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ 'the_inv_into$h' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'the_inv_into$b' ) @ ( B @ ( C @ 'the_inv_into$a' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).

thf(1380,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$',C: 'B_update_set$',D: 'B_update$'] :
      ( ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$' ) @ ( D @ 'member$a' ) )
        & ( C @ ( B @ 'inj_on$b' ) )
        & ( C @ ( B @ 'image$b' ) @ ( A @ 'inj_on$' ) ) )
     => ( ( D @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( C @ 'the_inv_into$h' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( D @ ( A @ ( C @ ( B @ 'image$b' ) @ 'the_inv_into$b' ) @ ( B @ ( C @ 'the_inv_into$a' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(161,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'iso_register$c' )
    <=> ( ? [B: 'A_update_b_update_fun$'] :
            ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
              = 'id$a' )
            & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
              = 'id$b' )
            & ( B @ 'register$c' ) )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).

thf(1248,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( ( ? [B: 'A_update_b_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
                = 'id$a' )
              & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
                = 'id$b' )
              & ( B @ 'register$c' ) )
          & ( A @ 'register$a' ) )
       => ( A @ 'iso_register$c' ) )
      & ( ( A @ 'iso_register$c' )
       => ( ? [B: 'A_update_b_update_fun$'] :
              ( ( ( A @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
                = 'id$a' )
              & ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
                = 'id$b' )
              & ( B @ 'register$c' ) )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(60,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$f' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'comp$bh' ) )
      = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$j' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).

thf(865,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$f' ) @ ( B @ ( A @ 'map_fun$h' ) @ 'comp$bh' ) )
      = ( D @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'map_fun$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(28,axiom,
    ! [A: 'B_update_set$'] : ( A @ ( 'id$a' @ 'inj_on$m' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).

thf(735,plain,
    ! [A: 'B_update_set$'] : ( A @ ( 'id$a' @ 'inj_on$m' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(264,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( B @ ( E @ 'member$' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
              = ( E @ ( A @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) )
        & ( ( B @ ( A @ 'image$' ) )
          = 'top$b' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).

thf(1642,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_set$',C: 'B_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( B @ ( E @ 'member$' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) )
              = ( E @ ( A @ ( D @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'fun_app$ab' ) ) ) )
        & ( ( B @ ( A @ 'image$' ) )
          = 'top$b' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(31,axiom,
    ( ( 'top$' @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) )
    = 'top$' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).

thf(752,plain,
    ( ( 'top$' @ ( 'id$b' @ 'image$f' @ 'fun_app$bq' ) )
    = 'top$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(463,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$g' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$m' ) )
        = ( C @ ( B @ 'register_pair$o' ) @ ( A @ 'comp$az' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).

thf(2385,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'compatible$g' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'register_pair$m' ) )
        = ( C @ ( B @ 'register_pair$o' ) @ ( A @ 'comp$az' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(274,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register$l' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).

thf(1678,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( A @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'register$l' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(83,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ! [B: 'A_update$'] :
          ( ( B @ ( A @ 'fun_app$ab' ) )
          = B )
    <=> ( A = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).

thf(950,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( ( A = 'id$b' )
       => ! [B: 'A_update$'] :
            ( ( B @ ( A @ 'fun_app$ab' ) )
            = B ) )
      & ( ! [B: 'A_update$'] :
            ( ( B @ ( A @ 'fun_app$ab' ) )
            = B )
       => ( A = 'id$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).

thf(1097,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$aa' ) @ ( A @ 'fun_app$d' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$ab' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$j' @ 'fun_app$an' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$w' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(592,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( 'top$e' @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'inj_on$f' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).

thf(2815,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( 'top$e' @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'inj_on$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(570,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$am' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$e' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom236) ).

thf(2736,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ 'register$b' )
        & ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$am' ) )
        = ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_pair$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(361,axiom,
    ! [A: 'A_update_set_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$b' ) @ ( A @ 'fun_app$bv' ) )
      = ( D @ ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).

thf(2008,plain,
    ! [A: 'A_update_set_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$b' ) @ ( A @ 'fun_app$bv' ) )
      = ( D @ ( C @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'image$f' @ 'fun_app$bq' ) @ ( A @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$f' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$o' ) @ ( F @ ( B @ 'map_fun$k' ) @ 'map_fun$ak' ) @ ( I @ ( E @ 'map_fun$c' ) @ 'map_fun$aj' ) ) )
        = 'comp$c' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).

thf(1527,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$f' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$e' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$o' ) @ ( F @ ( B @ 'map_fun$k' ) @ 'map_fun$ak' ) @ ( I @ ( E @ 'map_fun$c' ) @ 'map_fun$aj' ) ) )
        = 'comp$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(141,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ 'register$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).

thf(1148,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

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$'] : ( 'comp$d' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$n' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$l' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$j' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).

thf(1673,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$'] : ( 'comp$d' @ ( 'comp$c' @ ( B @ ( C @ 'rel_fun$n' ) @ ( A @ ( C @ 'rel_fun$m' ) @ 'rel_fun$l' ) @ ( B @ ( A @ 'rel_fun$k' ) @ 'rel_fun$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(74,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( ( A @ ( 'top$' @ 'inv_into$b' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).

thf(918,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'iso_register$a' )
     => ( ( A @ ( 'top$' @ 'inv_into$b' ) @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(407,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).

thf(2186,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ 'comp$i' ) )
        = ( D @ ( C @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

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$'] : ( 'comp$e' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$at' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$as' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ar' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom638) ).

thf(807,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$'] : ( 'comp$e' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$at' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$as' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ar' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(148,axiom,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( B @ ( A @ ( 'uuq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).

thf(1172,plain,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( ( A = B )
       => ( B @ ( A @ ( 'uuq$' @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
      & ( ( B @ ( A @ ( 'uuq$' @ 'fun_app$j' ) @ 'fun_app$i' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

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$'] : ( 'comp$e' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$at' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$as' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ar' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom619) ).

thf(1056,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$'] : ( 'comp$e' @ ( 'comp$d' @ ( B @ ( C @ 'rel_fun$at' ) @ ( A @ ( C @ 'rel_fun$al' ) @ 'rel_fun$as' ) @ ( B @ ( A @ 'rel_fun$ao' ) @ 'rel_fun$ar' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(219,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( A @ 'comp$k' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).

thf(1473,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( 'top$a' @ 'inv_into$a' ) @ ( A @ 'comp$k' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(119,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
      = ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$y' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).

thf(1065,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'comp$ad' ) )
      = ( C @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ ( A @ 'comp$y' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).

thf(2668,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$',F: 'B_update$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( F @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(256,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ 'comp$x' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).

thf(1610,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( 'top$b' @ ( A @ 'inj_on$b' ) )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ ( B @ 'comp$x' ) @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(543,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).

thf(2651,plain,
    ! [A: 'A_update_c_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'image$g' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(582,axiom,
    ! [A: 'C_update_c_update_fun_b_update_b_update_fun_fun$',B: 'B_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$c' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$bo' ) )
        = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).

thf(2783,plain,
    ! [A: 'C_update_c_update_fun_b_update_b_update_fun_fun$',B: 'B_update_c_update_fun$'] :
      ( ( B @ ( A @ 'iso_tuple_update_accessor_cong_assist$c' ) )
     => ( ( 'id$' @ ( A @ 'fun_app$bo' ) )
        = 'id$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(574,axiom,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$d' ) ) )
     => ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).

thf(2751,plain,
    ! [A: 'A_update_a_update_bool_fun_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$d' ) ) )
     => ( ( C @ ( B @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(588,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$ai' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom152) ).

thf(2800,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update$'] :
      ( ( ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) )
        = ( D @ ( C @ 'fun_app$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(137,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) )
     => ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).

thf(1129,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ 'inj_on$i' ) )
     => ( C @ ( B @ 'image$' ) @ ( A @ 'inj_on$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(192,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) )
     => ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).

thf(1378,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'inj_on$j' ) )
     => ( C @ ( B @ 'image$a' ) @ ( A @ 'inj_on$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(487,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$v' ) )
          = 'id$a' )
        & ( B @ 'register$i' )
        & ( A @ 'register$j' ) )
     => ( A @ 'iso_register$f' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).

thf(2467,plain,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_c_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$v' ) )
          = 'id$a' )
        & ( B @ 'register$i' )
        & ( A @ 'register$j' ) )
     => ( A @ 'iso_register$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(350,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ! [C: 'B_update$',D: 'B_update$'] :
            ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).

thf(1976,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( ! [C: 'B_update$',D: 'B_update$'] :
            ( ( D @ ( B @ 'fun_app$d' ) @ ( C @ ( A @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) )
            = ( C @ ( A @ 'fun_app$d' ) @ ( D @ ( B @ 'fun_app$d' ) @ 'comp_update$a' @ 'fun_app$ab' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(171,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( 'top$e' @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'inj_on$h' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).

thf(1299,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( 'top$e' @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'inj_on$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$g' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$t' ) @ ( F @ ( B @ 'map_fun$m' ) @ 'map_fun$as' ) @ ( I @ ( E @ 'map_fun$g' ) @ 'map_fun$ar' ) ) )
        = 'comp$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom371) ).

thf(2699,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$'] :
      ( ( ( I @ ( H @ ( G @ 'quotient3$g' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$b' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$' ) ) ) )
     => ( ( 'comp$d' @ ( H @ ( C @ 'map_fun$t' ) @ ( F @ ( B @ 'map_fun$m' ) @ 'map_fun$as' ) @ ( I @ ( E @ 'map_fun$g' ) @ 'map_fun$ar' ) ) )
        = 'comp$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$g' ) @ ( H @ ( C @ 'fun_app$g' ) @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
        & ! [H: 'C_update$',I: 'C_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( H @ ( H @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( I @ ( H @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
           => ( I @ ( B @ 'fun_app$ag' ) @ ( H @ ( B @ 'fun_app$ag' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( G @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).

thf(871,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$'] :
      ( ( ! [H: 'A_update$',I: 'A_update$'] :
            ( ( I @ ( H @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) )
           => ( I @ ( C @ 'fun_app$g' ) @ ( H @ ( C @ 'fun_app$g' ) @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
        & ! [H: 'C_update$',I: 'C_update$'] :
            ( ( ( I @ ( I @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( H @ ( H @ ( A @ 'fun_app$j' ) @ 'fun_app$i' ) )
              & ( I @ ( H @ ( G @ 'fun_app$j' ) @ 'fun_app$i' ) ) )
           => ( I @ ( B @ 'fun_app$ag' ) @ ( H @ ( B @ 'fun_app$ag' ) @ ( D @ 'fun_app$n' ) @ 'fun_app$m' ) ) )
        & ( F @ ( E @ ( D @ 'quotient3$d' ) ) )
        & ( C @ ( B @ ( A @ 'quotient3$f' ) ) ) )
     => ( F @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( B @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ ( A @ ( G @ 'relcompp$a' ) @ ( A @ 'relcompp$a' ) @ 'quotient3$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(394,axiom,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$b' @ ( 'uur$' @ ( A @ 'rel_fun$bt' ) @ ( 'uus$' @ ( A @ 'rel_fun$al' ) @ 'rel_fun$bs' ) @ ( 'uvb$' @ 'rel_fun$br' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom645) ).

thf(2138,plain,
    ! [A: 'C_update_b_update_bool_fun_fun$'] : ( 'comp$e' @ ( 'comp$b' @ ( 'uur$' @ ( A @ 'rel_fun$bt' ) @ ( 'uus$' @ ( A @ 'rel_fun$al' ) @ 'rel_fun$bs' ) @ ( 'uvb$' @ 'rel_fun$br' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(160,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'iso_register$b' )
    <=> ( ? [B: 'C_update_a_update_fun$'] :
            ( ( ( A @ ( B @ 'comp$k' ) )
              = 'id$b' )
            & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
              = 'id$' )
            & ( B @ 'register$b' ) )
        & ( A @ 'register$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).

thf(1236,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( ( ? [B: 'C_update_a_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$k' ) )
                = 'id$b' )
              & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
                = 'id$' )
              & ( B @ 'register$b' ) )
          & ( A @ 'register$' ) )
       => ( A @ 'iso_register$b' ) )
      & ( ( A @ 'iso_register$b' )
       => ( ? [B: 'C_update_a_update_fun$'] :
              ( ( ( A @ ( B @ 'comp$k' ) )
                = 'id$b' )
              & ( ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
                = 'id$' )
              & ( B @ 'register$b' ) )
          & ( A @ 'register$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(93,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$m' ) )
    <=> ( ( C @ ( A @ 'fun_app$g' ) )
        = ( C @ ( B @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).

thf(987,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update$'] :
      ( ( ( ( C @ ( A @ 'fun_app$g' ) )
          = ( C @ ( B @ 'fun_app$g' ) ) )
       => ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$m' ) ) )
      & ( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$m' ) )
       => ( ( C @ ( A @ 'fun_app$g' ) )
          = ( C @ ( B @ 'fun_app$g' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

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$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
     => ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$d' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).

thf(1352,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$'] :
      ( ( ( B @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) )
     => ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$d' ) )
        = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'fun_app$bl' ) )
      = ( E @ ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$t' ) @ 'fun_app$bm' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).

thf(2731,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$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) @ ( B @ ( A @ 'map_fun$s' ) @ 'fun_app$bl' ) )
      = ( E @ ( D @ ( B @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'map_fun$t' ) @ 'fun_app$bm' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(638,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).

thf(2966,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'fun_app$ai' ) )
      = ( C @ ( B @ 'fun_app$ag' ) @ ( A @ 'fun_app$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(164,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$x' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).

thf(1268,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
     => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( B @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'comp$x' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(527,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$q' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$v' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).

thf(2600,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_c_update_fun$',C: 'C_update_a_update_fun$',D: 'B_update_a_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ 'register$b' )
        & ( B @ 'register$' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'register_tensor$p' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'comp$q' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( C @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'register_tensor$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(237,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uun$' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).

thf(1537,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uun$' ) @ ( 'uum$' @ 'pred_fun$a' ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
        = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(250,axiom,
    ( ( 'id$b' @ 'vimage$b' )
    = 'id$w' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom668) ).

thf(1582,plain,
    ( ( 'id$b' @ 'vimage$b' )
    = 'id$w' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(103,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).

thf(1019,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(338,axiom,
    ! [A: 'B_update_b_update_fun$'] :
      ( ! [B: 'B_update$'] :
          ( ( B @ ( A @ 'fun_app$aa' ) )
          = B )
    <=> ( A = 'id$a' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).

thf(1923,plain,
    ! [A: 'B_update_b_update_fun$'] :
      ( ( ( A = 'id$a' )
       => ! [B: 'B_update$'] :
            ( ( B @ ( A @ 'fun_app$aa' ) )
            = B ) )
      & ( ! [B: 'B_update$'] :
            ( ( B @ ( A @ 'fun_app$aa' ) )
            = B )
       => ( A = 'id$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(653,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ 'preregister$d' ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'preregister$g' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).

thf(3020,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ 'preregister$d' ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'preregister$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(52,axiom,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( A = B )
    <=> ? [C: 'A_update$'] :
          ( ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
            = B )
          & ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
            = A )
          & ( 'top$' @ ( C @ 'member$' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).

thf(822,plain,
    ! [A: 'A_update$',B: 'A_update$'] :
      ( ( ? [C: 'A_update$'] :
            ( ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
              = B )
            & ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
              = A )
            & ( 'top$' @ ( C @ 'member$' ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ? [C: 'A_update$'] :
            ( ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
              = B )
            & ( ( C @ ( 'id$b' @ 'fun_app$ab' ) )
              = A )
            & ( 'top$' @ ( C @ 'member$' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(500,axiom,
    ( ( 'id$b' @ ( 'id$' @ 'register_tensor$b' ) )
    = 'id$e' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).

thf(2507,plain,
    ( ( 'id$b' @ ( 'id$' @ 'register_tensor$b' ) )
    = 'id$e' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(254,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$g' ) )
                = ( F @ ( D @ 'fun_app$g' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).

thf(1597,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 @ ( C @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) )
          = ( B @ ( D @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$g' ) )
                = ( F @ ( D @ 'fun_app$g' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(552,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$v' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$g' ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).

thf(2687,plain,
    ! [A: 'B_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$v' ) )
          = 'id$a' )
        & ( ( B @ ( A @ 'comp$' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$g' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(207,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$l' ) )
     => ( A @ ( B @ 'comp$ab' ) @ 'register$' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).

thf(1431,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$l' ) )
     => ( A @ ( B @ 'comp$ab' ) @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(575,axiom,
    ! [A: 'C_update_set$'] : ( A @ ( 'id$' @ 'inj_on$j' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).

thf(2754,plain,
    ! [A: 'C_update_set$'] : ( A @ ( 'id$' @ 'inj_on$j' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

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$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).

thf(2640,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$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$g' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$g' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) )
        = ( C @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'fun_app$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(347,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).

thf(1962,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id$b' @ 'fun_app$ab' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(79,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( 'top$d' @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'inj_on$e' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).

thf(935,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$c' ) )
     => ( 'top$d' @ ( A @ ( 'comp$d' @ 'fun_app$af' ) @ 'inj_on$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(110,axiom,
    ( 'uus$'
    = ( 'id$b' @ ( 'top$' @ 'grp$b' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).

thf(1037,plain,
    ( 'uus$'
    = ( 'id$b' @ ( 'top$' @ 'grp$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(294,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( ! [E: 'A_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$g' ) @ ( E @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( E @ ( A @ 'fun_app$g' ) @ ( F @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_update$a' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'fun_app$as' ) )
        = ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).

thf(1769,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( ! [E: 'A_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$g' ) @ ( E @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) )
            = ( E @ ( A @ 'fun_app$g' ) @ ( F @ ( B @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) )
        & ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_update$a' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'fun_app$as' ) )
        = ( D @ ( B @ 'fun_app$g' ) @ ( C @ ( A @ 'fun_app$g' ) @ 'comp_update$' @ 'fun_app$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

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

thf(2170,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) @ 'compatible$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(404,axiom,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$' @ ( 'top$a' @ 'grp$' ) @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).

thf(2177,plain,
    ! [A: 'C_update$',B: 'C_update$'] :
      ( ( A = B )
     => ( B @ ( A @ ( 'id$' @ ( 'top$a' @ 'grp$' ) @ 'fun_app$j' ) @ 'fun_app$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

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$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).

thf(1014,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$'] :
      ( ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$d' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) )
        = ( C @ ( E @ ( D @ ( 'comp$e' @ 'fun_app$ak' ) @ 'fun_app$aj' ) @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(449,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) )
     => ( C @ ( B @ 'inj_on$a' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).

thf(2321,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'inj_on$l' ) )
     => ( C @ ( B @ 'inj_on$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(190,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( D @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).

thf(1367,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update_b_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( D @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = ( D @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(413,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$f' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).

thf(2206,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'quotient3$f' ) ) )
     => ( ( 'id$' @ ( B @ ( C @ 'map_fun$o' ) @ 'fun_app$bi' ) )
        = 'id$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(288,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( 'top$' @ ( A @ 'inj_on$' ) )
    <=> ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
        = 'id$b' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).

thf(1737,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' )
       => ( 'top$' @ ( A @ 'inj_on$' ) ) )
      & ( ( 'top$' @ ( A @ 'inj_on$' ) )
       => ( ( A @ ( A @ ( 'top$' @ 'inv_into$b' ) @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) )
          = 'id$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(553,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).

thf(2690,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$b' @ 'fun_app$y' ) @ 'fun_app$x' ) @ 'image$h' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(4,axiom,
    ( ( 'id$b' @ ( 'id$b' @ 'map_fun$b' ) )
    = 'id$n' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).

thf(659,plain,
    ( ( 'id$b' @ ( 'id$b' @ 'map_fun$b' ) )
    = 'id$n' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(408,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$b' ) )
      = ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).

thf(2191,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_c_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$b' ) )
      = ( A @ ( B @ ( 'comp$a' @ 'fun_app$w' ) @ 'fun_app$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(152,axiom,
    ! [A: 'A_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$y' ) @ 'fun_app$ce' ) @ 'fun_app$by' ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom655) ).

thf(1204,plain,
    ! [A: 'A_update_b_update_bool_fun_fun$'] : ( 'id$a' @ ( 'id$b' @ ( A @ ( A @ 'rel_fun$y' ) @ 'fun_app$ce' ) @ 'fun_app$by' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = ( D @ ( C @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).

thf(1449,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$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) )
        = ( D @ ( C @ ( E @ ( 'comp$d' @ 'fun_app$af' ) @ 'fun_app$ae' ) @ 'image$d' @ 'fun_app$br' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(305,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id$a' @ 'fun_app$aa' ) @ ( 'pred_DEADID$a' @ 'fun_app$k' ) )
    <=> ( A @ ( 'pred_DEADID$a' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).

thf(1812,plain,
    ! [A: 'B_update$'] :
      ( ( ( A @ ( 'pred_DEADID$a' @ 'fun_app$k' ) )
       => ( A @ ( 'id$a' @ 'fun_app$aa' ) @ ( 'pred_DEADID$a' @ 'fun_app$k' ) ) )
      & ( ( A @ ( 'id$a' @ 'fun_app$aa' ) @ ( 'pred_DEADID$a' @ 'fun_app$k' ) )
       => ( A @ ( 'pred_DEADID$a' @ 'fun_app$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(21,axiom,
    ( ( 'id$b' @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) )
    = 'id$b' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).

thf(708,plain,
    ( ( 'id$b' @ ( 'top$' @ 'inv_into$f' @ 'fun_app$al' ) )
    = 'id$b' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$x' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ad' ) )
          = ( D @ ( C @ 'comp$y' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = ( F @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).

thf(1912,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$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$x' ) )
          = F )
        & ( ( B @ ( A @ 'comp$ad' ) )
          = ( D @ ( C @ 'comp$y' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) @ ( A @ 'comp$f' @ 'fun_app$al' ) )
        = ( F @ ( C @ ( 'comp$c' @ 'fun_app$ad' ) @ 'fun_app$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(642,axiom,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$e' @ ( 'uur$' @ ( A @ 'rel_fun$bw' ) @ ( 'uus$' @ ( A @ 'rel_fun$bp' ) @ 'rel_fun$bv' ) @ ( 'uvb$' @ 'rel_fun$bu' ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom646) ).

thf(2980,plain,
    ! [A: 'B_update_c_update_bool_fun_fun$'] : ( 'comp$b' @ ( 'comp$e' @ ( 'uur$' @ ( A @ 'rel_fun$bw' ) @ ( 'uus$' @ ( A @ 'rel_fun$bp' ) @ 'rel_fun$bv' ) @ ( 'uvb$' @ 'rel_fun$bu' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(5149,plain,
    $false,
    inference(e,[status(thm)],[2630,809,2031,2072,2263,909,1840,2787,2544,2331,2612,1469,1168,2295,2306,760,2341,2480,1083,1982,666,1818,1295,1855,1211,1158,683,1882,2395,1618,2527,1939,3012,2114,1533,677,1437,2117,2104,2231,1068,2808,1522,2671,2676,2282,1591,1705,1426,1608,1137,2933,1919,913,1640,2844,670,1164,1999,797,2476,2627,2168,1260,898,2216,2723,1782,782,885,1904,2405,2886,1359,2400,2067,1287,1660,785,1264,2897,2126,2571,2654,1628,2603,2916,2562,2488,1545,2713,1087,1319,1479,770,881,1931,1773,2989,1875,2388,2373,1347,1115,2635,2222,2616,2794,2259,2880,937,2555,2335,1283,1109,1632,2451,2236,1858,1864,1828,2925,2291,1383,1843,2437,2861,1896,734,2002,1345,1433,2750,1201,2718,1564,981,766,2618,2833,2281,1447,2483,2424,774,1104,1697,2586,2982,2884,1651,2011,1206,1691,925,2364,1338,2047,2621,2574,661,2905,714,2061,2773,1636,1047,1730,2705,894,2428,2805,778,1519,2277,862,1570,1666,2969,2937,2606,788,2986,2015,1560,2441,2673,1387,1723,2890,729,916,1032,1968,757,2344,710,1012,2958,1423,2464,1938,2758,1555,2820,2872,1951,2200,2609,1836,2181,1079,1027,2327,1195,1407,1634,1392,1936,2157,1017,2709,2509,1878,2858,1118,697,1234,1541,1567,1361,2830,2868,686,3010,1584,2038,1039,2798,1683,3000,2323,1292,933,1810,2172,1214,2349,837,2285,997,1588,701,2845,1984,1852,1715,1979,1150,2519,1530,1456,2900,1831,1131,654,1552,2851,2566,1799,2140,2756,1333,1991,2203,921,1170,2995,2529,1732,2909,2702,2761,1846,1054,2963,1035,794,2338,2121,1764,1680,2033,2585,689,2894,1135,1648,965,1727,1510,1301,2734,819,1916,1884,1389,2568,1535,2716,1965,2817,1124,843,1125,2525,2657,2393,1752,958,1403,1795,2398,1226,1488,2827,2134,1428,1669,2308,1312,3002,1997,1090,2557,1224,1356,1675,1058,1107,1464,947,979,2311,2478,2229,2084,1574,1048,2257,2839,2197,2065,2415,1894,1349,2097,2955,2246,737,2945,890,2025,2742,2314,816,2267,2261,700,2647,2553,2928,2461,2329,1820,858,1557,799,1909,726,2923,1325,1029,3006,943,1022,2252,2725,2212,868,2086,780,2369,2288,2797,2022,2101,1364,2303,851,1805,2069,1562,983,2075,2418,1044,2550,2244,1435,1775,2592,1694,2693,1076,2239,675,2952,1873,812,749,2684,2846,754,968,2582,1662,2614,2318,2271,680,663,2471,1905,1420,2878,2503,2597,1958,2942,2513,1547,1003,855,1516,1025,887,971,2588,2678,2175,2407,2720,2831,705,2977,1499,673,2165,1869,2219,1317,1901,1085,2486,1218,1336,1987,2224,840,1785,2354,907,1766,1849,703,2579,1749,1504,1094,1008,1372,1272,1934,2948,2411,2500,656,1802,1955,2145,1485,2711,2728,1717,2435,1180,2696,1834,903,2194,2865,2875,1421,2013,1654,1412,1781,2209,2997,2490,2110,1010,2919,1453,2643,1866,2775,2792,2907,2443,1341,2853,1481,1101,2823,1745,2971,2431,1822,2130,731,995,961,2594,1721,963,2273,2389,1476,1062,1508,2811,2004,2447,1861,2081,2475,2183,763,1513,2623,1994,2912,2041,1440,929,2036,1309,2739,2494,1444,2779,2019,1161,1614,2421,2142,2123,999,2517,1280,2255,2233,1395,2522,1380,1248,865,735,1642,752,2385,1678,950,1097,2815,2736,2008,1527,1148,1673,918,2186,807,1172,1056,1473,1065,2668,1610,2651,2783,2751,2800,1129,1378,2467,1976,1299,2699,871,2138,1236,987,1352,2731,2966,1268,2600,1537,1582,1019,1923,3020,822,2507,1597,2687,1431,2754,2640,1962,935,1037,1769,2170,2177,1014,2321,1367,2206,1737,2690,659,2191,1204,1449,1812,708,1912,2980]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP384_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.54  % Computer : n017.cluster.edu
% 0.13/0.54  % Model    : x86_64 x86_64
% 0.13/0.54  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.54  % Memory   : 8046.5625MB
% 0.13/0.54  % OS       : Linux 6.8.0-71-generic
% 0.13/0.54  % CPULimit : 300
% 0.13/0.54  % WCLimit  : 300
% 0.13/0.54  % DateTime : Fri Sep 25 19:04:48 UTC 2026
% 0.13/0.54  % CPUTime  : 
% 0.13/0.54  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.12  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.59/1.87  % [INFO] 	 Parsing done (747ms). 
% 3.59/1.88  % [INFO] 	 Running in sequential loop mode. 
% 4.70/2.27  % [INFO] 	 eprover registered as external prover. 
% 4.70/2.28  % [INFO] 	 Scanning for conjecture ... 
% 5.30/2.59  % [INFO] 	 Found a conjecture (or negated_conjecture) and 668 axioms. Running axiom selection ... 
% 6.95/2.95  % [INFO] 	 Axiom selection finished. Selected 651 axioms (removed 17 axioms). 
% 8.51/3.46  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 8.91/3.51  % [INFO] 	 Type checking passed. 
% 8.91/3.51  % [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 ... 
% 53.19/13.57  % External prover 'e' found a proof!
% 53.19/13.57  % [INFO] 	 Killing All external provers ... 
% 53.19/13.57  % Time passed: 12902ms (effective reasoning time: 11683ms)
% 53.19/13.57  % 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)>
% 53.19/13.58  % 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
% 53.19/13.58  % No. of inferences in proof: 1306
% 53.19/13.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12902 ms resp. 11683 ms w/o parsing
% 56.49/14.08  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.49/14.09  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------