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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP383_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n008.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 23.90s 6.60s
% Output   : Refutation 25.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  512
% Syntax   : Number of formulae    : 1026 ( 282 unt;   0 typ;   0 def)
%            Number of atoms       : 2504 (1135 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 14987 (  14   ~;   0   |; 658   &;13495   @)
%                                         (  24 <=>; 796  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :  255 ( 254 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  477 ( 475 usr;  31 con; 0-4 aty)
%            Number of variables   : 3688 (   0   ^;3688   !;   0   ?;3688   :)

% Comments : 
%------------------------------------------------------------------------------
thf('C_a_prod_update_a_b_prod_update_fun$_type',type,
    'C_a_prod_update_a_b_prod_update_fun$': $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('D_c_d_prod_prod_update_b_b_prod_update_fun$_type',type,
    'D_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

thf('C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $tType ).

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

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

thf('C_d_prod_d_prod_update_b_b_prod_update_fun$_type',type,
    'C_d_prod_d_prod_update_b_b_prod_update_fun$': $tType ).

thf('D_b_prod_update$_type',type,
    'D_b_prod_update$': $tType ).

thf('C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_set$_type',type,
    'C_d_prod_update_a_update_fun_set$': $tType ).

thf('B_update_b_update_prod$_type',type,
    'B_update_b_update_prod$': $tType ).

thf('C_d_prod_update_b_b_prod_update_fun$_type',type,
    'C_d_prod_update_b_b_prod_update_fun$': $tType ).

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

thf('C_d_prod_update_c_d_prod_update_prod$_type',type,
    'C_d_prod_update_c_d_prod_update_prod$': $tType ).

thf('A_update_d_d_prod_update_fun$_type',type,
    'A_update_d_d_prod_update_fun$': $tType ).

thf('C_d_prod_update_b_update_fun$_type',type,
    'C_d_prod_update_b_update_fun$': $tType ).

thf('A_update_c_d_prod_update_bool_fun_fun$_type',type,
    'A_update_c_d_prod_update_bool_fun_fun$': $tType ).

thf('B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$_type',type,
    'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

thf('C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('C_update_d_a_prod_update_fun$_type',type,
    'C_update_d_a_prod_update_fun$': $tType ).

thf('B_itself$_type',type,
    'B_itself$': $tType ).

thf('D_c_prod_update_b_b_prod_update_fun$_type',type,
    'D_c_prod_update_b_b_prod_update_fun$': $tType ).

thf('B_update_c_update_fun_c_update_b_update_fun_fun$_type',type,
    'B_update_c_update_fun_c_update_b_update_fun_fun$': $tType ).

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

thf('D_update_a_update_fun_bool_fun$_type',type,
    'D_update_a_update_fun_bool_fun$': $tType ).

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

thf('C_update_d_update_bool_fun_fun$_type',type,
    'C_update_d_update_bool_fun_fun$': $tType ).

thf('C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$_type',type,
    'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

thf('D_update_d_update_prod$_type',type,
    'D_update_d_update_prod$': $tType ).

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

thf('C_d_prod_update_a_b_prod_update_fun$_type',type,
    'C_d_prod_update_a_b_prod_update_fun$': $tType ).

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

thf('C_update_c_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

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

thf('A_update_d_update_bool_fun_fun$_type',type,
    'A_update_d_update_bool_fun_fun$': $tType ).

thf('C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('D_d_prod_update_b_update_fun$_type',type,
    'D_d_prod_update_b_update_fun$': $tType ).

thf('D_update_c_update_prod_a_update_a_update_prod_fun$_type',type,
    'D_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('A_update_b_a_prod_update_fun$_type',type,
    'A_update_b_a_prod_update_fun$': $tType ).

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

thf('B_update_b_d_prod_update_fun$_type',type,
    'B_update_b_d_prod_update_fun$': $tType ).

thf('C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$_type',type,
    'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

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

thf('C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$_type',type,
    'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

thf('C_a_prod_update_b_b_prod_update_fun$_type',type,
    'C_a_prod_update_b_b_prod_update_fun$': $tType ).

thf('A_d_prod_update_a_update_fun$_type',type,
    'A_d_prod_update_a_update_fun$': $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_d_prod_update_c_d_prod_update_fun$_type',type,
    'C_d_prod_update_c_d_prod_update_fun$': $tType ).

thf('C_update_d_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

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

thf('A_c_prod_update_b_b_prod_update_fun$_type',type,
    'A_c_prod_update_b_b_prod_update_fun$': $tType ).

thf('C_update_b_update_b_update_prod_fun$_type',type,
    'C_update_b_update_b_update_prod_fun$': $tType ).

thf('C_update_b_a_prod_update_fun$_type',type,
    'C_update_b_a_prod_update_fun$': $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('D_update_a_b_prod_update_fun$_type',type,
    'D_update_a_b_prod_update_fun$': $tType ).

thf('D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$_type',type,
    'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $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('D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$_type',type,
    'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('A_d_prod_update_b_a_prod_update_fun$_type',type,
    'A_d_prod_update_b_a_prod_update_fun$': $tType ).

thf('D_update_set$_type',type,
    'D_update_set$': $tType ).

thf('D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('D_c_prod_update_a_b_prod_update_fun$_type',type,
    'D_c_prod_update_a_b_prod_update_fun$': $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('D_d_prod_update_a_b_prod_update_fun$_type',type,
    'D_d_prod_update_a_b_prod_update_fun$': $tType ).

thf('C_b_prod_update$_type',type,
    'C_b_prod_update$': $tType ).

thf('C_d_prod_update_c_update_prod$_type',type,
    'C_d_prod_update_c_update_prod$': $tType ).

thf('D_update_bool_fun$_type',type,
    'D_update_bool_fun$': $tType ).

thf('D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

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

thf('B_update_d_update_fun$_type',type,
    'B_update_d_update_fun$': $tType ).

thf('D_update_d_update_fun$_type',type,
    'D_update_d_update_fun$': $tType ).

thf('C_c_prod_update_a_b_prod_update_fun$_type',type,
    'C_c_prod_update_a_b_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('A_itself$_type',type,
    'A_itself$': $tType ).

thf('D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

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

thf('B_d_prod_update$_type',type,
    'B_d_prod_update$': $tType ).

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

thf('C_d_prod_c_prod_update_b_b_prod_update_fun$_type',type,
    'C_d_prod_c_prod_update_b_b_prod_update_fun$': $tType ).

thf('D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$_type',type,
    'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

thf('D_update_c_update_fun$_type',type,
    'D_update_c_update_fun$': $tType ).

thf('C_update_d_update_prod$_type',type,
    'C_update_d_update_prod$': $tType ).

thf('C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('A_update_b_d_prod_update_fun$_type',type,
    'A_update_b_d_prod_update_fun$': $tType ).

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

thf('C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$_type',type,
    'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

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

thf('C_d_prod_update_c_update_bool_fun_fun$_type',type,
    'C_d_prod_update_c_update_bool_fun_fun$': $tType ).

thf('D_update_c_d_prod_update_prod$_type',type,
    'D_update_c_d_prod_update_prod$': $tType ).

thf('D_update_a_update_fun$_type',type,
    'D_update_a_update_fun$': $tType ).

thf('B_update_a_b_prod_update_fun$_type',type,
    'B_update_a_b_prod_update_fun$': $tType ).

thf('C_d_prod_d_prod_update_a_a_prod_update_fun$_type',type,
    'C_d_prod_d_prod_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_c_d_prod_update_bool_fun_fun$_type',type,
    'C_d_prod_update_c_d_prod_update_bool_fun_fun$': $tType ).

thf('B_update_d_update_fun_c_update_b_update_fun_fun$_type',type,
    'B_update_d_update_fun_c_update_b_update_fun_fun$': $tType ).

thf('A_update_b_update_b_update_prod_fun$_type',type,
    'A_update_b_update_b_update_prod_fun$': $tType ).

thf('D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$_type',type,
    'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

thf('C_update_c_d_prod_update_fun$_type',type,
    'C_update_c_d_prod_update_fun$': $tType ).

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

thf('D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

thf('D_c_prod_update_b_update_fun$_type',type,
    'D_c_prod_update_b_update_fun$': $tType ).

thf('C_d_prod_update_b_update_bool_fun_fun$_type',type,
    'C_d_prod_update_b_update_bool_fun_fun$': $tType ).

thf('B_a_prod_update_b_update_fun$_type',type,
    'B_a_prod_update_b_update_fun$': $tType ).

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

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

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

thf('A_b_prod_update_b_update_fun$_type',type,
    'A_b_prod_update_b_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

thf('C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

thf('A_d_prod_update_b_update_fun$_type',type,
    'A_d_prod_update_b_update_fun$': $tType ).

thf('D_d_prod_update_b_b_prod_update_fun$_type',type,
    'D_d_prod_update_b_b_prod_update_fun$': $tType ).

thf('D_update_a_update_bool_fun_fun$_type',type,
    'D_update_a_update_bool_fun_fun$': $tType ).

thf('B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$_type',type,
    'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

thf('A_d_prod_update$_type',type,
    'A_d_prod_update$': $tType ).

thf('C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

thf('C_update_c_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('C_update_d_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('D_update_c_update_prod$_type',type,
    'D_update_c_update_prod$': $tType ).

thf('B_update_d_update_fun_d_update_b_update_fun_fun$_type',type,
    'B_update_d_update_fun_d_update_b_update_fun_fun$': $tType ).

thf('A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$_type',type,
    'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$': $tType ).

thf('D_update_c_d_prod_update_bool_fun_fun$_type',type,
    'D_update_c_d_prod_update_bool_fun_fun$': $tType ).

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

thf('D_c_prod_update_a_a_prod_update_fun$_type',type,
    'D_c_prod_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

thf('D_c_d_prod_prod_update_a_a_prod_update_fun$_type',type,
    'D_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_b_update_b_update_prod_fun$_type',type,
    'C_d_prod_update_b_update_b_update_prod_fun$': $tType ).

thf('A_update_a_d_prod_update_fun$_type',type,
    'A_update_a_d_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_bool_fun_fun$': $tType ).

thf('D_update_b_update_fun$_type',type,
    'D_update_b_update_fun$': $tType ).

thf('A_update_a_update_prod_b_update_b_update_prod_fun$_type',type,
    'A_update_a_update_prod_b_update_b_update_prod_fun$': $tType ).

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

thf('D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$': $tType ).

thf('B_update_c_d_prod_update_fun$_type',type,
    'B_update_c_d_prod_update_fun$': $tType ).

thf('A_update_c_d_prod_update_fun$_type',type,
    'A_update_c_d_prod_update_fun$': $tType ).

thf('C_d_prod_c_prod_update_a_a_prod_update_fun$_type',type,
    'C_d_prod_c_prod_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('C_d_prod_update_d_update_bool_fun_fun$_type',type,
    'C_d_prod_update_d_update_bool_fun_fun$': $tType ).

thf('D_update_d_b_prod_update_fun$_type',type,
    'D_update_d_b_prod_update_fun$': $tType ).

thf('A_c_prod_update_b_a_prod_update_fun$_type',type,
    'A_c_prod_update_b_a_prod_update_fun$': $tType ).

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

thf('A_update_a_b_prod_update_fun$_type',type,
    'A_update_a_b_prod_update_fun$': $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('B_update_b_a_prod_update_fun$_type',type,
    'B_update_b_a_prod_update_fun$': $tType ).

thf('D_update_a_update_a_update_prod_fun$_type',type,
    'D_update_a_update_a_update_prod_fun$': $tType ).

thf('C_update_d_b_prod_update_fun$_type',type,
    'C_update_d_b_prod_update_fun$': $tType ).

thf('B_update_d_a_prod_update_fun$_type',type,
    'B_update_d_a_prod_update_fun$': $tType ).

thf('A_update_d_a_prod_update_fun$_type',type,
    'A_update_d_a_prod_update_fun$': $tType ).

thf('D_update$_type',type,
    'D_update$': $tType ).

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

thf('C_update_c_update_prod$_type',type,
    'C_update_c_update_prod$': $tType ).

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

thf('C_update_a_a_prod_update_fun$_type',type,
    'C_update_a_a_prod_update_fun$': $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('C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$_type',type,
    'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

thf('B_update_c_update_fun_a_update_a_update_fun_fun$_type',type,
    'B_update_c_update_fun_a_update_a_update_fun_fun$': $tType ).

thf('C_update_c_d_prod_update_prod$_type',type,
    'C_update_c_d_prod_update_prod$': $tType ).

thf('A_update_d_b_prod_update_fun$_type',type,
    'A_update_d_b_prod_update_fun$': $tType ).

thf('C_update_a_b_prod_update_fun$_type',type,
    'C_update_a_b_prod_update_fun$': $tType ).

thf('B_update_c_d_prod_update_bool_fun_fun$_type',type,
    'B_update_c_d_prod_update_bool_fun_fun$': $tType ).

thf('D_update_d_update_prod_b_update_b_update_prod_fun$_type',type,
    'D_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('C_d_prod_update_a_update_fun$_type',type,
    'C_d_prod_update_a_update_fun$': $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_d_prod_update_d_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$_type',type,
    'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

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

thf('D_a_prod_update_a_b_prod_update_fun$_type',type,
    'D_a_prod_update_a_b_prod_update_fun$': $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('C_update_b_b_prod_update_fun$_type',type,
    'C_update_b_b_prod_update_fun$': $tType ).

thf('B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$_type',type,
    'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

thf('D_a_prod_update$_type',type,
    'D_a_prod_update$': $tType ).

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

thf('C_c_d_prod_prod_update_a_a_prod_update_fun$_type',type,
    'C_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

thf('B_update_d_b_prod_update_fun$_type',type,
    'B_update_d_b_prod_update_fun$': $tType ).

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

thf('B_update_b_b_prod_update_fun$_type',type,
    'B_update_b_b_prod_update_fun$': $tType ).

thf('A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$_type',type,
    'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$': $tType ).

thf('D_update_b_update_bool_fun_fun$_type',type,
    'D_update_b_update_bool_fun_fun$': $tType ).

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

thf('C_d_prod_update_c_update_fun$_type',type,
    'C_d_prod_update_c_update_fun$': $tType ).

thf('C_d_prod_update_a_a_prod_update_fun$_type',type,
    'C_d_prod_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

thf('C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$_type',type,
    'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('D_update_a_update_fun_set$_type',type,
    'D_update_a_update_fun_set$': $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_c_d_prod_update_fun_a_update_a_update_fun_fun$_type',type,
    'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$': $tType ).

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

thf('C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$_type',type,
    'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

thf('C_update_b_d_prod_update_fun$_type',type,
    'C_update_b_d_prod_update_fun$': $tType ).

thf('D_c_prod_update$_type',type,
    'D_c_prod_update$': $tType ).

thf('C_c_prod_update_b_a_prod_update_fun$_type',type,
    'C_c_prod_update_b_a_prod_update_fun$': $tType ).

thf('D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$_type',type,
    'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

thf('A_update_d_c_prod_update_fun$_type',type,
    'A_update_d_c_prod_update_fun$': $tType ).

thf('D_update_d_update_bool_fun_fun$_type',type,
    'D_update_d_update_bool_fun_fun$': $tType ).

thf('A_d_prod_update_b_b_prod_update_fun$_type',type,
    'A_d_prod_update_b_b_prod_update_fun$': $tType ).

thf('C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

thf('D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('D_update_c_update_bool_fun_fun$_type',type,
    'D_update_c_update_bool_fun_fun$': $tType ).

thf('B_update_d_update_fun_a_update_a_update_fun_fun$_type',type,
    'B_update_d_update_fun_a_update_a_update_fun_fun$': $tType ).

thf('B_update_c_update_fun_d_update_b_update_fun_fun$_type',type,
    'B_update_c_update_fun_d_update_b_update_fun_fun$': $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('D_a_prod_update_b_update_fun$_type',type,
    'D_a_prod_update_b_update_fun$': $tType ).

thf('C_update_a_c_prod_update_fun$_type',type,
    'C_update_a_c_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_bool_fun$_type',type,
    'C_d_prod_update_a_update_fun_bool_fun$': $tType ).

thf('C_update_c_d_prod_update_bool_fun_fun$_type',type,
    'C_update_c_d_prod_update_bool_fun_fun$': $tType ).

thf('C_d_prod_update$_type',type,
    'C_d_prod_update$': $tType ).

thf('D_update_b_b_prod_update_fun$_type',type,
    'D_update_b_b_prod_update_fun$': $tType ).

thf('C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$_type',type,
    'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

thf('D_update_a_d_prod_update_fun$_type',type,
    'D_update_a_d_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_a_update_prod_fun$_type',type,
    'C_d_prod_update_a_update_a_update_prod_fun$': $tType ).

thf('D_update_b_update_b_update_prod_fun$_type',type,
    'D_update_b_update_b_update_prod_fun$': $tType ).

thf('D_update_a_update_fun_d_update_b_update_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun$': $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('C_c_d_prod_prod_update_b_b_prod_update_fun$_type',type,
    'C_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

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

thf('B_update_d_update_bool_fun_fun$_type',type,
    'B_update_d_update_bool_fun_fun$': $tType ).

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

thf('A_update_a_update_prod$_type',type,
    'A_update_a_update_prod$': $tType ).

thf('D_d_prod_update_a_a_prod_update_fun$_type',type,
    'D_d_prod_update_a_a_prod_update_fun$': $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('D_update_d_update_prod_a_update_a_update_prod_fun$_type',type,
    'D_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

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

thf('A_update_a_update_fun_d_update_b_update_fun_fun$_type',type,
    'A_update_a_update_fun_d_update_b_update_fun_fun$': $tType ).

thf('C_update_d_update_fun$_type',type,
    'C_update_d_update_fun$': $tType ).

thf('C_d_prod_update_d_update_prod$_type',type,
    'C_d_prod_update_d_update_prod$': $tType ).

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

thf('B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$_type',type,
    'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$': $tType ).

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

thf('D_update_b_d_prod_update_fun$_type',type,
    'D_update_b_d_prod_update_fun$': $tType ).

thf('B_c_prod_update$_type',type,
    'B_c_prod_update$': $tType ).

thf('C_update_a_update_a_update_prod_fun$_type',type,
    'C_update_a_update_a_update_prod_fun$': $tType ).

thf('A_update_d_update_fun$_type',type,
    'A_update_d_update_fun$': $tType ).

thf('D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$_type',type,
    'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

thf('D_d_prod_update$_type',type,
    'D_d_prod_update$': $tType ).

thf('C_d_prod_update_bool_fun$_type',type,
    'C_d_prod_update_bool_fun$': $tType ).

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

thf('A_update_b_b_prod_update_fun$_type',type,
    'A_update_b_b_prod_update_fun$': $tType ).

thf('D_update_b_a_prod_update_fun$_type',type,
    'D_update_b_a_prod_update_fun$': $tType ).

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

thf('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$': $tType ).

thf('D_update_c_update_prod_b_update_b_update_prod_fun$_type',type,
    'D_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

thf('A_update_a_a_prod_update_fun$_type',type,
    'A_update_a_a_prod_update_fun$': $tType ).

thf('C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$_type',type,
    'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$': $tType ).

thf('B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$_type',type,
    'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$': $tType ).

thf('C_d_prod_update_set$_type',type,
    'C_d_prod_update_set$': $tType ).

thf('comp$s_decl',type,
    'comp$s': 'A_b_prod_update_b_update_fun$' > 'C_a_prod_update_a_b_prod_update_fun$' > 'C_a_prod_update_b_update_fun$' ).

thf('register$au_decl',type,
    'register$au': 'D_update_b_b_prod_update_fun$' > $o ).

thf('fun_app$cx_decl',type,
    'fun_app$cx': 'C_update_d_update_fun$' > 'C_update$' > 'D_update$' ).

thf('type_definition$j_decl',type,
    'type_definition$j': 'B_update_d_update_fun$' > 'D_update_b_update_fun$' > 'D_update_set$' > $o ).

thf('uvl$_decl',type,
    'uvl$': 'C_update_a_update_fun$' > 'C_update_a_a_prod_update_fun$' ).

thf('register$_decl',type,
    'register$': 'C_update_a_update_fun_bool_fun$' ).

thf('comp$as_decl',type,
    'comp$as': 'C_update_a_update_fun$' > 'D_update_c_update_fun$' > 'D_update_a_update_fun$' ).

thf('preregister$n_decl',type,
    'preregister$n': 'C_update_d_update_fun$' > $o ).

thf('fun_app$g_decl',type,
    'fun_app$g': 'B_update_a_b_prod_update_fun$' > 'B_update$' > 'A_b_prod_update$' ).

thf('register_tensor$p_decl',type,
    'register_tensor$p': 'A_update_b_update_fun$' > 'A_update_b_update_fun$' > 'A_a_prod_update_b_b_prod_update_fun$' ).

thf('pred_fun$_decl',type,
    'pred_fun$': 'C_update_bool_fun$' > 'B_update_bool_fun$' > 'C_update_b_update_fun$' > $o ).

thf('quotient$l_decl',type,
    'quotient$l': 'D_update_d_update_bool_fun_fun$' > 'D_update_a_update_fun$' > 'A_update_d_update_fun$' > 'D_update_a_update_bool_fun_fun$' > $o ).

thf('fun_app$dt_decl',type,
    'fun_app$dt': 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' > 'A_update_a_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('relcompp$f_decl',type,
    'relcompp$f': 'A_update_a_update_bool_fun_fun$' > 'A_update_c_update_bool_fun_fun$' > 'A_update_c_update_bool_fun_fun$' ).

thf('register$ai_decl',type,
    'register$ai': 'D_c_prod_update_b_update_fun$' > $o ).

thf('comp$cf_decl',type,
    'comp$cf': 'A_update_d_update_fun$' > 'B_update_a_update_fun$' > 'B_update_d_update_fun$' ).

thf('register_tensor$s_decl',type,
    'register_tensor$s': 'C_update_a_update_fun$' > 'D_update_a_update_fun$' > 'C_d_prod_update_a_a_prod_update_fun$' ).

thf('register$ao_decl',type,
    'register$ao': 'D_update_b_d_prod_update_fun$' > $o ).

thf('register$ay_decl',type,
    'register$ay': 'A_update_d_b_prod_update_fun$' > $o ).

thf('comp_update$_decl',type,
    'comp_update$': 'A_update$' > 'A_update_a_update_fun$' ).

thf('comp$be_decl',type,
    'comp$be': 'C_update_b_update_b_update_prod_fun$' > 'C_update_c_update_fun$' > 'C_update_b_update_b_update_prod_fun$' ).

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

thf('relcompp$h_decl',type,
    'relcompp$h': 'C_d_prod_update_a_update_bool_fun_fun$' > 'A_update_c_d_prod_update_bool_fun_fun$' > 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' ).

thf('compatible$j_decl',type,
    'compatible$j': 'B_update_b_update_fun$' > 'A_update_b_update_fun$' > $o ).

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

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

thf('comp$h_decl',type,
    'comp$h': 'D_update_b_update_fun$' > 'A_update_d_update_fun$' > 'A_update_b_update_fun$' ).

thf('register_pair$w_decl',type,
    'register_pair$w': 'A_update_b_a_prod_update_fun$' > 'C_update_b_a_prod_update_fun$' > 'A_c_prod_update_b_a_prod_update_fun$' ).

thf('comp$av_decl',type,
    'comp$av': 'A_update_a_update_fun_d_update_b_update_fun_fun$' > 'B_update_c_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_update_fun_d_update_b_update_fun_fun$' ).

thf('register_pair$e_decl',type,
    'register_pair$e': 'A_update_b_update_fun$' > 'B_update_b_update_fun$' > 'A_b_prod_update_b_update_fun$' ).

thf('map_prod$k_decl',type,
    'map_prod$k': 'C_d_prod_update_b_update_fun$' > 'D_update_b_update_fun$' > 'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' ).

thf('id_update$c_decl',type,
    'id_update$c': 'B_update$' ).

thf('register$q_decl',type,
    'register$q': 'A_c_prod_update_b_b_prod_update_fun$' > $o ).

thf('tensor_update$h_decl',type,
    'tensor_update$h': 'C_update$' > 'D_update$' > 'C_d_prod_update$' ).

thf('comp$bi_decl',type,
    'comp$bi': 'A_update_b_update_b_update_prod_fun$' > 'A_update_a_update_fun$' > 'A_update_b_update_b_update_prod_fun$' ).

thf('uur$_decl',type,
    'uur$': 'C_update_b_update_fun$' > 'C_update_d_b_prod_update_fun$' ).

thf('comp$w_decl',type,
    'comp$w': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_c_d_prod_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('convol$_decl',type,
    'convol$': 'C_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_update_b_update_b_update_prod_fun$' ).

thf('tensor_update$k_decl',type,
    'tensor_update$k': 'D_update$' > 'C_update$' > 'D_c_prod_update$' ).

thf('fun_app$bn_decl',type,
    'fun_app$bn': 'C_a_prod_update_a_b_prod_update_fun$' > 'C_a_prod_update$' > 'A_b_prod_update$' ).

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

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

thf('map_fun$d_decl',type,
    'map_fun$d': 'C_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ).

thf('fun_app$e_decl',type,
    'fun_app$e': 'C_update_a_c_prod_update_fun$' > 'C_update$' > 'A_c_prod_update$' ).

thf('fun_app$du_decl',type,
    'fun_app$du': 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_c_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('register$ak_decl',type,
    'register$ak': 'D_d_prod_update_b_update_fun$' > $o ).

thf('register_tensor$y_decl',type,
    'register_tensor$y': 'C_d_prod_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_d_prod_c_prod_update_b_b_prod_update_fun$' ).

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

thf('fun_app$a_decl',type,
    'fun_app$a': 'A_update_b_a_prod_update_fun$' > 'A_update$' > 'B_a_prod_update$' ).

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

thf('fun_app$bp_decl',type,
    'fun_app$bp': 'C_c_prod_update_b_a_prod_update_fun$' > 'C_c_prod_update$' > 'B_a_prod_update$' ).

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

thf('preregister$j_decl',type,
    'preregister$j': 'C_d_prod_update_a_update_fun_bool_fun$' ).

thf('comp$j_decl',type,
    'comp$j': 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' ).

thf('fun_app$br_decl',type,
    'fun_app$br': 'C_a_prod_update_b_b_prod_update_fun$' > 'C_a_prod_update$' > 'B_b_prod_update$' ).

thf('comp$an_decl',type,
    'comp$an': 'D_update_b_update_fun$' > 'C_update_d_update_fun$' > 'C_update_b_update_fun$' ).

thf('collect$e_decl',type,
    'collect$e': 'C_d_prod_update_a_update_fun_bool_fun$' > 'C_d_prod_update_a_update_fun_set$' ).

thf('comp$ao_decl',type,
    'comp$ao': 'D_update_b_update_fun$' > 'D_update_d_update_fun$' > 'D_update_b_update_fun$' ).

thf('image$b_decl',type,
    'image$b': 'C_update_a_update_fun$' > 'C_update_set$' > 'A_update_set$' ).

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

thf('fun_app$bm_decl',type,
    'fun_app$bm': 'C_c_prod_update_a_b_prod_update_fun$' > 'C_c_prod_update$' > 'A_b_prod_update$' ).

thf('register$ax_decl',type,
    'register$ax': 'C_update_d_b_prod_update_fun$' > $o ).

thf('register_tensor$a_decl',type,
    'register_tensor$a': 'C_update_a_update_fun$' > 'C_update_b_update_fun$' > 'C_c_prod_update_a_b_prod_update_fun$' ).

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

thf('comp$k_decl',type,
    'comp$k': 'A_a_prod_update_b_update_fun$' > 'D_d_prod_update_a_a_prod_update_fun$' > 'D_d_prod_update_b_update_fun$' ).

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

thf('register$ae_decl',type,
    'register$ae': 'C_d_prod_update_a_update_fun_bool_fun$' ).

thf('comp$bv_decl',type,
    'comp$bv': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' > 'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

thf('compatible$k_decl',type,
    'compatible$k': 'D_update_a_update_fun$' > 'A_update_a_update_fun$' > $o ).

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

thf('fun_app$aj_decl',type,
    'fun_app$aj': 'A_update_bool_fun$' > 'A_update$' > $o ).

thf('tensor_update$a_decl',type,
    'tensor_update$a': 'A_update$' > 'D_update_a_d_prod_update_fun$' ).

thf('fun_app$cy_decl',type,
    'fun_app$cy': 'C_d_prod_update_c_update_fun$' > 'C_d_prod_update$' > 'C_update$' ).

thf('fun_app$u_decl',type,
    'fun_app$u': 'C_update_a_update_fun$' > 'C_update$' > 'A_update$' ).

thf('uvm$_decl',type,
    'uvm$': 'C_update_b_update_fun$' > 'C_update_b_a_prod_update_fun$' ).

thf('register_tensor$q_decl',type,
    'register_tensor$q': 'D_update_b_update_fun$' > 'D_update_b_update_fun$' > 'D_d_prod_update_b_b_prod_update_fun$' ).

thf('compatible$z_decl',type,
    'compatible$z': 'C_update_a_update_fun$' > 'B_update_a_update_fun$' > $o ).

thf('map_fun$i_decl',type,
    'map_fun$i': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' ).

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

thf('separating$d_decl',type,
    'separating$d': 'B_itself$' > 'A_update_set$' > $o ).

thf('comp$m_decl',type,
    'comp$m': 'A_b_prod_update_b_update_fun$' > 'D_c_prod_update_a_b_prod_update_fun$' > 'D_c_prod_update_b_update_fun$' ).

thf('fun_app$bu_decl',type,
    'fun_app$bu': 'A_c_prod_update_b_b_prod_update_fun$' > 'A_c_prod_update$' > 'B_b_prod_update$' ).

thf('fun_app$bv_decl',type,
    'fun_app$bv': 'D_update_a_update_fun_d_update_b_update_fun_fun$' > 'D_update_a_update_fun$' > 'D_update_b_update_fun$' ).

thf('comp$i_decl',type,
    'comp$i': 'C_update_b_update_fun$' > 'A_update_c_update_fun$' > 'A_update_b_update_fun$' ).

thf('compatible$aa_decl',type,
    'compatible$aa': 'C_update_b_update_fun$' > 'B_update_b_update_fun$' > $o ).

thf('fun_app$v_decl',type,
    'fun_app$v': 'C_update_a_a_prod_update_fun$' > 'C_update$' > 'A_a_prod_update$' ).

thf('fun_app$bg_decl',type,
    'fun_app$bg': 'D_update_d_update_fun$' > 'D_update$' > 'D_update$' ).

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

thf('register$aw_decl',type,
    'register$aw': 'C_update_d_a_prod_update_fun$' > $o ).

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

thf('comp$x_decl',type,
    'comp$x': 'D_update_a_update_fun$' > 'D_update_d_update_fun$' > 'D_update_a_update_fun$' ).

thf('uvn$_decl',type,
    'uvn$': 'D_update_b_update_fun$' > 'D_update_b_a_prod_update_fun$' ).

thf('comp$bp_decl',type,
    'comp$bp': 'A_update_a_update_fun_d_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' ).

thf('map_fun$m_decl',type,
    'map_fun$m': 'D_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' ).

thf('compatible$as_decl',type,
    'compatible$as': 'A_update_b_a_prod_update_fun$' > 'C_update_b_a_prod_update_fun$' > $o ).

thf('register_tensor$h_decl',type,
    'register_tensor$h': 'A_update_b_update_fun$' > 'C_update_a_update_fun$' > 'A_c_prod_update_b_a_prod_update_fun$' ).

thf('separating$_decl',type,
    'separating$': 'A_itself$' > 'D_update_set$' > $o ).

thf('register_pair$_decl',type,
    'register_pair$': 'C_update_a_update_fun$' > 'D_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' ).

thf('register$bi_decl',type,
    'register$bi': 'A_update_a_a_prod_update_fun$' > $o ).

thf('fun_app$ch_decl',type,
    'fun_app$ch': 'C_a_prod_update_b_update_fun$' > 'C_a_prod_update$' > 'B_update$' ).

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

thf('fun_app$k_decl',type,
    'fun_app$k': 'C_update_a_update_fun_bool_fun$' > 'C_update_a_update_fun$' > $o ).

thf('register$ab_decl',type,
    'register$ab': 'A_b_prod_update_b_update_fun$' > $o ).

thf('register$x_decl',type,
    'register$x': 'C_update_c_update_fun$' > $o ).

thf('register_tensor$k_decl',type,
    'register_tensor$k': 'D_update_a_update_fun$' > 'C_update_a_update_fun$' > 'D_c_prod_update_a_a_prod_update_fun$' ).

thf('fun_app$bo_decl',type,
    'fun_app$bo': 'C_d_prod_update_a_b_prod_update_fun$' > 'C_d_prod_update$' > 'A_b_prod_update$' ).

thf('fun_app$bf_decl',type,
    'fun_app$bf': '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('fun_app$cp_decl',type,
    'fun_app$cp': 'B_update_d_update_fun_a_update_a_update_fun_fun$' > 'B_update_d_update_fun$' > 'A_update_a_update_fun$' ).

thf('fun_app$bq_decl',type,
    'fun_app$bq': 'C_c_prod_update_b_b_prod_update_fun$' > 'C_c_prod_update$' > 'B_b_prod_update$' ).

thf('register$o_decl',type,
    'register$o': 'C_d_prod_update_b_b_prod_update_fun$' > $o ).

thf('relcompp$l_decl',type,
    'relcompp$l': 'A_update_a_update_bool_fun_fun$' > 'A_update_d_update_bool_fun_fun$' > 'A_update_d_update_bool_fun_fun$' ).

thf('fun_app$dw_decl',type,
    'fun_app$dw': 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_d_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

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

thf('fun_app$ba_decl',type,
    'fun_app$ba': 'A_update_d_c_prod_update_fun$' > 'A_update$' > 'D_c_prod_update$' ).

thf('uui$_decl',type,
    'uui$': 'D_update_b_update_fun$' > 'D_update_b_d_prod_update_fun$' ).

thf('fun_app$aa_decl',type,
    'fun_app$aa': 'A_update_d_update_fun$' > 'A_update$' > 'D_update$' ).

thf('preregister$i_decl',type,
    'preregister$i': 'D_update_a_update_fun_bool_fun$' ).

thf('fun_app$cg_decl',type,
    'fun_app$cg': 'C_c_prod_update_b_update_fun$' > 'C_c_prod_update$' > 'B_update$' ).

thf('fun_app$ck_decl',type,
    'fun_app$ck': 'D_c_prod_update_b_update_fun$' > 'D_c_prod_update$' > 'B_update$' ).

thf('register$ac_decl',type,
    'register$ac': 'A_a_prod_update_b_update_fun$' > $o ).

thf('convol$f_decl',type,
    'convol$f': 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_a_update_a_update_prod_fun$' ).

thf('register_tensor$ad_decl',type,
    'register_tensor$ad': 'A_update_c_update_fun$' > 'A_update_c_update_fun$' > 'A_a_prod_update_c_c_prod_update_fun$' ).

thf('fun_app$ca_decl',type,
    'fun_app$ca': 'B_a_prod_update_b_update_fun$' > 'B_a_prod_update$' > 'B_update$' ).

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

thf('convol$b_decl',type,
    'convol$b': 'C_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_update_a_update_a_update_prod_fun$' ).

thf('comp_update$d_decl',type,
    'comp_update$d': 'B_b_prod_update$' > 'B_b_prod_update$' > 'B_b_prod_update$' ).

thf('register_tensor$v_decl',type,
    'register_tensor$v': 'D_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'D_c_d_prod_prod_update_a_a_prod_update_fun$' ).

thf('register_pair$f_decl',type,
    'register_pair$f': 'D_update_b_update_fun$' > 'A_update_b_update_fun$' > 'D_a_prod_update_b_update_fun$' ).

thf('uvh$_decl',type,
    'uvh$': 'D_update_a_update_fun$' > 'D_update_b_a_prod_update_fun$' ).

thf('map_fun$l_decl',type,
    'map_fun$l': 'D_update_b_update_fun$' > 'C_update_b_update_fun$' > 'B_update_c_update_fun_d_update_b_update_fun_fun$' ).

thf('comp$bz_decl',type,
    'comp$bz': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$' > 'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' ).

thf('fun_app$s_decl',type,
    'fun_app$s': 'C_update_b_a_prod_update_fun$' > 'C_update$' > 'B_a_prod_update$' ).

thf('register_pair$a_decl',type,
    'register_pair$a': 'C_update_b_update_fun$' > 'D_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('quotient$m_decl',type,
    'quotient$m': 'D_update_d_update_bool_fun_fun$' > 'D_update_b_update_fun$' > 'B_update_d_update_fun$' > 'D_update_b_update_bool_fun_fun$' > $o ).

thf('fun_app$bh_decl',type,
    'fun_app$bh': 'D_update_c_update_fun$' > 'D_update$' > 'C_update$' ).

thf('type_definition$f_decl',type,
    'type_definition$f': 'A_update_c_update_fun$' > 'C_update_a_update_fun$' > 'C_update_set$' > $o ).

thf('map_prod$h_decl',type,
    'map_prod$h': 'C_d_prod_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$' ).

thf('fun_app$cj_decl',type,
    'fun_app$cj': 'A_a_prod_update_b_update_fun$' > 'A_a_prod_update$' > 'B_update$' ).

thf('register_tensor$d_decl',type,
    'register_tensor$d': 'C_update_b_update_fun$' > 'C_update_a_update_fun$' > 'C_c_prod_update_b_a_prod_update_fun$' ).

thf('map_fun$g_decl',type,
    'map_fun$g': 'C_d_prod_update_a_update_fun$' > 'A_update_b_update_fun$' > 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('fun_app$dv_decl',type,
    'fun_app$dv': 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('uvc$_decl',type,
    'uvc$': 'A_update_a_c_prod_update_fun$' ).

thf('register_tensor$t_decl',type,
    'register_tensor$t': 'C_d_prod_update_a_update_fun$' > 'D_update_a_update_fun$' > 'C_d_prod_d_prod_update_a_a_prod_update_fun$' ).

thf('fcomp$e_decl',type,
    'fcomp$e': 'C_update_a_update_fun$' > 'A_update_b_update_fun$' > 'C_update_b_update_fun$' ).

thf('comp$bb_decl',type,
    'comp$bb': 'C_update_b_update_fun$' > 'C_d_prod_update_c_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('register_tensor$b_decl',type,
    'register_tensor$b': 'C_update_a_update_fun$' > 'A_update_b_update_fun$' > 'C_a_prod_update_a_b_prod_update_fun$' ).

thf('register_pair$h_decl',type,
    'register_pair$h': 'C_update_b_update_fun$' > 'A_update_b_update_fun$' > 'C_a_prod_update_b_update_fun$' ).

thf('compatible$o_decl',type,
    'compatible$o': 'A_update_b_update_fun$' > 'D_update_b_update_fun$' > $o ).

thf('map_fun$k_decl',type,
    'map_fun$k': 'D_update_a_update_fun$' > 'A_update_b_update_fun$' > 'A_update_a_update_fun_d_update_b_update_fun_fun$' ).

thf('comp_update$j_decl',type,
    'comp_update$j': 'D_c_prod_update$' > 'D_c_prod_update$' > 'D_c_prod_update$' ).

thf('comp$cg_decl',type,
    'comp$cg': 'D_update_b_update_fun$' > 'B_update_d_update_fun$' > 'B_update_b_update_fun$' ).

thf('comp$bt_decl',type,
    'comp$bt': 'B_update_bool_fun$' > 'A_update_b_update_fun$' > 'A_update_bool_fun$' ).

thf('compatible$af_decl',type,
    'compatible$af': 'C_update_d_update_fun$' > 'D_update_d_update_fun$' > $o ).

thf('comp$r_decl',type,
    'comp$r': 'A_b_prod_update_b_update_fun$' > 'C_c_prod_update_a_b_prod_update_fun$' > 'C_c_prod_update_b_update_fun$' ).

thf('register_tensor$l_decl',type,
    'register_tensor$l': 'D_update_a_update_fun$' > 'C_update_b_update_fun$' > 'D_c_prod_update_a_b_prod_update_fun$' ).

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

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

thf('fun_app$cc_decl',type,
    'fun_app$cc': 'A_d_prod_update_a_update_fun$' > 'A_d_prod_update$' > 'A_update$' ).

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

thf('fun_app$cd_decl',type,
    'fun_app$cd': 'A_d_prod_update_b_update_fun$' > 'A_d_prod_update$' > 'B_update$' ).

thf('fun_app$f_decl',type,
    'fun_app$f': 'A_update_a_b_prod_update_fun$' > 'A_update$' > 'A_b_prod_update$' ).

thf('convol$c_decl',type,
    'convol$c': 'D_update_a_update_fun$' > 'D_update_a_update_fun$' > 'D_update_a_update_a_update_prod_fun$' ).

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

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

thf('comp_update$l_decl',type,
    'comp_update$l': 'C_a_prod_update$' > 'C_a_prod_update$' > 'C_a_prod_update$' ).

thf('fun_app$m_decl',type,
    'fun_app$m': 'D_update_b_update_fun$' > 'D_update$' > 'B_update$' ).

thf('member$c_decl',type,
    'member$c': 'A_update$' > 'A_update_set$' > $o ).

thf('register_pair$n_decl',type,
    'register_pair$n': 'B_update_a_update_fun$' > 'A_update_a_update_fun$' > 'B_a_prod_update$' > 'A_update$' ).

thf('fun_app$cz_decl',type,
    'fun_app$cz': 'C_update_c_d_prod_update_fun$' > 'C_update$' > 'C_d_prod_update$' ).

thf('register$c_decl',type,
    'register$c': 'C_update_b_update_fun$' > $o ).

thf('comp$bq_decl',type,
    'comp$bq': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_update_a_update_a_update_prod_fun$' > 'C_update_b_update_b_update_prod_fun$' ).

thf('compatible$c_decl',type,
    'compatible$c': 'A_update_b_update_fun$' > 'A_update_b_update_fun$' > $o ).

thf('register$u_decl',type,
    'register$u': 'C_d_prod_update_b_update_fun$' > $o ).

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

thf('fun_app$cb_decl',type,
    'fun_app$cb': 'B_update_c_update_fun$' > 'B_update$' > 'C_update$' ).

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

thf('map_prod$_decl',type,
    'map_prod$': 'A_update_b_update_fun$' > 'A_update_b_update_fun$' > 'A_update_a_update_prod_b_update_b_update_prod_fun$' ).

thf('register$y_decl',type,
    'register$y': 'A_d_prod_update_a_update_fun$' > $o ).

thf('comp$ca_decl',type,
    'comp$ca': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'D_update_c_update_prod_a_update_a_update_prod_fun$' > 'D_update_c_update_prod_b_update_b_update_prod_fun$' ).

thf('uus$_decl',type,
    'uus$': 'A_update_b_update_fun$' > 'A_update_d_b_prod_update_fun$' ).

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

thf('register$al_decl',type,
    'register$al': 'C_update_d_update_fun$' > $o ).

thf('comp$aa_decl',type,
    'comp$aa': 'A_a_prod_update_b_b_prod_update_fun$' > 'D_d_prod_update_a_a_prod_update_fun$' > 'D_d_prod_update_b_b_prod_update_fun$' ).

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

thf('comp$e_decl',type,
    'comp$e': 'C_update_a_update_fun$' > 'C_update_c_update_fun$' > 'C_update_a_update_fun$' ).

thf('fun_app$au_decl',type,
    'fun_app$au': 'D_update_a_update_fun$' > 'D_update$' > 'A_update$' ).

thf('fun_app$bz_decl',type,
    'fun_app$bz': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update$' > 'B_update$' ).

thf('register$k_decl',type,
    'register$k': 'C_d_prod_update_a_b_prod_update_fun$' > $o ).

thf('register_tensor$o_decl',type,
    'register_tensor$o': 'A_update_b_update_fun$' > 'D_update_a_update_fun$' > 'A_d_prod_update_b_a_prod_update_fun$' ).

thf('register$s_decl',type,
    'register$s': 'D_update_c_update_fun$' > $o ).

thf('comp$bx_decl',type,
    'comp$bx': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$' > 'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' ).

thf('comp$ak_decl',type,
    'comp$ak': 'C_update_a_update_fun$' > 'A_update_c_update_fun$' > 'A_update_a_update_fun$' ).

thf('comp$at_decl',type,
    'comp$at': 'A_update_a_update_fun$' > 'D_update_a_update_fun$' > 'D_update_a_update_fun$' ).

thf('comp$ai_decl',type,
    'comp$ai': 'A_a_prod_update_b_b_prod_update_fun$' > 'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$' > 'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('comp$d_decl',type,
    'comp$d': 'B_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_update_b_update_fun$' ).

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

thf('comp$u_decl',type,
    'comp$u': 'B_a_prod_update_b_update_fun$' > 'A_d_prod_update_b_a_prod_update_fun$' > 'A_d_prod_update_b_update_fun$' ).

thf('compatible$t_decl',type,
    'compatible$t': 'B_update_b_update_fun$' > 'C_update_b_update_fun$' > $o ).

thf('register_pair$d_decl',type,
    'register_pair$d': 'D_update_b_update_fun$' > 'C_update_b_update_fun$' > 'D_c_prod_update_b_update_fun$' ).

thf('comp$aj_decl',type,
    'comp$aj': 'C_c_prod_update_a_a_prod_update_fun$' > 'A_a_prod_update_c_c_prod_update_fun$' > 'A_a_prod_update_a_a_prod_update_fun$' ).

thf('comp$aw_decl',type,
    'comp$aw': 'A_update_a_update_fun_c_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ).

thf('uux$_decl',type,
    'uux$': 'A_update_c_update_fun$' > 'A_update_d_c_prod_update_fun$' ).

thf('fun_app$az_decl',type,
    'fun_app$az': 'B_update_a_update_fun$' > 'B_update$' > 'A_update$' ).

thf('register$bd_decl',type,
    'register$bd': 'A_update_d_a_prod_update_fun$' > $o ).

thf('uvq$_decl',type,
    'uvq$': 'A_update_b_update_fun$' > 'A_update_a_b_prod_update_fun$' ).

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

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

thf('comp$bl_decl',type,
    'comp$bl': 'A_update_b_update_b_update_prod_fun$' > 'D_update_a_update_fun$' > 'D_update_b_update_b_update_prod_fun$' ).

thf('compatible$_decl',type,
    'compatible$': 'C_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$' ).

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

thf('map_fun$h_decl',type,
    'map_fun$h': 'C_d_prod_update_b_update_fun$' > 'C_update_b_update_fun$' > 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('register$v_decl',type,
    'register$v': 'A_update_d_update_fun$' > $o ).

thf('fun_app$c_decl',type,
    'fun_app$c': 'D_update_a_d_prod_update_fun$' > 'D_update$' > 'A_d_prod_update$' ).

thf('fun_app$ce_decl',type,
    'fun_app$ce': 'C_d_prod_update_c_d_prod_update_fun$' > 'C_d_prod_update$' > 'C_d_prod_update$' ).

thf('compatible$s_decl',type,
    'compatible$s': 'B_update_b_update_fun$' > 'D_update_b_update_fun$' > $o ).

thf('fun_app$cr_decl',type,
    'fun_app$cr': 'B_update_c_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_update_fun$' > 'A_update_a_update_fun$' ).

thf('register_tensor$f_decl',type,
    'register_tensor$f': 'C_update_b_update_fun$' > 'A_update_b_update_fun$' > 'C_a_prod_update_b_b_prod_update_fun$' ).

thf('fun_app$dy_decl',type,
    'fun_app$dy': 'B_update_set_b_update_fun$' > 'B_update_set$' > 'B_update$' ).

thf('comp$bk_decl',type,
    'comp$bk': 'A_update_b_update_b_update_prod_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

thf('fun_app$aw_decl',type,
    'fun_app$aw': 'C_update_d_a_prod_update_fun$' > 'C_update$' > 'D_a_prod_update$' ).

thf('uve$_decl',type,
    'uve$': 'A_update_a_a_prod_update_fun$' ).

thf('separating$a_decl',type,
    'separating$a': 'B_itself$' > 'C_update_set$' > $o ).

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

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

thf('comp$ac_decl',type,
    'comp$ac': 'A_a_prod_update_b_b_prod_update_fun$' > 'C_d_prod_update_a_a_prod_update_fun$' > 'C_d_prod_update_b_b_prod_update_fun$' ).

thf('register_pair$b_decl',type,
    'register_pair$b': 'A_update_b_update_fun$' > 'A_update_b_update_fun$' > 'A_a_prod_update_b_update_fun$' ).

thf('fun_app$cl_decl',type,
    'fun_app$cl': 'D_a_prod_update_b_update_fun$' > 'D_a_prod_update$' > 'B_update$' ).

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

thf('comp$t_decl',type,
    'comp$t': 'B_a_prod_update_b_update_fun$' > 'C_c_prod_update_b_a_prod_update_fun$' > 'C_c_prod_update_b_update_fun$' ).

thf('register$ag_decl',type,
    'register$ag': 'C_c_prod_update_b_update_fun$' > $o ).

thf('fun_app$bl_decl',type,
    'fun_app$bl': 'C_c_prod_update_a_a_prod_update_fun$' > 'C_c_prod_update$' > 'A_a_prod_update$' ).

thf('fun_app$t_decl',type,
    'fun_app$t': 'C_update_a_b_prod_update_fun$' > 'C_update$' > 'A_b_prod_update$' ).

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

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

thf('comp_update$m_decl',type,
    'comp_update$m': 'C_d_prod_update$' > 'C_d_prod_update_c_d_prod_update_fun$' ).

thf('comp$ap_decl',type,
    'comp$ap': 'B_update_a_update_fun$' > 'D_update_b_update_fun$' > 'D_update_a_update_fun$' ).

thf('register_pair$j_decl',type,
    'register_pair$j': 'A_update_b_update_fun$' > 'D_update_b_update_fun$' > 'A_d_prod_update_b_update_fun$' ).

thf('register$aa_decl',type,
    'register$aa': 'A_c_prod_update_b_update_fun$' > $o ).

thf('quotient$g_decl',type,
    'quotient$g': 'C_update_c_update_bool_fun_fun$' > 'C_update_a_update_fun$' > 'A_update_c_update_fun$' > 'C_update_a_update_bool_fun_fun$' > $o ).

thf('comp$z_decl',type,
    'comp$z': 'C_update_b_update_fun$' > 'B_update_c_update_fun$' > 'B_update_b_update_fun$' ).

thf('convol$d_decl',type,
    'convol$d': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

thf('compatible$aj_decl',type,
    'compatible$aj': 'C_update_b_a_prod_update_fun$' > 'D_update_b_a_prod_update_fun$' > $o ).

thf('comp$bh_decl',type,
    'comp$bh': 'C_update_a_update_a_update_prod_fun$' > 'C_update_c_update_fun$' > 'C_update_a_update_a_update_prod_fun$' ).

thf('fun_app$bw_decl',type,
    'fun_app$bw': 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' > 'A_update_b_update_fun$' > 'D_update_a_update_fun_d_update_b_update_fun_fun$' ).

thf('compatible$ad_decl',type,
    'compatible$ad': 'D_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$' ).

thf('tensor_update$m_decl',type,
    'tensor_update$m': 'C_update$' > 'A_update$' > 'C_a_prod_update$' ).

thf('conversep$a_decl',type,
    'conversep$a': 'C_update_a_update_bool_fun_fun$' > 'A_update_c_update_bool_fun_fun$' ).

thf('collect$f_decl',type,
    'collect$f': 'C_update_a_update_fun_bool_fun$' > 'C_update_a_update_fun_set$' ).

thf('fun_app$x_decl',type,
    'fun_app$x': 'B_update_b_update_fun$' > 'B_update$' > 'B_update$' ).

thf('comp$br_decl',type,
    'comp$br': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_d_prod_update_a_update_a_update_prod_fun$' > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

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

thf('id_update$_decl',type,
    'id_update$': 'A_update$' ).

thf('convol$a_decl',type,
    'convol$a': 'A_update_b_update_fun$' > 'A_update_b_update_fun$' > 'A_update_b_update_b_update_prod_fun$' ).

thf('compatible$ag_decl',type,
    'compatible$ag': 'C_update_a_a_prod_update_fun$' > 'C_update_a_a_prod_update_fun$' > $o ).

thf('pred_fun$d_decl',type,
    'pred_fun$d': 'D_update_bool_fun$' > 'B_update_bool_fun$' > 'D_update_b_update_fun$' > $o ).

thf('pred_fun$e_decl',type,
    'pred_fun$e': 'D_update_bool_fun$' > 'A_update_bool_fun$' > 'D_update_a_update_fun_bool_fun$' ).

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

thf('relcompp$e_decl',type,
    'relcompp$e': 'C_update_a_update_bool_fun_fun$' > 'A_update_c_update_bool_fun_fun$' > 'C_update_c_update_bool_fun_fun$' ).

thf('map_prod$l_decl',type,
    'map_prod$l': 'C_d_prod_update_a_update_fun$' > 'D_update_a_update_fun$' > 'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$' ).

thf('register_pair$g_decl',type,
    'register_pair$g': 'C_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_c_prod_update_b_update_fun$' ).

thf('fun_app$_decl',type,
    'fun_app$': 'B_update_b_a_prod_update_fun$' > 'B_update$' > 'B_a_prod_update$' ).

thf('comp$bf_decl',type,
    'comp$bf': 'C_update_b_update_b_update_prod_fun$' > 'A_update_c_update_fun$' > 'A_update_b_update_b_update_prod_fun$' ).

thf('map_fun$a_decl',type,
    'map_fun$a': 'A_update_b_update_fun$' > 'C_update_a_update_fun$' > 'B_update_c_update_fun_a_update_a_update_fun_fun$' ).

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

thf('compatible$m_decl',type,
    'compatible$m': 'C_update_a_update_fun$' > 'C_update_a_update_fun_bool_fun$' ).

thf('comp$ae_decl',type,
    'comp$ae': 'A_a_prod_update_b_b_prod_update_fun$' > 'C_d_prod_d_prod_update_a_a_prod_update_fun$' > 'C_d_prod_d_prod_update_b_b_prod_update_fun$' ).

thf('fun_app$bc_decl',type,
    'fun_app$bc': 'A_update_d_a_prod_update_fun$' > 'A_update$' > 'D_a_prod_update$' ).

thf('relcompp$g_decl',type,
    'relcompp$g': 'C_update_a_update_bool_fun_fun$' > 'A_update_b_update_bool_fun_fun$' > 'C_update_b_update_bool_fun_fun$' ).

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

thf('map_fun$e_decl',type,
    'map_fun$e': 'A_update_b_update_fun$' > 'D_update_a_update_fun$' > 'B_update_d_update_fun_a_update_a_update_fun_fun$' ).

thf('uuf$_decl',type,
    'uuf$': 'C_update_a_update_fun_set$' > 'C_update_a_update_fun_bool_fun$' ).

thf('register_tensor$r_decl',type,
    'register_tensor$r': 'D_update_b_update_fun$' > 'C_update_b_update_fun$' > 'D_c_prod_update_b_b_prod_update_fun$' ).

thf('compatible$y_decl',type,
    'compatible$y': 'A_update_c_update_fun$' > 'D_update_c_update_fun$' > $o ).

thf('image$f_decl',type,
    'image$f': 'A_update_b_update_fun$' > 'A_update_set$' > 'B_update_set$' ).

thf('conversep$c_decl',type,
    'conversep$c': 'D_update_a_update_bool_fun_fun$' > 'A_update_d_update_bool_fun_fun$' ).

thf('register$aj_decl',type,
    'register$aj': 'D_a_prod_update_b_update_fun$' > $o ).

thf('uvd$_decl',type,
    'uvd$': 'A_update_a_b_prod_update_fun$' ).

thf('fun_app$n_decl',type,
    'fun_app$n': 'D_update_b_b_prod_update_fun$' > 'D_update$' > 'B_b_prod_update$' ).

thf('fun_app$cq_decl',type,
    'fun_app$cq': 'B_update_c_update_fun_d_update_b_update_fun_fun$' > 'B_update_c_update_fun$' > 'D_update_b_update_fun$' ).

thf('h$_decl',type,
    'h$': 'D_update_a_update_fun$' ).

thf('compatible$aq_decl',type,
    'compatible$aq': 'C_update_a_b_prod_update_fun$' > 'A_update_a_b_prod_update_fun$' > $o ).

thf('register_tensor$ac_decl',type,
    'register_tensor$ac': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('register$az_decl',type,
    'register$az': 'D_update_d_b_prod_update_fun$' > $o ).

thf('comp$az_decl',type,
    'comp$az': 'C_d_prod_update_a_update_fun$' > 'C_update_c_d_prod_update_fun$' > 'C_update_a_update_fun$' ).

thf('compatible$f_decl',type,
    'compatible$f': 'C_update_b_update_fun$' > 'D_update_b_update_fun$' > $o ).

thf('comp$y_decl',type,
    'comp$y': 'D_update_a_update_fun$' > 'C_update_d_update_fun$' > 'C_update_a_update_fun$' ).

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

thf('register_tensor$c_decl',type,
    'register_tensor$c': 'C_update_a_update_fun$' > 'D_update_b_update_fun$' > 'C_d_prod_update_a_b_prod_update_fun$' ).

thf('tensor_update$b_decl',type,
    'tensor_update$b': 'A_update$' > 'C_update_a_c_prod_update_fun$' ).

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

thf('comp$bs_decl',type,
    'comp$bs': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'D_update_a_update_a_update_prod_fun$' > 'D_update_b_update_b_update_prod_fun$' ).

thf('register_pair$r_decl',type,
    'register_pair$r': 'A_update_c_update_fun$' > 'D_update_c_update_fun$' > 'A_d_prod_update$' > 'C_update$' ).

thf('fun_app$bs_decl',type,
    'fun_app$bs': 'C_d_prod_update_b_b_prod_update_fun$' > 'C_d_prod_update$' > 'B_b_prod_update$' ).

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

thf('comp$bo_decl',type,
    'comp$bo': 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_d_update_fun_a_update_a_update_fun_fun$' > 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('map_prod$p_decl',type,
    'map_prod$p': 'D_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ).

thf('comp_update$b_decl',type,
    'comp_update$b': 'D_update$' > 'D_update_d_update_fun$' ).

thf('image$e_decl',type,
    'image$e': 'D_update_b_update_fun$' > 'D_update_set$' > 'B_update_set$' ).

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

thf('register_tensor$_decl',type,
    'register_tensor$': 'C_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_c_prod_update_a_a_prod_update_fun$' ).

thf('uvu$_decl',type,
    'uvu$': 'C_d_prod_update_bool_fun$' ).

thf('comp$bc_decl',type,
    'comp$bc': 'C_update_a_update_fun$' > 'C_d_prod_update_c_update_fun$' > 'C_d_prod_update_a_update_fun$' ).

thf('fun_app$ae_decl',type,
    'fun_app$ae': 'A_update_b_update_fun$' > 'A_update$' > 'B_update$' ).

thf('image$d_decl',type,
    'image$d': 'C_d_prod_update_b_update_fun$' > 'C_d_prod_update_set$' > 'B_update_set$' ).

thf('comp$bj_decl',type,
    'comp$bj': 'A_update_b_update_b_update_prod_fun$' > 'C_update_a_update_fun$' > 'C_update_b_update_b_update_prod_fun$' ).

thf('register_tensor$aa_decl',type,
    'register_tensor$aa': 'C_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'C_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('register$bc_decl',type,
    'register$bc': 'A_update_d_c_prod_update_fun$' > $o ).

thf('type_definition$h_decl',type,
    'type_definition$h': 'A_update_d_update_fun$' > 'D_update_a_update_fun$' > 'D_update_set$' > $o ).

thf('fun_app$ac_decl',type,
    'fun_app$ac': 'A_update_c_update_fun$' > 'A_update$' > 'C_update$' ).

thf('fun_app$cs_decl',type,
    'fun_app$cs': 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun$' > 'C_update_b_update_fun$' ).

thf('preregister$m_decl',type,
    'preregister$m': 'D_update_d_update_fun$' > $o ).

thf('compatible$ae_decl',type,
    'compatible$ae': 'C_update_c_update_fun$' > 'D_update_c_update_fun$' > $o ).

thf('comp$bd_decl',type,
    'comp$bd': 'A_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' ).

thf('register_pair$l_decl',type,
    'register_pair$l': 'A_update_b_update_fun$' > 'C_update_b_update_fun$' > 'A_c_prod_update_b_update_fun$' ).

thf('map_fun$c_decl',type,
    'map_fun$c': 'A_update_b_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' ).

thf('register_pair$p_decl',type,
    'register_pair$p': 'B_update_c_update_fun$' > 'A_update_c_update_fun$' > 'B_a_prod_update$' > 'C_update$' ).

thf('tensor_update$l_decl',type,
    'tensor_update$l': 'C_update$' > 'C_update$' > 'C_c_prod_update$' ).

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

thf('comp$cd_decl',type,
    'comp$cd': 'A_update_c_update_fun$' > 'B_update_a_update_fun$' > 'B_update_c_update_fun$' ).

thf('uvo$_decl',type,
    'uvo$': 'C_update_b_update_fun$' > 'C_update_a_b_prod_update_fun$' ).

thf('register$ar_decl',type,
    'register$ar': 'A_update_c_d_prod_update_fun$' > $o ).

thf('register$bg_decl',type,
    'register$bg': 'C_update_a_c_prod_update_fun$' > $o ).

thf('comp$ad_decl',type,
    'comp$ad': '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('map_fun$_decl',type,
    'map_fun$': 'C_update_a_update_fun$' > 'A_update_b_update_fun$' > 'A_update_a_update_fun_c_update_b_update_fun_fun$' ).

thf('register_pair$c_decl',type,
    'register_pair$c': 'D_update_b_update_fun$' > 'D_update_b_update_fun$' > 'D_d_prod_update_b_update_fun$' ).

thf('image$c_decl',type,
    'image$c': 'C_update_b_update_fun$' > 'C_update_set$' > 'B_update_set$' ).

thf('comp$l_decl',type,
    'comp$l': 'A_a_prod_update_b_update_fun$' > 'D_c_prod_update_a_a_prod_update_fun$' > 'D_c_prod_update_b_update_fun$' ).

thf('compatible$w_decl',type,
    'compatible$w': 'B_update_c_update_fun$' > 'A_update_c_update_fun$' > $o ).

thf('fun_app$q_decl',type,
    'fun_app$q': 'C_update_b_update_fun$' > 'C_update$' > 'B_update$' ).

thf('register_tensor$i_decl',type,
    'register_tensor$i': 'A_update_b_update_fun$' > 'C_update_b_update_fun$' > 'A_c_prod_update_b_b_prod_update_fun$' ).

thf('register_tensor$g_decl',type,
    'register_tensor$g': 'C_update_b_update_fun$' > 'D_update_b_update_fun$' > 'C_d_prod_update_b_b_prod_update_fun$' ).

thf('map_prod$n_decl',type,
    'map_prod$n': 'D_update_a_update_fun$' > 'C_update_a_update_fun$' > 'D_update_c_update_prod_a_update_a_update_prod_fun$' ).

thf('register$an_decl',type,
    'register$an': 'A_update_b_d_prod_update_fun$' > $o ).

thf('map_fun$j_decl',type,
    'map_fun$j': 'C_d_prod_update_b_update_fun$' > 'D_update_b_update_fun$' > 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' ).

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

thf('register_pair$s_decl',type,
    'register_pair$s': 'C_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_c_prod_update_a_update_fun$' ).

thf('compatible$d_decl',type,
    'compatible$d': 'A_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$' ).

thf('map_fun$f_decl',type,
    'map_fun$f': 'C_update_b_update_fun$' > 'D_update_b_update_fun$' > 'B_update_d_update_fun_c_update_b_update_fun_fun$' ).

thf('register_tensor$ae_decl',type,
    'register_tensor$ae': 'A_update_a_update_fun$' > 'A_update_a_update_fun$' > 'A_a_prod_update_a_a_prod_update_fun$' ).

thf('fun_app$cu_decl',type,
    'fun_app$cu': 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_d_prod_update_fun$' > 'A_update_a_update_fun$' ).

thf('fun_app$h_decl',type,
    'fun_app$h': 'A_update_a_a_prod_update_fun$' > 'A_update$' > 'A_a_prod_update$' ).

thf('comp$cb_decl',type,
    'comp$cb': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' > 'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

thf('comp_update$c_decl',type,
    'comp_update$c': 'C_update$' > 'C_update_c_update_fun$' ).

thf('comp$bm_decl',type,
    'comp$bm': 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_c_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('register_tensor$j_decl',type,
    'register_tensor$j': 'D_update_a_update_fun$' > 'D_update_a_update_fun$' > 'D_d_prod_update_a_a_prod_update_fun$' ).

thf('fun_app$bd_decl',type,
    'fun_app$bd': 'A_update_a_update_fun$' > 'A_update$' > 'A_update$' ).

thf('comp$bw_decl',type,
    'comp$bw': 'A_update_a_update_prod_b_update_b_update_prod_fun$' > 'C_update_d_update_prod_a_update_a_update_prod_fun$' > 'C_update_d_update_prod_b_update_b_update_prod_fun$' ).

thf('comp$_decl',type,
    'comp$': 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ).

thf('comp$ag_decl',type,
    'comp$ag': 'A_a_prod_update_b_b_prod_update_fun$' > 'C_d_prod_c_prod_update_a_a_prod_update_fun$' > 'C_d_prod_c_prod_update_b_b_prod_update_fun$' ).

thf('fun_app$cv_decl',type,
    'fun_app$cv': 'B_update_d_update_fun_c_update_b_update_fun_fun$' > 'B_update_d_update_fun$' > 'C_update_b_update_fun$' ).

thf('uuy$_decl',type,
    'uuy$': 'A_update_a_update_fun$' > 'A_update_d_a_prod_update_fun$' ).

thf('map_prod$f_decl',type,
    'map_prod$f': 'C_update_a_update_fun$' > 'D_update_a_update_fun$' > 'C_update_d_update_prod_a_update_a_update_prod_fun$' ).

thf('uul$_decl',type,
    'uul$': 'A_update_c_update_fun$' > 'A_update_c_d_prod_update_fun$' ).

thf('pred_fun$b_decl',type,
    'pred_fun$b': 'C_d_prod_update_bool_fun$' > 'B_update_bool_fun$' > 'C_d_prod_update_b_update_fun$' > $o ).

thf('type_definition$c_decl',type,
    'type_definition$c': 'C_update_d_update_fun$' > 'D_update_c_update_fun$' > 'D_update_set$' > $o ).

thf('type_definition$i_decl',type,
    'type_definition$i': 'B_update_c_update_fun$' > 'C_update_b_update_fun$' > 'C_update_set$' > $o ).

thf('comp$ax_decl',type,
    'comp$ax': 'A_update_a_update_fun_c_update_b_update_fun_fun$' > 'B_update_d_update_fun_a_update_a_update_fun_fun$' > 'B_update_d_update_fun_c_update_b_update_fun_fun$' ).

thf('map_prod$d_decl',type,
    'map_prod$d': 'C_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ).

thf('comp$af_decl',type,
    'comp$af': 'A_a_prod_update_b_b_prod_update_fun$' > 'D_c_d_prod_prod_update_a_a_prod_update_fun$' > 'D_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('uug$_decl',type,
    'uug$': 'C_update_b_update_fun$' > 'C_update_b_d_prod_update_fun$' ).

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

thf('compatible$g_decl',type,
    'compatible$g': 'D_update_a_update_fun$' > 'C_update_a_update_fun_bool_fun$' ).

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

thf('separating$b_decl',type,
    'separating$b': 'A_itself$' > 'C_update_set$' > $o ).

thf('tensor_update$j_decl',type,
    'tensor_update$j': 'D_update$' > 'A_update$' > 'D_a_prod_update$' ).

thf('compatible$i_decl',type,
    'compatible$i': 'C_update_b_update_fun$' > 'A_update_b_update_fun$' > $o ).

thf('fun_app$bj_decl',type,
    'fun_app$bj': 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('compatible$ak_decl',type,
    'compatible$ak': 'C_update_a_b_prod_update_fun$' > 'C_update_a_b_prod_update_fun$' > $o ).

thf('fun_app$by_decl',type,
    'fun_app$by': 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update$' > 'A_update$' ).

thf('register$z_decl',type,
    'register$z': 'A_d_prod_update_b_update_fun$' > $o ).

thf('register_pair$i_decl',type,
    'register_pair$i': 'B_update_b_update_fun$' > 'A_update_b_update_fun$' > 'B_a_prod_update_b_update_fun$' ).

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

thf('register_tensor$z_decl',type,
    'register_tensor$z': 'C_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_c_d_prod_prod_update_a_a_prod_update_fun$' ).

thf('grp$a_decl',type,
    'grp$a': '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('compatible$r_decl',type,
    'compatible$r': 'B_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$' ).

thf('convol$e_decl',type,
    'convol$e': 'D_update_b_update_fun$' > 'D_update_b_update_fun$' > 'D_update_b_update_b_update_prod_fun$' ).

thf('fun_app$bt_decl',type,
    'fun_app$bt': 'A_c_prod_update_b_a_prod_update_fun$' > 'A_c_prod_update$' > 'B_a_prod_update$' ).

thf('compatible$ar_decl',type,
    'compatible$ar': 'C_update_a_b_prod_update_fun$' > 'D_update_a_b_prod_update_fun$' > $o ).

thf('comp$f_decl',type,
    'comp$f': 'C_update_b_update_fun$' > 'C_update_c_update_fun$' > 'C_update_b_update_fun$' ).

thf('register$p_decl',type,
    'register$p': 'A_c_prod_update_b_a_prod_update_fun$' > $o ).

thf('register_pair$k_decl',type,
    'register_pair$k': 'A_update_a_update_fun$' > 'D_update_a_update_fun$' > 'A_d_prod_update_a_update_fun$' ).

thf('relcompp$j_decl',type,
    'relcompp$j': 'C_d_prod_update_a_update_bool_fun_fun$' > 'A_update_b_update_bool_fun_fun$' > 'C_d_prod_update_b_update_bool_fun_fun$' ).

thf('register_tensor$w_decl',type,
    'register_tensor$w': 'D_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'D_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('compatible$q_decl',type,
    'compatible$q': 'D_update_b_update_fun$' > 'D_update_b_update_fun$' > $o ).

thf('tensor_update$_decl',type,
    'tensor_update$': 'B_update$' > 'A_update_b_a_prod_update_fun$' ).

thf('compatible$ai_decl',type,
    'compatible$ai': 'C_update_b_a_prod_update_fun$' > 'A_update_b_a_prod_update_fun$' > $o ).

thf('preregister$l_decl',type,
    'preregister$l': 'C_d_prod_update_c_d_prod_update_fun$' > $o ).

thf('map_prod$o_decl',type,
    'map_prod$o': 'D_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

thf('register$am_decl',type,
    'register$am': 'C_update_b_d_prod_update_fun$' > $o ).

thf('uuo$_decl',type,
    'uuo$': 'D_update_b_update_fun$' > 'D_update_b_b_prod_update_fun$' ).

thf('uuh$_decl',type,
    'uuh$': 'A_update_b_update_fun$' > 'A_update_b_d_prod_update_fun$' ).

thf('comp$ce_decl',type,
    'comp$ce': 'A_update_c_d_prod_update_fun$' > 'B_update_a_update_fun$' > 'B_update_c_d_prod_update_fun$' ).

thf('member$a_decl',type,
    'member$a': 'D_update$' > 'D_update_set$' > $o ).

thf('image$a_decl',type,
    'image$a': 'D_update_a_update_fun$' > 'D_update_set$' > 'A_update_set$' ).

thf('fun_app$d_decl',type,
    'fun_app$d': 'A_update_a_c_prod_update_fun$' > 'A_update$' > 'A_c_prod_update$' ).

thf('fcomp$f_decl',type,
    'fcomp$f': 'C_d_prod_update_a_update_fun$' > 'A_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' ).

thf('comp$g_decl',type,
    'comp$g': 'B_update_b_update_fun$' > 'A_update_b_update_fun$' > 'A_update_b_update_fun$' ).

thf('uvv$_decl',type,
    'uvv$': 'D_update_bool_fun$' ).

thf('preregister$a_decl',type,
    'preregister$a': 'C_update_a_update_fun_bool_fun$' ).

thf('quotient$k_decl',type,
    'quotient$k': 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' > 'C_d_prod_update_b_update_fun$' > 'B_update_c_d_prod_update_fun$' > 'C_d_prod_update_b_update_bool_fun_fun$' > $o ).

thf('comp$p_decl',type,
    'comp$p': 'B_update_b_update_fun$' > 'D_update_b_update_fun$' > 'D_update_b_update_fun$' ).

thf('quotient$i_decl',type,
    'quotient$i': 'C_update_c_update_bool_fun_fun$' > 'C_update_b_update_fun$' > 'B_update_c_update_fun$' > 'C_update_b_update_bool_fun_fun$' > $o ).

thf('fun_app$bx_decl',type,
    'fun_app$bx': 'C_update_c_update_fun$' > 'C_update$' > 'C_update$' ).

thf('uuq$_decl',type,
    'uuq$': 'C_update_a_update_fun$' > 'C_update_d_a_prod_update_fun$' ).

thf('compatible$ac_decl',type,
    'compatible$ac': 'C_update_a_update_fun$' > 'A_update_a_update_fun$' > $o ).

thf('type_definition$d_decl',type,
    'type_definition$d': 'D_update_c_update_fun$' > 'C_update_d_update_fun$' > 'C_update_set$' > $o ).

thf('uvi$_decl',type,
    'uvi$': 'C_update_a_update_fun$' > 'C_update_b_a_prod_update_fun$' ).

thf('register_tensor$n_decl',type,
    'register_tensor$n': 'D_update_a_update_fun$' > 'D_update_b_update_fun$' > 'D_d_prod_update_a_b_prod_update_fun$' ).

thf('map_prod$m_decl',type,
    'map_prod$m': 'D_update_b_update_fun$' > 'C_update_b_update_fun$' > 'D_update_c_update_prod_b_update_b_update_prod_fun$' ).

thf('id_update$b_decl',type,
    'id_update$b': 'C_update$' ).

thf('comp$ba_decl',type,
    'comp$ba': 'C_d_prod_update_b_update_fun$' > 'C_update_c_d_prod_update_fun$' > 'C_update_b_update_fun$' ).

thf('type_definition$e_decl',type,
    'type_definition$e': 'D_update_d_update_fun$' > 'D_update_d_update_fun$' > 'D_update_set$' > $o ).

thf('comp$o_decl',type,
    'comp$o': 'A_b_prod_update_b_update_fun$' > 'D_d_prod_update_a_b_prod_update_fun$' > 'D_d_prod_update_b_update_fun$' ).

thf('relcompp$m_decl',type,
    'relcompp$m': 'D_update_a_update_bool_fun_fun$' > 'A_update_b_update_bool_fun_fun$' > 'D_update_b_update_bool_fun_fun$' ).

thf('uvp$_decl',type,
    'uvp$': 'C_update_a_update_fun$' > 'C_update_a_b_prod_update_fun$' ).

thf('comp$c_decl',type,
    'comp$c': 'B_update_a_update_fun$' > 'C_update_b_update_fun$' > 'C_update_a_update_fun$' ).

thf('comp$al_decl',type,
    'comp$al': 'C_update_b_update_fun$' > 'D_update_c_update_fun$' > 'D_update_b_update_fun$' ).

thf('image$_decl',type,
    'image$': 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_set$' > 'A_update_set$' ).

thf('comp$am_decl',type,
    'comp$am': 'A_update_b_update_fun$' > 'A_update_a_update_fun$' > 'A_update_b_update_fun$' ).

thf('map_prod$c_decl',type,
    'map_prod$c': 'C_update_b_update_fun$' > 'C_d_prod_update_b_update_fun$' > 'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

thf('register$bh_decl',type,
    'register$bh': 'B_update_a_b_prod_update_fun$' > $o ).

thf('uwc$_decl',type,
    'uwc$': 'A_update_set$' > 'D_update_a_update_fun_bool_fun$' ).

thf('type_definition$_decl',type,
    'type_definition$': 'A_update_a_update_fun$' > 'A_update_a_update_fun$' > 'A_update_set$' > $o ).

thf('member$_decl',type,
    'member$': 'C_d_prod_update$' > 'C_d_prod_update_set$' > $o ).

thf('uvr$_decl',type,
    'uvr$': 'D_update_b_update_fun$' > 'D_update_a_b_prod_update_fun$' ).

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

thf('register_tensor$x_decl',type,
    'register_tensor$x': 'C_d_prod_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_d_prod_c_prod_update_a_a_prod_update_fun$' ).

thf('quotient$j_decl',type,
    'quotient$j': 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' > 'C_d_prod_update_a_update_fun$' > 'A_update_c_d_prod_update_fun$' > 'C_d_prod_update_a_update_bool_fun_fun$' > $o ).

thf('register_pair$u_decl',type,
    'register_pair$u': 'A_update_b_a_prod_update_fun$' > 'D_update_b_a_prod_update_fun$' > 'A_d_prod_update_b_a_prod_update_fun$' ).

thf('pred_fun$c_decl',type,
    'pred_fun$c': 'C_d_prod_update_bool_fun$' > 'A_update_bool_fun$' > 'C_d_prod_update_a_update_fun_bool_fun$' ).

thf('comp$bn_decl',type,
    'comp$bn': 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' > 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('comp$n_decl',type,
    'comp$n': 'A_b_prod_update_b_update_fun$' > 'D_a_prod_update_a_b_prod_update_fun$' > 'D_a_prod_update_b_update_fun$' ).

thf('fun_app$i_decl',type,
    'fun_app$i': 'C_d_prod_update_a_update_fun_bool_fun$' > 'C_d_prod_update_a_update_fun$' > $o ).

thf('fun_app$o_decl',type,
    'fun_app$o': 'D_update_b_a_prod_update_fun$' > 'D_update$' > 'B_a_prod_update$' ).

thf('compatible$e_decl',type,
    'compatible$e': 'A_update_a_update_fun$' > 'B_update_a_update_fun$' > $o ).

thf('comp$ab_decl',type,
    'comp$ab': 'A_a_prod_update_b_b_prod_update_fun$' > 'D_c_prod_update_a_a_prod_update_fun$' > 'D_c_prod_update_b_b_prod_update_fun$' ).

thf('relcompp$i_decl',type,
    'relcompp$i': 'A_update_a_update_bool_fun_fun$' > 'A_update_c_d_prod_update_bool_fun_fun$' > 'A_update_c_d_prod_update_bool_fun_fun$' ).

thf('comp$ah_decl',type,
    'comp$ah': 'A_a_prod_update_b_b_prod_update_fun$' > 'C_c_d_prod_prod_update_a_a_prod_update_fun$' > 'C_c_d_prod_prod_update_b_b_prod_update_fun$' ).

thf('register_tensor$e_decl',type,
    'register_tensor$e': 'C_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_c_prod_update_b_b_prod_update_fun$' ).

thf('uvg$_decl',type,
    'uvg$': 'A_update_b_update_fun$' > 'A_update_b_a_prod_update_fun$' ).

thf('fun_app$co_decl',type,
    'fun_app$co': 'A_update_a_update_fun_d_update_b_update_fun_fun$' > 'A_update_a_update_fun$' > 'D_update_b_update_fun$' ).

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

thf('register_tensor$u_decl',type,
    'register_tensor$u': 'C_d_prod_update_b_update_fun$' > 'D_update_b_update_fun$' > 'C_d_prod_d_prod_update_b_b_prod_update_fun$' ).

thf('register$e_decl',type,
    'register$e': 'D_update_a_update_fun_bool_fun$' ).

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

thf('map_prod$g_decl',type,
    'map_prod$g': 'C_d_prod_update_b_update_fun$' > 'C_update_b_update_fun$' > 'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' ).

thf('fun_app$be_decl',type,
    'fun_app$be': 'C_update_a_update_fun_c_update_b_update_fun_fun$' > 'C_update_a_update_fun$' > 'C_update_b_update_fun$' ).

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

thf('compatible$ah_decl',type,
    'compatible$ah': 'C_update_b_a_prod_update_fun$' > 'C_update_b_a_prod_update_fun$' > $o ).

thf('register_tensor$ab_decl',type,
    'register_tensor$ab': 'C_d_prod_update_a_update_fun$' > 'C_d_prod_update_a_update_fun$' > 'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$' ).

thf('uut$_decl',type,
    'uut$': 'D_update_b_update_fun$' > 'D_update_d_b_prod_update_fun$' ).

thf('compatible$ao_decl',type,
    'compatible$ao': 'A_update_a_b_prod_update_fun$' > 'C_update_a_b_prod_update_fun$' > $o ).

thf('register$ah_decl',type,
    'register$ah': 'C_a_prod_update_b_update_fun$' > $o ).

thf('fun_app$cf_decl',type,
    'fun_app$cf': 'C_c_prod_update_a_update_fun$' > 'C_c_prod_update$' > 'A_update$' ).

thf('relcompp$k_decl',type,
    'relcompp$k': 'D_update_a_update_bool_fun_fun$' > 'A_update_d_update_bool_fun_fun$' > 'D_update_d_update_bool_fun_fun$' ).

thf('fcomp$g_decl',type,
    'fcomp$g': 'D_update_a_update_fun$' > 'A_update_b_update_fun$' > 'D_update_b_update_fun$' ).

thf('comp$q_decl',type,
    'comp$q': 'A_a_prod_update_b_update_fun$' > 'C_c_prod_update_a_a_prod_update_fun$' > 'C_c_prod_update_b_update_fun$' ).

thf('compatible$u_decl',type,
    'compatible$u': 'B_update_b_update_fun$' > 'B_update_b_update_fun$' > $o ).

thf('comp_update$h_decl',type,
    'comp_update$h': 'D_a_prod_update$' > 'D_a_prod_update$' > 'D_a_prod_update$' ).

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

thf('fun_app$ci_decl',type,
    'fun_app$ci': 'A_c_prod_update_b_update_fun$' > 'A_c_prod_update$' > 'B_update$' ).

thf('fun_app$dx_decl',type,
    'fun_app$dx': 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' > 'B_update_c_d_prod_update_fun$' > 'D_update_b_update_fun$' ).

thf('quotient$h_decl',type,
    'quotient$h': 'A_update_a_update_bool_fun_fun$' > 'A_update_b_update_fun$' > 'B_update_a_update_fun$' > 'A_update_b_update_bool_fun_fun$' > $o ).

thf('comp$b_decl',type,
    'comp$b': 'A_update_a_update_fun$' > 'C_update_a_update_fun$' > 'C_update_a_update_fun$' ).

thf('type_definition$g_decl',type,
    'type_definition$g': 'B_update_a_update_fun$' > 'A_update_b_update_fun$' > 'A_update_set$' > $o ).

thf('comp$ar_decl',type,
    'comp$ar': 'D_update_a_update_fun$' > 'A_update_d_update_fun$' > 'A_update_a_update_fun$' ).

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

thf('fun_app$j_decl',type,
    'fun_app$j': 'D_update_a_update_fun_bool_fun$' > 'D_update_a_update_fun$' > $o ).

thf('register$af_decl',type,
    'register$af': 'C_c_prod_update_a_update_fun$' > $o ).

thf('map_prod$e_decl',type,
    'map_prod$e': 'C_update_b_update_fun$' > 'D_update_b_update_fun$' > 'C_update_d_update_prod_b_update_b_update_prod_fun$' ).

thf('uvk$_decl',type,
    'uvk$': 'C_update_a_update_fun$' > 'C_update_a_a_prod_update_fun$' ).

thf('fun_app$bk_decl',type,
    'fun_app$bk': 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' > 'A_update_b_update_fun$' > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' ).

thf('fun_app$at_decl',type,
    'fun_app$at': 'D_update_a_b_prod_update_fun$' > 'D_update$' > 'A_b_prod_update$' ).

thf('fun_app$ct_decl',type,
    'fun_app$ct': 'A_update_a_update_fun_c_update_b_update_fun_fun$' > 'A_update_a_update_fun$' > 'C_update_b_update_fun$' ).

thf(466,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvk$' @ ( A @ 'uvl$' @ 'compatible$ag' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).

thf(2163,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvk$' @ ( A @ 'uvl$' @ 'compatible$ag' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(445,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$h' ) @ 'register$p' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).

thf(2094,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$h' ) @ 'register$p' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(240,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_d_prod_update_c_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$bc' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).

thf(1369,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_d_prod_update_c_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$bc' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) )
        = ( C @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(97,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$b' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom649) ).

thf(846,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$b' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(4,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$',D: 'A_update_a_update_fun_c_update_b_update_fun_fun$',E: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( C @ ( E @ 'fun_app$cu' ) @ ( D @ 'fun_app$ct' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
        = ( C @ ( E @ ( D @ 'comp$aw' ) @ 'fun_app$cs' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).

thf(518,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$',D: 'A_update_a_update_fun_c_update_b_update_fun_fun$',E: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( C @ ( E @ 'fun_app$cu' ) @ ( D @ 'fun_app$ct' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
        = ( C @ ( E @ ( D @ 'comp$aw' ) @ 'fun_app$cs' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(127,axiom,
    ! [A: 'D_update$',B: 'C_update$',C: 'D_update$',D: 'C_update$'] :
      ( ( D @ ( C @ 'tensor_update$k' ) @ ( B @ ( A @ 'tensor_update$k' ) @ 'comp_update$j' ) )
      = ( D @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( C @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'tensor_update$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).

thf(962,plain,
    ! [A: 'D_update$',B: 'C_update$',C: 'D_update$',D: 'C_update$'] :
      ( ( D @ ( C @ 'tensor_update$k' ) @ ( B @ ( A @ 'tensor_update$k' ) @ 'comp_update$j' ) )
      = ( D @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( C @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'tensor_update$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(188,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).

thf(1179,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(77,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( A @ ( B @ 'compatible$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).

thf(777,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( A @ ( B @ 'compatible$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(220,axiom,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'preregister$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).

thf(1295,plain,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'preregister$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(493,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_pair$' ) @ ( 'register$ae' @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).

thf(2250,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_pair$' ) @ ( 'register$ae' @ 'fun_app$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(297,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).

thf(1586,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(277,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).

thf(1501,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_set$'] :
      ( ( C @ ( B @ 'image$b' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(380,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$av' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$l' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).

thf(1879,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$av' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$l' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(230,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$e' ) )
      = ( D @ ( B @ 'map_prod$f' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bw' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).

thf(1337,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$e' ) )
      = ( D @ ( B @ 'map_prod$f' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bw' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(331,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).

thf(1718,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$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(114,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$' ) @ 'comp$bf' ) )
      = ( C @ ( B @ 'comp$i' ) @ ( C @ ( A @ 'comp$i' ) @ 'convol$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).

thf(909,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$' ) @ 'comp$bf' ) )
      = ( C @ ( B @ 'comp$i' ) @ ( C @ ( A @ 'comp$i' ) @ 'convol$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(36,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( ( D @ ( B @ 'fun_app$az' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).

thf(628,plain,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( ( D @ ( B @ 'fun_app$az' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(406,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_d_update_fun$'] :
      ( ( C @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).

thf(1956,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_d_update_fun$'] :
      ( ( C @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(404,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'register$u' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).

thf(1950,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'register$u' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(505,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$w' )
        & ( C @ 'register$w' )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ad' ) @ ( B @ ( A @ 'register_tensor$' ) @ 'comp$aj' ) )
        = ( D @ ( B @ 'comp$ak' ) @ ( C @ ( A @ 'comp$ak' ) @ 'register_tensor$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).

thf(2280,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'A_update_c_update_fun$'] :
      ( ( ( D @ 'register$w' )
        & ( C @ 'register$w' )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'register_tensor$ad' ) @ ( B @ ( A @ 'register_tensor$' ) @ 'comp$aj' ) )
        = ( D @ ( B @ 'comp$ak' ) @ ( C @ ( A @ 'comp$ak' ) @ 'register_tensor$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(168,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$ca' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).

thf(1110,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$ca' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(132,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: 'D_update_a_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$at' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).

thf(977,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: 'D_update_a_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$at' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(155,axiom,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id_update$b' @ 'comp_update$c' @ 'fun_app$bx' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).

thf(1068,plain,
    ! [A: 'C_update$'] :
      ( ( A @ ( 'id_update$b' @ 'comp_update$c' @ 'fun_app$bx' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(437,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$aw' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).

thf(2062,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$aw' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(307,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$e' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bo' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).

thf(1618,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$e' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bo' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(492,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvr$' @ ( A @ 'uvp$' @ 'compatible$ar' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).

thf(2248,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvr$' @ ( A @ 'uvp$' @ 'compatible$ar' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(285,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bk' ) )
      = ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'convol$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).

thf(1544,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bk' ) )
      = ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'convol$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(448,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$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$q' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).

thf(2099,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$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$q' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(453,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ 'uvp$' @ ( A @ 'uvo$' @ 'compatible$ak' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).

thf(2114,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ 'uvp$' @ ( A @ 'uvo$' @ 'compatible$ak' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(31,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$c' ) @ 'register$ak' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).

thf(614,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$c' ) @ 'register$ak' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(181,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
     => ( ( E @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$au' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).

thf(1158,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
     => ( ( E @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$au' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(72,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$y' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$r' ) ) )
        = ( C @ ( A @ 'fun_app$ac' ) @ ( D @ ( B @ 'fun_app$bh' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).

thf(762,plain,
    ! [A: 'A_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$y' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$r' ) ) )
        = ( C @ ( A @ 'fun_app$ac' ) @ ( D @ ( B @ 'fun_app$bh' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(395,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$s' ) ) )
     => ( B @ ( C @ ( A @ 'comp$d' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).

thf(1924,plain,
    ! [A: 'B_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$s' ) ) )
     => ( B @ ( C @ ( A @ 'comp$d' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(485,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvo$' @ ( A @ 'uvp$' @ 'compatible$ak' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).

thf(2210,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvo$' @ ( A @ 'uvp$' @ 'compatible$ak' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(64,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_d_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$e' ) @ 'fun_app$cp' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$ct' ) )
      = ( E @ ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$f' ) @ 'fun_app$cv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).

thf(730,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_d_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$e' ) @ 'fun_app$cp' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$ct' ) )
      = ( E @ ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$f' ) @ 'fun_app$cv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(381,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$d' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bv' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).

thf(1882,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$d' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bv' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(13,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( ! [E: 'B_update_c_d_prod_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
              = ( E @ ( D @ 'fun_app$cu' ) @ ( C @ 'fun_app$ct' ) ) )
         => $false )
        & ( ( B @ ( A @ 'comp$aw' ) )
          = ( D @ ( C @ 'comp$aw' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).

thf(550,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ~ ( ~ ! [E: 'B_update_c_d_prod_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
              = ( E @ ( D @ 'fun_app$cu' ) @ ( C @ 'fun_app$ct' ) ) )
        & ( ( B @ ( A @ 'comp$aw' ) )
          = ( D @ ( C @ 'comp$aw' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(418,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvg$' @ 'fun_app$a' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$ae' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).

thf(1999,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvg$' @ 'fun_app$a' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$ae' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(227,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'register$ag' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).

thf(1327,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'register$ag' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(313,axiom,
    ! [A: 'B_update_c_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$',F: 'A_update_b_update_fun$',G: 'C_update_a_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ak' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$i' ) ) ) )
     => ( ( G @ ( C @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( G @ ( E @ ( B @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$z' ) @ 'comp$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom694) ).

thf(1640,plain,
    ! [A: 'B_update_c_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$',F: 'A_update_b_update_fun$',G: 'C_update_a_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ak' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$i' ) ) ) )
     => ( ( G @ ( C @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( G @ ( E @ ( B @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$z' ) @ 'comp$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(153,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_d_update_fun$'] :
      ( ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).

thf(1063,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_d_update_fun$'] :
      ( ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(431,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$as' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( G @ ( E @ ( B @ 'comp$as' ) @ 'comp$y' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom690) ).

thf(2042,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$as' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( G @ ( E @ ( B @ 'comp$as' ) @ 'comp$y' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(462,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$x' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ag' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$y' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).

thf(2146,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$x' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ag' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$y' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(276,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'C_update_a_update_fun$',D: 'C_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).

thf(1497,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'C_update_a_update_fun$',D: 'C_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(479,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$u' ) )
        = 'id_update$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).

thf(2195,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$u' ) )
        = 'id_update$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(328,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_tensor$i' ) @ 'fun_app$bu' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'tensor_update$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).

thf(1705,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_tensor$i' ) @ 'fun_app$bu' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'tensor_update$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(110,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uvd$' @ 'fun_app$f' ) )
      = ( 'id_update$c' @ ( A @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).

thf(898,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uvd$' @ 'fun_app$f' ) )
      = ( 'id_update$c' @ ( A @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(487,axiom,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( 'preregister$i' @ 'fun_app$j' ) )
        & ( A @ 'preregister$n' ) )
     => ( A @ ( B @ 'comp$y' ) @ ( 'preregister$a' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).

thf(2216,plain,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( 'preregister$i' @ 'fun_app$j' ) )
        & ( A @ 'preregister$n' ) )
     => ( A @ ( B @ 'comp$y' ) @ ( 'preregister$a' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(392,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_update_a_update_fun$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).

thf(1914,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_update_a_update_fun$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(425,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).

thf(2020,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(148,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ 'comp$am' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).

thf(1046,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$b' ) )
     => ( A @ ( B @ 'comp$am' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(399,axiom,
    ! [A: 'B_update$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).

thf(1935,plain,
    ! [A: 'B_update$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(237,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( ! [E: 'C_d_prod_update$'] :
              ( ( E @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$by' ) @ ( C @ 'fun_app$ae' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).

thf(1359,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ~ ( ~ ! [E: 'C_d_prod_update$'] :
              ( ( E @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$by' ) @ ( C @ 'fun_app$ae' ) ) )
        & ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(244,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bj' ) )
      = ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'convol$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).

thf(1386,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bj' ) )
      = ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'convol$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(441,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvh$' @ 'fun_app$o' ) )
      = ( B @ ( A @ 'fun_app$au' ) @ ( 'id_update$c' @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).

thf(2082,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvh$' @ 'fun_app$o' ) )
      = ( B @ ( A @ 'fun_app$au' ) @ ( 'id_update$c' @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(383,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_c_update_fun$'] :
      ( ( C @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).

thf(1887,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_c_update_fun$'] :
      ( ( C @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(43,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).

thf(651,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(246,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update_d_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ 'comp$ao' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).

thf(1391,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update_d_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ 'comp$ao' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(294,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$bp' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).

thf(1576,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'comp$bp' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(316,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
      = ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).

thf(1650,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
      = ( C @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(314,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvi$' @ 'fun_app$s' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$c' @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).

thf(1645,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvi$' @ 'fun_app$s' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$c' @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(333,axiom,
    ! [A: 'C_d_prod_update_c_d_prod_update_fun$',B: 'C_d_prod_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$' )
        & ( A @ 'preregister$l' ) )
     => ( A @ ( B @ 'comp$w' ) @ 'preregister$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).

thf(1724,plain,
    ! [A: 'C_d_prod_update_c_d_prod_update_fun$',B: 'C_d_prod_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$' )
        & ( A @ 'preregister$l' ) )
     => ( A @ ( B @ 'comp$w' ) @ 'preregister$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(268,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$g' @ 'fun_app$k' ) ) )
     => ( B @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'compatible$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).

thf(1475,plain,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$g' @ 'fun_app$k' ) ) )
     => ( B @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'compatible$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(17,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
      = ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).

thf(565,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
      = ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(239,axiom,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$q' ) )
        = 'id_update$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).

thf(1366,plain,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( ( 'id_update$b' @ ( A @ 'fun_app$q' ) )
        = 'id_update$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(459,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).

thf(2136,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(211,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$m' ) )
        = ( D @ ( B @ 'comp$d' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).

thf(1265,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$l' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$m' ) )
        = ( D @ ( B @ 'comp$d' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(201,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$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
     => ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).

thf(1228,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$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
     => ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(271,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_b_update_fun$'] :
      ( ( ( D @ 'register$g' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$o' ) )
        = ( D @ ( B @ 'comp$p' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).

thf(1482,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_b_update_fun$'] :
      ( ( ( D @ 'register$g' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$n' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$o' ) )
        = ( D @ ( B @ 'comp$p' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(252,axiom,
    'f$' @ 'register$a',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).

thf(1409,plain,
    'f$' @ 'register$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(329,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$',F: 'A_update_b_update_fun$',G: 'D_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( G @ ( E @ ( B @ 'comp$e' ) @ 'comp$as' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom688) ).

thf(1709,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$',F: 'A_update_b_update_fun$',G: 'D_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( G @ ( E @ ( B @ 'comp$e' ) @ 'comp$as' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(354,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).

thf(1792,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(416,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: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$bd' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( F @ ( C @ 'comp$v' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).

thf(1985,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: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$bd' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( F @ ( C @ 'comp$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(344,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'convol$f' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$br' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'convol$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).

thf(1760,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'convol$f' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$br' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'convol$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(61,axiom,
    ! [A: 'D_update$'] :
      ( ( 'id_update$a' @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).

thf(719,plain,
    ! [A: 'D_update$'] :
      ( ( 'id_update$a' @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(81,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( ! [E: 'A_update$',F: 'D_update$'] :
            ( ( F @ ( B @ 'fun_app$m' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).

thf(785,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( ! [E: 'A_update$',F: 'D_update$'] :
            ( ( F @ ( B @ 'fun_app$m' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(501,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$b' ) @ 'register$j' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).

thf(2269,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$b' ) @ 'register$j' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(378,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$q' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).

thf(1871,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$q' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(390,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$v' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$af' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$w' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).

thf(1907,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$v' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$af' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$w' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(228,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'D_update$',D: 'C_update$'] :
      ( ( ! [E: 'D_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$m' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( ( D @ ( C @ 'tensor_update$k' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'fun_app$ck' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).

thf(1330,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'D_update$',D: 'C_update$'] :
      ( ( ! [E: 'D_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$m' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( ( D @ ( C @ 'tensor_update$k' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'fun_app$ck' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(24,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun_a_update_a_update_fun_fun$',E: 'B_update_d_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ax' ) )
        = ( D @ ( C @ 'comp$ax' ) ) )
     => ( ( E @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( E @ ( D @ 'fun_app$cp' ) @ ( C @ 'fun_app$ct' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).

thf(587,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun_a_update_a_update_fun_fun$',E: 'B_update_d_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ax' ) )
        = ( D @ ( C @ 'comp$ax' ) ) )
     => ( ( E @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( E @ ( D @ 'fun_app$cp' ) @ ( C @ 'fun_app$ct' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(266,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$n' ) )
    <=> ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).

thf(1462,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ! [C: 'C_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$c' ) )
       => ( B @ ( A @ 'compatible$n' ) ) )
      & ( ( B @ ( A @ 'compatible$n' ) )
       => ( ! [C: 'C_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(124,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$i' ) )
    <=> ( ! [C: 'C_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).

thf(949,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ! [C: 'C_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$c' ) )
       => ( B @ ( A @ 'compatible$i' ) ) )
      & ( ( B @ ( A @ 'compatible$i' ) )
       => ( ! [C: 'C_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(474,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( A @ ( B @ 'compatible$g' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).

thf(2185,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( A @ ( B @ 'compatible$g' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(264,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$a' )
     => ( ( C @ ( A @ 'fun_app$ae' ) @ ( B @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).

thf(1455,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$a' )
     => ( ( C @ ( A @ 'fun_app$ae' ) @ ( B @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(39,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 @ ( C @ 'convol$b' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bq' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'convol$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).

thf(638,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 @ ( C @ 'convol$b' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bq' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'convol$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(242,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ! [E: 'A_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_pair$l' ) @ 'fun_app$ci' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).

thf(1379,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ! [E: 'A_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_pair$l' ) @ 'fun_app$ci' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(280,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bl' ) )
      = ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'convol$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).

thf(1514,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bl' ) )
      = ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'convol$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(384,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$f' ) )
      = ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).

thf(1890,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$f' ) )
      = ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(233,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$f' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bw' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).

thf(1347,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$f' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bw' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(291,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$m' ) )
      = ( D @ ( B @ 'map_prod$n' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$ca' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).

thf(1568,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$m' ) )
      = ( D @ ( B @ 'map_prod$n' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$ca' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(509,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$d' ) @ 'register$l' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).

thf(2301,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$d' ) @ 'register$l' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(202,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
      = ( C @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).

thf(1232,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
      = ( C @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(371,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$e' ) @ 'register$ab' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).

thf(1847,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$e' ) @ 'register$ab' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(421,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$bz' ) )
        = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).

thf(2007,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$bz' ) )
        = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(273,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$k' ) )
     => ( A @ ( B @ 'compatible$d' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).

thf(1489,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$k' ) )
     => ( A @ ( B @ 'compatible$d' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(82,axiom,
    ! [A: 'D_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$s' ) )
     => ( A @ ( B @ 'comp$al' ) @ 'register$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).

thf(789,plain,
    ! [A: 'D_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$s' ) )
     => ( A @ ( B @ 'comp$al' ) @ 'register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(25,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$' ) @ 'comp$be' ) )
      = ( C @ ( B @ 'comp$f' ) @ ( C @ ( A @ 'comp$f' ) @ 'convol$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).

thf(591,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$' ) @ 'comp$be' ) )
      = ( C @ ( B @ 'comp$f' ) @ ( C @ ( A @ 'comp$f' ) @ 'convol$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(34,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).

thf(623,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(229,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'C_update_a_update_fun$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).

thf(1334,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'C_update_a_update_fun$',F: 'C_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(1,conjecture,
    'g$' @ ( 'register$' @ 'fun_app$k' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture59) ).

thf(2,negated_conjecture,
    ~ ( 'g$' @ ( 'register$' @ 'fun_app$k' ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(514,plain,
    ~ ( 'g$' @ ( 'register$' @ 'fun_app$k' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(424,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).

thf(2017,plain,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(223,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( B @ 'register$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).

thf(1302,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( B @ 'register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(71,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'C_d_prod_update$'] :
            ( ( B @ ( E @ 'member$' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
              = ( E @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) )
        & ( ( B @ ( A @ 'image$' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom629) ).

thf(756,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'C_d_prod_update$'] :
            ( ( B @ ( E @ 'member$' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
              = ( E @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) )
        & ( ( B @ ( A @ 'image$' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(330,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$x' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( E @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).

thf(1714,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$x' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( E @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(427,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$g' ) )
      = ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).

thf(2027,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$g' ) )
      = ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(146,axiom,
    ! [A: 'C_d_prod_update_b_update_fun$',B: 'C_d_prod_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( C @ 'tensor_update$h' ) @ ( A @ 'fun_app$bz' ) )
            = ( D @ ( C @ 'tensor_update$h' ) @ ( B @ 'fun_app$bz' ) ) )
        & ( B @ 'preregister$' )
        & ( A @ 'preregister$' ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).

thf(1040,plain,
    ! [A: 'C_d_prod_update_b_update_fun$',B: 'C_d_prod_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( C @ 'tensor_update$h' ) @ ( A @ 'fun_app$bz' ) )
            = ( D @ ( C @ 'tensor_update$h' ) @ ( B @ 'fun_app$bz' ) ) )
        & ( B @ 'preregister$' )
        & ( A @ 'preregister$' ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(311,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_d_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$e' ) @ 'fun_app$cp' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$j' ) @ 'fun_app$dw' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).

thf(1632,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_d_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$e' ) @ 'fun_app$cp' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$j' ) @ 'fun_app$dw' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(176,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ! [E: 'C_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$q' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_pair$h' ) @ 'fun_app$ch' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).

thf(1136,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ! [E: 'C_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$q' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_pair$h' ) @ 'fun_app$ch' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(93,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bi' ) )
      = ( C @ ( B @ 'comp$am' ) @ ( C @ ( A @ 'comp$am' ) @ 'convol$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).

thf(834,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$a' ) @ 'comp$bi' ) )
      = ( C @ ( B @ 'comp$am' ) @ ( C @ ( A @ 'comp$am' ) @ 'convol$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(376,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'B_update_b_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( D @ 'comp$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).

thf(1864,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'B_update_b_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( D @ 'comp$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(456,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$a' ) @ 'register$i' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).

thf(2122,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$a' ) @ 'register$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(243,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).

thf(1383,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(20,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$l' ) @ 'register$aa' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).

thf(574,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$l' ) @ 'register$aa' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(150,axiom,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uui$' @ 'register$ao' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).

thf(1051,plain,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uui$' @ 'register$ao' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(91,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'D_update_d_update_fun$',F: 'D_update_d_update_fun$',G: 'D_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$p' ) @ 'comp$ao' ) )
          = ( E @ ( I @ ( B @ 'comp$at' ) @ 'comp$x' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$e' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom679) ).

thf(821,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'D_update_d_update_fun$',F: 'D_update_d_update_fun$',G: 'D_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$p' ) @ 'comp$ao' ) )
          = ( E @ ( I @ ( B @ 'comp$at' ) @ 'comp$x' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$e' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(370,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_tensor$f' ) @ 'fun_app$br' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).

thf(1843,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_tensor$f' ) @ 'fun_app$br' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(198,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',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$cx' ) @ ( A @ 'fun_app$au' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).

thf(1215,plain,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',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$cx' ) @ ( A @ 'fun_app$au' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(262,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'fun_app$cc' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).

thf(1447,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'fun_app$cc' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(104,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uul$' @ 'fun_app$ab' ) )
      = ( 'id_update$a' @ ( B @ ( A @ 'fun_app$ac' ) @ 'tensor_update$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).

thf(866,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uul$' @ 'fun_app$ab' ) )
      = ( 'id_update$a' @ ( B @ ( A @ 'fun_app$ac' ) @ 'tensor_update$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(76,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$co' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$m' ) @ 'fun_app$dx' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).

thf(774,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$co' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$m' ) @ 'fun_app$dx' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(419,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bm' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).

thf(2002,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$a' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bm' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(491,axiom,
    ! [A: 'A_update_set$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'uwa$' @ 'fun_app$k' ) )
    <=> ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).

thf(2242,plain,
    ! [A: 'A_update_set$',B: 'C_update_a_update_fun$'] :
      ( ( ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$' ) )
       => ( B @ ( A @ 'uwa$' @ 'fun_app$k' ) ) )
      & ( ( B @ ( A @ 'uwa$' @ 'fun_app$k' ) )
       => ( A @ ( 'top$b' @ ( B @ 'image$b' ) @ 'less_eq$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(250,axiom,
    ! [A: 'B_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).

thf(1405,plain,
    ! [A: 'B_update$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(402,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).

thf(1943,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(282,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$',E: 'B_update_c_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$cr' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$h' ) @ 'fun_app$du' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).

thf(1521,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$',E: 'B_update_c_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$cr' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$h' ) @ 'fun_app$du' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(483,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$j' ) ) )
     => ( ( D @ ( C @ 'register_tensor$d' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$t' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ 'comp$d' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).

thf(2205,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$j' ) ) )
     => ( ( D @ ( C @ 'register_tensor$d' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$t' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ 'comp$d' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(413,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$bd' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).

thf(1975,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$bd' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(133,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'D_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
              = ( E @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).

thf(981,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'D_update$'] :
            ( ( B @ ( E @ 'member$a' ) )
           => ( ( E @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
              = ( E @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) )
        & ( ( B @ ( A @ 'image$a' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(73,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( B @ 'register$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).

thf(766,plain,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( B @ 'register$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(184,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$ae' ) ) )
     => ( B @ ( C @ 'comp$al' ) @ ( A @ ( C @ 'comp$f' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).

thf(1169,plain,
    ! [A: 'C_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$ae' ) ) )
     => ( B @ ( C @ 'comp$al' ) @ ( A @ ( C @ 'comp$f' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(52,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'convol$c' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bs' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'convol$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).

thf(687,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'convol$c' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bs' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'convol$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(166,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvl$' @ 'fun_app$v' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$u' ) @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).

thf(1104,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvl$' @ 'fun_app$v' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$u' ) @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(205,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( ! [E: 'A_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$d' @ 'fun_app$h' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'fun_app$cj' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).

thf(1242,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( ! [E: 'A_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$ae' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$d' @ 'fun_app$h' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'fun_app$cj' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(98,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$f' ) @ 'register$aj' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).

thf(849,plain,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$f' ) @ 'register$aj' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(422,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'uuh$' @ 'register$an' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).

thf(2011,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'uuh$' @ 'register$an' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(49,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom645) ).

thf(678,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( 'top$a' @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
      = ( 'top$a' @ ( B @ 'image$a' ) @ ( A @ 'image$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(46,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
    <=> ( ! [C: 'A_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).

thf(661,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ! [C: 'A_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$a' ) )
       => ( B @ ( A @ 'compatible$a' ) ) )
      & ( ( B @ ( A @ 'compatible$a' ) )
       => ( ! [C: 'A_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(193,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update$',D: 'A_update_a_update_fun$',E: 'D_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$bg' ) @ ( A @ 'fun_app$au' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).

thf(1199,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update$',D: 'A_update_a_update_fun$',E: 'D_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$bg' ) @ ( A @ 'fun_app$au' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(179,axiom,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'uug$' @ 'register$am' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).

thf(1153,plain,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'uug$' @ 'register$am' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(87,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_c_update_fun$',F: 'C_update_c_update_fun$',G: 'C_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'C_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$e' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$e' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom680) ).

thf(810,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_c_update_fun$',F: 'C_update_c_update_fun$',G: 'C_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'C_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$e' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$e' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(432,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$n' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$ca' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).

thf(2047,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$n' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$ca' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(512,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$z' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ah' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$aa' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).

thf(2307,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$z' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ah' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(347,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$aa' ) ) )
     => ( C @ ( B @ 'comp$p' ) @ ( A @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).

thf(1768,plain,
    ! [A: 'C_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$aa' ) ) )
     => ( C @ ( B @ 'comp$p' ) @ ( A @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(7,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$',D: 'A_update_a_update_fun_d_update_b_update_fun_fun$',E: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( C @ ( E @ 'fun_app$cr' ) @ ( D @ 'fun_app$co' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
        = ( C @ ( E @ ( D @ 'comp$av' ) @ 'fun_app$cq' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).

thf(529,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$',D: 'A_update_a_update_fun_d_update_b_update_fun_fun$',E: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( C @ ( E @ 'fun_app$cr' ) @ ( D @ 'fun_app$co' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
        = ( C @ ( E @ ( D @ 'comp$av' ) @ 'fun_app$cq' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(324,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).

thf(1691,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(214,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_d_prod_update_c_update_fun$',C: 'C_d_prod_update$',D: 'A_update_a_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cy' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) @ 'fun_app$bz' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).

thf(1274,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_d_prod_update_c_update_fun$',C: 'C_d_prod_update$',D: 'A_update_a_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cy' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) @ 'fun_app$bz' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(232,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$b' )
     => ( ( C @ ( A @ 'fun_app$bd' ) @ ( B @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).

thf(1343,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$b' )
     => ( ( C @ ( A @ 'fun_app$bd' ) @ ( B @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(186,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ae' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$u' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).

thf(1174,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ae' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(54,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$c' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = 'top$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom631) ).

thf(693,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$b' @ ( A @ 'image$b' ) )
          = 'top$c' ) )
     => ( ( 'top$b' @ ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = 'top$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(289,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$e' ) )
      = ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).

thf(1560,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'fcomp$e' ) )
      = ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(69,axiom,
    ! [A: 'D_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$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom639) ).

thf(746,plain,
    ! [A: 'D_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$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(162,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).

thf(1091,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(362,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ai' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$ac' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).

thf(1824,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( C @ ( 'register$ae' @ 'fun_app$i' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ai' ) )
        = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'register_tensor$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(464,axiom,
    ! [A: 'C_update_a_update_fun_bool_fun$',B: 'C_update_a_update_fun_bool_fun$'] :
      ( ! [C: 'C_update_a_update_fun$'] :
          ( ( C @ ( A @ 'fun_app$k' ) )
        <=> ( C @ ( B @ 'fun_app$k' ) ) )
     => ( ( A @ 'collect$f' )
        = ( B @ 'collect$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).

thf(2150,plain,
    ! [A: 'C_update_a_update_fun_bool_fun$',B: 'C_update_a_update_fun_bool_fun$'] :
      ( ! [C: 'C_update_a_update_fun$'] :
          ( ( ( C @ ( B @ 'fun_app$k' ) )
           => ( C @ ( A @ 'fun_app$k' ) ) )
          & ( ( C @ ( A @ 'fun_app$k' ) )
           => ( C @ ( B @ 'fun_app$k' ) ) ) )
     => ( ( A @ 'collect$f' )
        = ( B @ 'collect$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(400,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( A @ 'register$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).

thf(1938,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( A @ 'register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(302,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).

thf(1602,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(394,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).

thf(1920,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(410,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'uux$' @ 'register$bc' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).

thf(1968,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'uux$' @ 'register$bc' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(99,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$h' ) )
     => ( A @ ( B @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).

thf(852,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$h' ) )
     => ( A @ ( B @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(323,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$w' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$p' ) ) )
        = ( D @ ( B @ 'fun_app$ac' ) @ ( C @ ( A @ 'fun_app$cb' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).

thf(1687,plain,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$w' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$p' ) ) )
        = ( D @ ( B @ 'fun_app$ac' ) @ ( C @ ( A @ 'fun_app$cb' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(23,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( ! [E: 'B_update_c_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
              = ( E @ ( D @ 'fun_app$cr' ) @ ( C @ 'fun_app$co' ) ) )
         => $false )
        & ( ( B @ ( A @ 'comp$av' ) )
          = ( D @ ( C @ 'comp$av' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).

thf(583,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ~ ( ~ ! [E: 'B_update_c_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
              = ( E @ ( D @ 'fun_app$cr' ) @ ( C @ 'fun_app$co' ) ) )
        & ( ( B @ ( A @ 'comp$av' ) )
          = ( D @ ( C @ 'comp$av' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(471,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$g' @ 'fun_app$k' ) )
     => ( A @ ( B @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).

thf(2179,plain,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$g' @ 'fun_app$k' ) )
     => ( A @ ( B @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(196,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$z' ) ) )
     => ( C @ ( B @ 'comp$ap' ) @ ( A @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).

thf(1210,plain,
    ! [A: 'C_update_a_update_fun$',B: 'B_update_a_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$z' ) ) )
     => ( C @ ( B @ 'comp$ap' ) @ ( A @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(192,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( 'id$' @ 'comp$p' ) ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).

thf(1195,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'D_update$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( 'id$' @ 'comp$p' ) ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(216,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update_c_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ 'comp$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).

thf(1281,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'C_update_c_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ 'comp$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(452,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$o' ) ) )
     => ( B @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).

thf(2112,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$o' ) ) )
     => ( B @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(391,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$as' ) )
          = ( D @ ( C @ 'comp$at' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).

thf(1910,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$as' ) )
          = ( D @ ( C @ 'comp$at' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(131,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$b' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom646) ).

thf(974,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$b' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(367,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).

thf(1836,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
      = ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(472,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$c' ) @ 'register$k' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).

thf(2181,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$c' ) @ 'register$k' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(158,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( A @ 'register$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).

thf(1079,plain,
    ! [A: 'A_update_a_update_fun$',B: 'B_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$e' ) )
     => ( A @ 'register$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(143,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( A @ 'register$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).

thf(1027,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( A @ 'register$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(249,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'register$ai' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).

thf(1402,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'register$ai' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(234,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'compatible$n' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).

thf(1350,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'compatible$n' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(299,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$j' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$k' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).

thf(1592,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$j' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$k' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(161,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).

thf(1089,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(415,axiom,
    ! [A: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_c_d_prod_update_fun$',D: 'C_d_prod_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$j' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$j' ) @ ( G @ ( C @ 'comp$ce' ) @ ( B @ ( F @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( D @ 'conversep$b' @ ( E @ 'relcompp$i' ) @ ( D @ 'relcompp$h' ) @ 'quotient$k' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom674) ).

thf(1983,plain,
    ! [A: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_c_d_prod_update_fun$',D: 'C_d_prod_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$j' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$j' ) @ ( G @ ( C @ 'comp$ce' ) @ ( B @ ( F @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( D @ 'conversep$b' @ ( E @ 'relcompp$i' ) @ ( D @ 'relcompp$h' ) @ 'quotient$k' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(178,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
    <=> ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).

thf(1143,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ! [C: 'A_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$a' ) )
       => ( B @ ( A @ 'compatible$c' ) ) )
      & ( ( B @ ( A @ 'compatible$c' ) )
       => ( ! [C: 'A_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(355,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'C_update_a_update_fun$',D: 'C_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).

thf(1794,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'C_update_a_update_fun$',D: 'C_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$b' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(411,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$ac' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).

thf(1970,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$ac' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(63,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$at' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).

thf(725,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$at' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(105,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$p' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$at' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom677) ).

thf(869,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$p' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$at' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(80,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$v' ) )
     => ( A @ ( B @ 'comp$h' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).

thf(783,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$v' ) )
     => ( A @ ( B @ 'comp$h' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(101,axiom,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$f' )
     => ( ( 'id_update$c' @ ( A @ 'fun_app$az' ) )
        = 'id_update$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).

thf(857,plain,
    ! [A: 'B_update_a_update_fun$'] :
      ( ( A @ 'register$f' )
     => ( ( 'id_update$c' @ ( A @ 'fun_app$az' ) )
        = 'id_update$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(213,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom615) ).

thf(1270,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(373,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).

thf(1851,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(349,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$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$e' ) )
          = ( D @ ( C @ 'comp$b' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).

thf(1772,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$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$e' ) )
          = ( D @ ( C @ 'comp$b' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(208,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'preregister$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).

thf(1259,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'preregister$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(30,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).

thf(610,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(342,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvk$' @ 'fun_app$v' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$' @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).

thf(1755,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvk$' @ 'fun_app$v' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$' @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(322,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$bz' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).

thf(1683,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$bz' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(219,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvn$' @ 'fun_app$o' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$m' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).

thf(1292,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvn$' @ 'fun_app$o' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$m' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(14,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( B @ ( A @ 'register_pair$j' ) @ 'register$z' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).

thf(554,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( B @ ( A @ 'register_pair$j' ) @ 'register$z' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(257,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'uvw$' ) @ 'fun_app$aj' ) )
    <=> ( ( C @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( B @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).

thf(1424,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update$'] :
      ( ( ( ( C @ ( A @ 'fun_app$ae' ) )
          = ( C @ ( B @ 'fun_app$ae' ) ) )
       => ( C @ ( B @ ( A @ 'uvw$' ) @ 'fun_app$aj' ) ) )
      & ( ( C @ ( B @ ( A @ 'uvw$' ) @ 'fun_app$aj' ) )
       => ( ( C @ ( A @ 'fun_app$ae' ) )
          = ( C @ ( B @ 'fun_app$ae' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(6,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
      = ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).

thf(526,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
      = ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(305,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$e' @ 'fun_app$j' ) ) )
     => ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).

thf(1612,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$e' @ 'fun_app$j' ) ) )
     => ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(159,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( ! [E: 'D_update$'] :
              ( ( E @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$au' ) @ ( C @ 'fun_app$ae' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).

thf(1082,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ~ ( ~ ! [E: 'D_update$'] :
              ( ( E @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$au' ) @ ( C @ 'fun_app$ae' ) ) )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(426,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_d_update_fun$',E: 'A_update_b_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$b' ) )
          = ( D @ ( C @ 'comp$y' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ 'comp$an' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).

thf(2023,plain,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_d_update_fun$',E: 'A_update_b_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$b' ) )
          = ( D @ ( C @ 'comp$y' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ 'comp$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(111,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$c' ) )
     => ( ( 'top$' @ ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = 'top$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).

thf(901,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$' @ ( A @ 'image$' ) )
          = 'top$c' ) )
     => ( ( 'top$' @ ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = 'top$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(157,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uvw$' ) @ ( 'uvv$' @ 'pred_fun$e' ) @ 'fun_app$j' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).

thf(1075,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uvw$' ) @ ( 'uvv$' @ 'pred_fun$e' ) @ 'fun_app$j' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(195,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).

thf(1207,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(442,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_c_update_fun$',E: 'A_update_b_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$b' ) )
          = ( D @ ( C @ 'comp$e' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ 'comp$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).

thf(2085,plain,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_c_update_fun$',E: 'A_update_b_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$b' ) )
          = ( D @ ( C @ 'comp$e' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ 'comp$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(180,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$e' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$ax' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).

thf(1155,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$e' ) @ ( B @ ( A @ 'map_fun$' ) @ 'comp$ax' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(12,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
      = ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).

thf(547,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$av' ) @ 'fun_app$cq' ) )
      = ( C @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(337,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).

thf(1744,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(94,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'compatible$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).

thf(837,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'compatible$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(165,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).

thf(1099,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$x' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(221,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'register$b' )
     => ( A @ 'uuy$' @ 'register$bd' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).

thf(1297,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'register$b' )
     => ( A @ 'uuy$' @ 'register$bd' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(263,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_b_update_fun$',D: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( C @ ( 'id$' @ 'comp$v' ) ) )
     => ( ( D @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).

thf(1451,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_b_update_fun$',D: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( C @ ( 'id$' @ 'comp$v' ) ) )
     => ( ( D @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(365,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_pair$h' ) @ 'register$ah' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).

thf(1831,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_pair$h' ) @ 'register$ah' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(44,axiom,
    ! [A: 'B_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvs$' @ 'fun_app$ae' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).

thf(654,plain,
    ! [A: 'B_update$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvs$' @ 'fun_app$ae' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(287,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',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$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$b' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).

thf(1552,plain,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',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$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$y' ) )
          = ( D @ ( C @ 'comp$b' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(398,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$d' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$b' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom678) ).

thf(1932,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_b_update_fun$',H: 'A_update_b_update_fun$',I: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$d' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$b' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(136,axiom,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'preregister$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).

thf(1002,plain,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'preregister$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(78,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$b' )
        & ( A @ 'preregister$o' ) )
     => ( A @ ( B @ 'comp$f' ) @ 'preregister$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom201) ).

thf(779,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$b' )
        & ( A @ 'preregister$o' ) )
     => ( A @ ( B @ 'comp$f' ) @ 'preregister$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(503,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ! [E: 'C_update$',F: 'D_update$'] :
            ( ( F @ ( B @ 'fun_app$au' ) @ ( E @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( E @ ( A @ 'fun_app$u' ) @ ( F @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).

thf(2272,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ! [E: 'C_update$',F: 'D_update$'] :
            ( ( F @ ( B @ 'fun_app$au' ) @ ( E @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( E @ ( A @ 'fun_app$u' ) @ ( F @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(226,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).

thf(1324,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(169,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$k' ) )
      = ( D @ ( B @ 'map_prod$l' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bz' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).

thf(1114,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$k' ) )
      = ( D @ ( B @ 'map_prod$l' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bz' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(42,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$',C: 'D_update$'] :
      ( ( A @ 'register$g' )
     => ( ( C @ ( A @ 'fun_app$m' ) @ ( B @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).

thf(647,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$',C: 'D_update$'] :
      ( ( A @ 'register$g' )
     => ( ( C @ ( A @ 'fun_app$m' ) @ ( B @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(350,axiom,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$w' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$p' ) ) )
        = ( C @ ( A @ 'fun_app$cb' ) @ ( D @ ( B @ 'fun_app$ac' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).

thf(1776,plain,
    ! [A: 'B_update_c_update_fun$',B: 'A_update_c_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$w' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$p' ) ) )
        = ( C @ ( A @ 'fun_app$cb' ) @ ( D @ ( B @ 'fun_app$ac' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(210,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( A @ ( B @ 'compatible$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).

thf(1263,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( A @ ( B @ 'compatible$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(135,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$x' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( G @ ( E @ ( B @ 'comp$x' ) @ 'comp$y' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom691) ).

thf(997,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$x' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( G @ ( E @ ( B @ 'comp$x' ) @ 'comp$y' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(3,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
      = ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).

thf(515,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$aw' ) @ 'fun_app$cs' ) )
      = ( C @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(207,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
    <=> ( ! [C: 'A_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).

thf(1249,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( ! [C: 'A_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$g' )
          & ( A @ 'register$a' ) )
       => ( B @ ( A @ 'compatible$o' ) ) )
      & ( ( B @ ( A @ 'compatible$o' ) )
       => ( ! [C: 'A_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$g' )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(434,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).

thf(2052,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
      = ( C @ ( B @ ( A @ 'comp$g' ) @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(301,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$m' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$n' ) )
        = ( D @ ( B @ 'comp$g' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).

thf(1599,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$m' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$n' ) )
        = ( D @ ( B @ 'comp$g' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(206,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).

thf(1246,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(482,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$ae' ) ) )
     => ( B @ ( C @ 'comp$as' ) @ ( A @ ( C @ 'comp$e' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).

thf(2203,plain,
    ! [A: 'C_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$ae' ) ) )
     => ( B @ ( C @ 'comp$as' ) @ ( A @ ( C @ 'comp$e' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(160,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
      = ( C @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).

thf(1086,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
      = ( C @ ( B @ 'comp$x' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(484,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvm$' @ ( A @ 'uvi$' @ 'compatible$ah' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).

thf(2208,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvm$' @ ( A @ 'uvi$' @ 'compatible$ah' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(118,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ 'register$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).

thf(921,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ 'register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(439,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).

thf(2076,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(217,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( B @ ( 'register$e' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).

thf(1286,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( B @ ( 'register$e' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(156,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$b' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).

thf(1071,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$b' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(48,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: 'D_update_a_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ 'comp$p' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).

thf(674,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: 'D_update_a_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ 'comp$p' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(443,axiom,
    ! [A: 'C_update$',B: 'A_update$',C: 'C_update$',D: 'A_update$'] :
      ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'tensor_update$m' ) @ 'comp_update$l' ) )
      = ( D @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( C @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'tensor_update$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).

thf(2089,plain,
    ! [A: 'C_update$',B: 'A_update$',C: 'C_update$',D: 'A_update$'] :
      ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'tensor_update$m' ) @ 'comp_update$l' ) )
      = ( D @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( C @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'tensor_update$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(386,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvr$' @ 'fun_app$at' ) )
      = ( B @ ( A @ 'fun_app$m' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).

thf(1895,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uvr$' @ 'fun_app$at' ) )
      = ( B @ ( A @ 'fun_app$m' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(476,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$x' ) )
     => ( A @ ( B @ 'comp$e' ) @ ( 'register$' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).

thf(2189,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$x' ) )
     => ( A @ ( B @ 'comp$e' ) @ ( 'register$' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(120,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$x' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( G @ ( E @ ( B @ 'comp$x' ) @ 'comp$x' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom693) ).

thf(926,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$x' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( G @ ( E @ ( B @ 'comp$x' ) @ 'comp$x' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(290,axiom,
    ! [A: 'B_update_d_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_a_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ar' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$j' ) ) ) )
     => ( ( G @ ( C @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( G @ ( E @ ( B @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$cg' ) @ 'comp$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom695) ).

thf(1563,plain,
    ! [A: 'B_update_d_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_a_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$ar' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$j' ) ) ) )
     => ( ( G @ ( C @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( G @ ( E @ ( B @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$cg' ) @ 'comp$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(45,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).

thf(657,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(489,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$k' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ab' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$r' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).

thf(2235,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$k' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ab' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$r' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(215,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$h' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bx' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).

thf(1278,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$h' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bx' ) )
      = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(315,axiom,
    ! [A: 'D_update_d_update_bool_fun_fun$',B: 'D_update_a_update_fun$',C: 'A_update_d_update_fun$',D: 'D_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$l' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$m' ) @ ( G @ ( C @ 'comp$cf' ) @ ( B @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( D @ 'conversep$c' @ ( E @ 'relcompp$l' ) @ ( D @ 'relcompp$k' ) @ 'quotient$m' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom675) ).

thf(1648,plain,
    ! [A: 'D_update_d_update_bool_fun_fun$',B: 'D_update_a_update_fun$',C: 'A_update_d_update_fun$',D: 'D_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$l' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$m' ) @ ( G @ ( C @ 'comp$cf' ) @ ( B @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( D @ 'conversep$c' @ ( E @ 'relcompp$l' ) @ ( D @ 'relcompp$k' ) @ 'quotient$m' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(128,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom648) ).

thf(965,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(346,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update_a_update_fun$',E: 'C_update_c_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bx' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).

thf(1764,plain,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update_a_update_fun$',E: 'C_update_c_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bx' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(470,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$b' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$s' ) )
        = ( D @ ( B @ 'comp$g' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$h' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).

thf(2176,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( D @ 'register$a' )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$b' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$s' ) )
        = ( D @ ( B @ 'comp$g' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(321,axiom,
    ! [A: 'C_update$',B: 'D_update$',C: 'C_update$',D: 'D_update$'] :
      ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'tensor_update$h' ) @ 'comp_update$m' @ 'fun_app$ce' ) )
      = ( D @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( C @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'tensor_update$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).

thf(1680,plain,
    ! [A: 'C_update$',B: 'D_update$',C: 'C_update$',D: 'D_update$'] :
      ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'tensor_update$h' ) @ 'comp_update$m' @ 'fun_app$ce' ) )
      = ( D @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( C @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'tensor_update$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(338,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$e' ) @ 'register$m' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).

thf(1747,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$e' ) @ 'register$m' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(300,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).

thf(1595,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(241,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$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).

thf(1374,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$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ 'comp$d' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(65,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_d_update_fun$',E: 'A_update_b_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$at' ) )
          = ( D @ ( C @ 'comp$x' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ 'comp$ao' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).

thf(733,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_d_update_fun$',E: 'A_update_b_update_fun$',F: 'D_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = F )
        & ( ( B @ ( A @ 'comp$at' ) )
          = ( D @ ( C @ 'comp$x' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ 'comp$ao' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(497,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$' ) @ 'register$h' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).

thf(2260,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_tensor$' ) @ 'register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(326,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_update_c_d_prod_update_fun$',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$cz' ) @ ( A @ 'fun_app$by' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).

thf(1698,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_update_c_d_prod_update_fun$',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$cz' ) @ ( A @ 'fun_app$by' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(407,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ 'comp$az' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).

thf(1959,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ 'comp$az' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(494,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( B @ 'register$b' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( A @ ( B @ 'comp$b' ) @ ( 'register$' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).

thf(2253,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_a_update_fun$'] :
      ( ( ( B @ 'register$b' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( A @ ( B @ 'comp$b' ) @ ( 'register$' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(429,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( 'id$' @ 'comp$d' ) ) )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).

thf(2033,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( 'id$' @ 'comp$d' ) ) )
     => ( ( D @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(463,axiom,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( 'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$a' ) @ 'preregister$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).

thf(2149,plain,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( 'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$a' ) @ 'preregister$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(199,axiom,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( 'uvv$' @ 'pred_fun$d' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvv$' @ 'pred_fun$e' ) @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).

thf(1219,plain,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvv$' @ 'pred_fun$e' ) @ 'fun_app$j' ) )
       => ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( 'uvv$' @ 'pred_fun$d' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( 'uvv$' @ 'pred_fun$d' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvv$' @ 'pred_fun$e' ) @ 'fun_app$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(92,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$q' ) )
    <=> ( ! [C: 'D_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).

thf(824,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( ! [C: 'D_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$g' )
          & ( A @ 'register$g' ) )
       => ( B @ ( A @ 'compatible$q' ) ) )
      & ( ( B @ ( A @ 'compatible$q' ) )
       => ( ! [C: 'D_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$g' )
          & ( A @ 'register$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(112,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uux$' @ 'fun_app$ba' ) )
      = ( B @ ( A @ 'fun_app$ac' ) @ ( 'id_update$a' @ 'tensor_update$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).

thf(904,plain,
    ! [A: 'A_update_c_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uux$' @ 'fun_app$ba' ) )
      = ( B @ ( A @ 'fun_app$ac' ) @ ( 'id_update$a' @ 'tensor_update$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(138,axiom,
    ! [A: 'A_update$'] :
      ( ( 'id_update$' @ ( A @ 'comp_update$' @ 'fun_app$bd' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).

thf(1007,plain,
    ! [A: 'A_update$'] :
      ( ( 'id_update$' @ ( A @ 'comp_update$' @ 'fun_app$bd' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(96,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'D_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$x' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$x' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom685) ).

thf(843,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'D_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$x' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$x' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(340,axiom,
    'id_update$' @ 'tensor_update$d' @ 'register$bi',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).

thf(1752,plain,
    'id_update$' @ 'tensor_update$d' @ 'register$bi',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(397,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'register_tensor$h' ) )
      = ( B @ 'uvi$' @ ( A @ 'uvg$' @ 'register_pair$w' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).

thf(1929,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'register_tensor$h' ) )
      = ( B @ 'uvi$' @ ( A @ 'uvg$' @ 'register_pair$w' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(68,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).

thf(743,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'D_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ ( A @ 'compatible$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(107,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$' @ ( B @ 'image$' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom641) ).

thf(875,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$' @ ( B @ 'image$' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(22,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun_a_update_a_update_fun_fun$',E: 'B_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$av' ) )
        = ( D @ ( C @ 'comp$av' ) ) )
     => ( ( E @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( E @ ( D @ 'fun_app$cr' ) @ ( C @ 'fun_app$co' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).

thf(579,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun_a_update_a_update_fun_fun$',E: 'B_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$av' ) )
        = ( D @ ( C @ 'comp$av' ) ) )
     => ( ( E @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( E @ ( D @ 'fun_app$cr' ) @ ( C @ 'fun_app$co' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(409,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvq$' @ 'fun_app$f' ) )
      = ( B @ ( A @ 'fun_app$ae' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).

thf(1965,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uvq$' @ 'fun_app$f' ) )
      = ( B @ ( A @ 'fun_app$ae' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(172,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$r' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$c' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).

thf(1124,plain,
    ! [A: 'B_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_b_update_fun$'] :
      ( ( ( C @ 'register$c' )
        & ( B @ ( A @ 'compatible$r' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$c' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(352,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'B_update_b_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( D @ 'comp$p' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).

thf(1784,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'B_update_b_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( C @ ( D @ 'comp$p' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(245,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ 'register$f' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( B @ ( C @ 'comp$ap' ) @ ( A @ ( C @ 'comp$c' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).

thf(1389,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'B_update_a_update_fun$'] :
      ( ( ( C @ 'register$f' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( B @ ( C @ 'comp$ap' ) @ ( A @ ( C @ 'comp$c' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(59,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bn' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).

thf(713,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_fun$c' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'comp$bn' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(204,axiom,
    ! [A: 'B_update$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).

thf(1239,plain,
    ! [A: 'B_update$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$'] :
      ( ( C @ ( B @ ( A @ 'uvs$' @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(435,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).

thf(2055,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(85,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'D_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$as' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$as' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom684) ).

thf(804,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_d_update_fun$',F: 'D_update_c_update_fun$',G: 'D_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'D_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
          = ( E @ ( I @ ( B @ 'comp$as' ) @ 'comp$y' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$a' @ ( F @ ( E @ 'type_definition$c' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$as' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(57,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom651) ).

thf(704,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_set$'] :
      ( ( D @ ( C @ 'image$a' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(236,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uvc$' @ 'fun_app$d' ) )
      = ( 'id_update$b' @ ( A @ 'tensor_update$b' @ 'fun_app$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).

thf(1356,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uvc$' @ 'fun_app$d' ) )
      = ( 'id_update$b' @ ( A @ 'tensor_update$b' @ 'fun_app$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(320,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'C_update_d_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ 'comp$an' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).

thf(1675,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_b_update_fun$',D: 'C_update_d_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = C )
     => ( ( D @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( C @ 'comp$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(40,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$i' ) )
     => ( A @ ( B @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).

thf(641,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$i' ) )
     => ( A @ ( B @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(465,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ 'uvp$' @ ( A @ 'uvq$' @ 'compatible$ao' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).

thf(2161,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ 'uvp$' @ ( A @ 'uvq$' @ 'compatible$ao' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(312,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$',F: 'A_update_b_update_fun$',G: 'C_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( G @ ( E @ ( B @ 'comp$e' ) @ 'comp$e' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom686) ).

thf(1635,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$',F: 'A_update_b_update_fun$',G: 'C_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$e' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( G @ ( E @ ( B @ 'comp$e' ) @ 'comp$e' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(336,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$c' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom634) ).

thf(1733,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$b' @ ( B @ 'image$b' ) @ ( F @ 'member$c' ) )
              & ( 'top$b' @ ( A @ 'image$b' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(152,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_update_c_d_prod_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$az' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).

thf(1058,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_update_c_d_prod_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$az' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(167,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uve$' @ 'fun_app$h' ) )
      = ( 'id_update$' @ ( A @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).

thf(1107,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'uve$' @ 'fun_app$h' ) )
      = ( 'id_update$' @ ( A @ 'tensor_update$d' @ 'fun_app$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(28,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$y' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$r' ) ) )
        = ( D @ ( B @ 'fun_app$bh' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).

thf(604,plain,
    ! [A: 'A_update_c_update_fun$',B: 'D_update_c_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$y' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$r' ) ) )
        = ( D @ ( B @ 'fun_app$bh' ) @ ( C @ ( A @ 'fun_app$ac' ) @ 'comp_update$c' @ 'fun_app$bx' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(440,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).

thf(2079,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(455,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$k' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$l' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).

thf(2119,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$k' ) @ ( B @ ( A @ 'register_pair$b' ) @ 'comp$l' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_pair$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(170,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$j' ) ) )
     => ( ( D @ ( C @ 'register_tensor$o' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$u' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$j' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).

thf(1117,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$j' ) ) )
     => ( ( D @ ( C @ 'register_tensor$o' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$u' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(293,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( B @ ( 'register$e' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).

thf(1574,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( B @ ( 'register$e' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(283,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvm$' @ 'fun_app$s' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$q' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).

thf(1524,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvm$' @ 'fun_app$s' ) )
      = ( 'id_update$' @ ( B @ ( A @ 'fun_app$q' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(149,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$j' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$aa' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).

thf(1048,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$j' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$aa' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register_tensor$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(332,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$f' ) @ 'register$n' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).

thf(1722,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$f' ) @ 'register$n' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(454,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$a' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$r' ) )
        = ( D @ ( B @ 'comp$d' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).

thf(2116,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'C_update_b_update_fun$'] :
      ( ( ( D @ 'register$c' )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$a' ) @ ( B @ ( A @ 'register_pair$e' ) @ 'comp$r' ) )
        = ( D @ ( B @ 'comp$d' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(66,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$c' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = 'top$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom633) ).

thf(737,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ( 'top$c' @ ( B @ 'image$f' ) )
          = 'top$d' )
        & ( ( 'top$a' @ ( A @ 'image$a' ) )
          = 'top$c' ) )
     => ( ( 'top$a' @ ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = 'top$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(292,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$p' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$cb' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$o' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).

thf(1571,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$p' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$cb' ) )
      = ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( C @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(50,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).

thf(681,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'A_update$',D: 'B_update$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(251,axiom,
    'id_update$' @ 'tensor_update$b' @ 'register$bg',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).

thf(1408,plain,
    'id_update$' @ 'tensor_update$b' @ 'register$bg',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(147,axiom,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$' ) @ ( 'uvx$' @ 'rel_fun$ak' ) )
      = ( B @ ( 'comp$' @ 'fun_app$bf' ) @ ( A @ 'uwa$' @ 'collect$f' @ 'grp$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom625) ).

thf(1043,plain,
    ! [A: 'A_update_set$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'grp$' ) @ ( 'uvx$' @ 'rel_fun$ak' ) )
      = ( B @ ( 'comp$' @ 'fun_app$bf' ) @ ( A @ 'uwa$' @ 'collect$f' @ 'grp$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(357,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) )
     => ( ( E @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$by' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).

thf(1801,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) )
     => ( ( E @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( E @ ( D @ 'fun_app$by' ) @ ( C @ 'fun_app$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(103,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).

thf(863,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( C @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
      = ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(438,axiom,
    ! [A: 'C_d_prod_update_a_update_fun_bool_fun$',B: 'C_d_prod_update_a_update_fun_bool_fun$'] :
      ( ! [C: 'C_d_prod_update_a_update_fun$'] :
          ( ( C @ ( A @ 'fun_app$i' ) )
        <=> ( C @ ( B @ 'fun_app$i' ) ) )
     => ( ( A @ 'collect$e' )
        = ( B @ 'collect$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).

thf(2065,plain,
    ! [A: 'C_d_prod_update_a_update_fun_bool_fun$',B: 'C_d_prod_update_a_update_fun_bool_fun$'] :
      ( ! [C: 'C_d_prod_update_a_update_fun$'] :
          ( ( ( C @ ( B @ 'fun_app$i' ) )
           => ( C @ ( A @ 'fun_app$i' ) ) )
          & ( ( C @ ( A @ 'fun_app$i' ) )
           => ( C @ ( B @ 'fun_app$i' ) ) ) )
     => ( ( A @ 'collect$e' )
        = ( B @ 'collect$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(89,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( A @ 'comp$h' ) @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).

thf(816,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$h' ) ) )
     => ( B @ ( C @ ( A @ 'comp$h' ) @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(310,axiom,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$al' ) )
     => ( A @ ( B @ 'comp$an' ) @ 'register$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).

thf(1630,plain,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$al' ) )
     => ( A @ ( B @ 'comp$an' ) @ 'register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(500,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$b' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).

thf(2267,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$b' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(56,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$at' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).

thf(700,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_d_update_fun$',C: 'A_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'A_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$am' ) )
          = F )
        & ( ( B @ ( A @ 'comp$x' ) )
          = ( D @ ( C @ 'comp$at' ) ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(288,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'D_update$',D: 'A_update_a_update_fun$',E: 'D_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$bh' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).

thf(1556,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'D_update$',D: 'A_update_a_update_fun$',E: 'D_update_a_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$bh' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(142,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$as' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).

thf(1022,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_c_update_fun$',C: 'D_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$as' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( C @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(187,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$i' ) ) )
     => ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).

thf(1177,plain,
    ! [A: 'C_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update_a_update_fun$'] :
      ( ( ( C @ ( 'register$e' @ 'fun_app$j' ) )
        & ( B @ ( A @ 'compatible$i' ) ) )
     => ( C @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(405,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$',C: 'C_update$'] :
      ( ( A @ 'register$c' )
     => ( ( C @ ( A @ 'fun_app$q' ) @ ( B @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).

thf(1952,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$',C: 'C_update$'] :
      ( ( A @ 'register$c' )
     => ( ( C @ ( A @ 'fun_app$q' ) @ ( B @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(361,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$'] :
              ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$ae' ) ) )
         => $false )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).

thf(1820,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$'] :
              ( ( E @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$u' ) @ ( C @ 'fun_app$ae' ) ) )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(335,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$t' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).

thf(1731,plain,
    ! [A: 'B_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$t' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(26,axiom,
    ! [A: 'A_update_set$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'uwc$' @ 'fun_app$j' ) )
    <=> ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).

thf(594,plain,
    ! [A: 'A_update_set$',B: 'D_update_a_update_fun$'] :
      ( ( ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$' ) )
       => ( B @ ( A @ 'uwc$' @ 'fun_app$j' ) ) )
      & ( ( B @ ( A @ 'uwc$' @ 'fun_app$j' ) )
       => ( A @ ( 'top$a' @ ( B @ 'image$a' ) @ 'less_eq$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(84,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).

thf(799,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$am' ) )
        = C )
     => ( ( D @ ( B @ 'comp$at' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(182,axiom,
    ! [A: 'A_update$',B: 'A_update$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$' @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
      = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'comp_update$' @ 'fun_app$bd' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).

thf(1162,plain,
    ! [A: 'A_update$',B: 'A_update$',C: 'A_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$' @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
      = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'comp_update$' @ 'fun_app$bd' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(35,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( A @ ( B @ 'compatible$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).

thf(626,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( A @ ( B @ 'compatible$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(116,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$',E: 'B_update_c_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$cr' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$co' ) )
      = ( E @ ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$l' ) @ 'fun_app$cq' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).

thf(915,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$',E: 'B_update_c_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$a' ) @ 'fun_app$cr' ) @ ( B @ ( A @ 'map_fun$k' ) @ 'fun_app$co' ) )
      = ( E @ ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_fun$l' ) @ 'fun_app$cq' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(396,axiom,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id_update$' @ 'comp_update$' @ 'fun_app$bd' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).

thf(1926,plain,
    ! [A: 'A_update$'] :
      ( ( A @ ( 'id_update$' @ 'comp_update$' @ 'fun_app$bd' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(74,axiom,
    ! [A: 'D_update_c_update_fun$'] :
      ( ( A @ 'register$s' )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$bh' ) )
        = 'id_update$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).

thf(768,plain,
    ! [A: 'D_update_c_update_fun$'] :
      ( ( A @ 'register$s' )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$bh' ) )
        = 'id_update$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(154,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'uus$' @ 'register$ay' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).

thf(1066,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'uus$' @ 'register$ay' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(29,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( C @ ( B @ 'comp$f' ) @ ( A @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).

thf(608,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( C @ ( B @ 'comp$f' ) @ ( A @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(269,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).

thf(1477,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(334,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).

thf(1726,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
        = ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(510,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( A @ ( 'preregister$a' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).

thf(2303,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( A @ ( 'preregister$a' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(325,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$g' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).

thf(1694,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'B_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$g' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$g' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(358,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).

thf(1805,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_set$',C: 'D_update_a_update_fun$',D: 'D_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$a' ) )
        = ( D @ ( C @ 'image$a' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) )
        = ( D @ ( C @ ( E @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(115,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id_update$c' @ 'comp_update$a' @ 'fun_app$x' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).

thf(912,plain,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'id_update$c' @ 'comp_update$a' @ 'fun_app$x' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(51,axiom,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$af' ) ) )
     => ( B @ ( C @ 'comp$ao' ) @ ( A @ ( C @ 'comp$an' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).

thf(685,plain,
    ! [A: 'C_update_d_update_fun$',B: 'D_update_d_update_fun$',C: 'D_update_b_update_fun$'] :
      ( ( ( C @ 'register$g' )
        & ( B @ ( A @ 'compatible$af' ) ) )
     => ( B @ ( C @ 'comp$ao' ) @ ( A @ ( C @ 'comp$an' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(5,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aw' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( D @ ( C @ 'fun_app$cs' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).

thf(521,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aw' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( D @ ( C @ 'fun_app$cs' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(185,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$o' ) )
      = ( D @ ( B @ 'map_prod$p' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$cb' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).

thf(1171,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'map_prod$o' ) )
      = ( D @ ( B @ 'map_prod$p' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$cb' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(369,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ 'comp$at' ) @ ( A @ ( C @ 'comp$b' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).

thf(1841,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_a_update_fun$'] :
      ( ( ( C @ 'register$b' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ 'comp$at' ) @ ( A @ ( C @ 'comp$b' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(247,axiom,
    ! [A: 'C_update_a_update_fun_set$'] :
      ( ( A @ 'uuf$' @ 'collect$f' )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).

thf(1396,plain,
    ! [A: 'C_update_a_update_fun_set$'] :
      ( ( A @ 'uuf$' @ 'collect$f' )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(486,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$d' ) @ 'fun_app$bp' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).

thf(2212,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$d' ) @ 'fun_app$bp' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(125,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( A @ ( B @ 'compatible$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).

thf(959,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( A @ ( B @ 'compatible$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(460,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_tensor$c' ) @ 'fun_app$bo' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).

thf(2139,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_tensor$c' ) @ 'fun_app$bo' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(108,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).

thf(883,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(145,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
              = ( E @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).

thf(1034,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$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
              = ( E @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) )
        & ( ( B @ ( A @ 'image$b' ) )
          = 'top$c' ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(359,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).

thf(1809,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(446,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvl$' @ ( A @ 'uvk$' @ 'compatible$ag' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom511) ).

thf(2096,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvl$' @ ( A @ 'uvk$' @ 'compatible$ag' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(343,axiom,
    ! [A: 'C_d_prod_update_b_update_fun$'] :
      ( ( A @ 'register$u' )
     => ( A @ 'preregister$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).

thf(1758,plain,
    ! [A: 'C_d_prod_update_b_update_fun$'] :
      ( ( A @ 'register$u' )
     => ( A @ 'preregister$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(194,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).

thf(1203,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(502,axiom,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( 'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).

thf(2271,plain,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( 'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$f' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(389,axiom,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uuo$' @ 'register$au' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).

thf(1905,plain,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uuo$' @ 'register$au' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(430,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_b_update_fun$',D: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).

thf(2037,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_b_update_fun$',D: 'C_d_prod_update$'] :
      ( ( ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( D @ ( C @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(457,axiom,
    ! [A: 'C_update_a_update_fun_set$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'uuf$' @ 'fun_app$k' ) )
    <=> ( A @ ( B @ 'member$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).

thf(2124,plain,
    ! [A: 'C_update_a_update_fun_set$',B: 'C_update_a_update_fun$'] :
      ( ( ( A @ ( B @ 'member$f' ) )
       => ( B @ ( A @ 'uuf$' @ 'fun_app$k' ) ) )
      & ( ( B @ ( A @ 'uuf$' @ 'fun_app$k' ) )
       => ( A @ ( B @ 'member$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(32,axiom,
    ! [A: 'D_update$'] :
      ( ( A @ ( 'id_update$a' @ 'comp_update$b' @ 'fun_app$bg' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).

thf(617,plain,
    ! [A: 'D_update$'] :
      ( ( A @ ( 'id_update$a' @ 'comp_update$b' @ 'fun_app$bg' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(231,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_d_prod_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) )
      = ( C @ ( B @ 'comp$bc' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).

thf(1340,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_d_prod_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$bb' ) )
      = ( C @ ( B @ 'comp$bc' ) @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(267,axiom,
    ! [A: 'C_update$'] :
      ( ( 'id_update$b' @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).

thf(1472,plain,
    ! [A: 'C_update$'] :
      ( ( 'id_update$b' @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(129,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'C_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$y' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$y' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom683) ).

thf(968,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'C_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$y' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$y' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(420,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( B @ ( A @ 'register_pair$' ) @ ( 'register$ae' @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).

thf(2005,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( B @ ( A @ 'register_pair$' ) @ ( 'register$ae' @ 'fun_app$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(254,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uuq$' @ 'fun_app$aw' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$a' @ 'tensor_update$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).

thf(1413,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uuq$' @ 'fun_app$aw' ) )
      = ( B @ ( A @ 'fun_app$u' ) @ ( 'id_update$a' @ 'tensor_update$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(62,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).

thf(722,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(403,axiom,
    ! [A: 'D_update_a_update_fun$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( A @ ( 'preregister$i' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).

thf(1948,plain,
    ! [A: 'D_update_a_update_fun$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( A @ ( 'preregister$i' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(224,axiom,
    ! [A: 'A_itself$',B: 'D_update_set$'] :
      ( ( B @ ( A @ 'separating$' ) )
    <=> ! [C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
          ( ( ! [E: 'D_update$'] :
                ( ( B @ ( E @ 'member$a' ) )
               => ( ( E @ ( C @ 'fun_app$au' ) )
                  = ( E @ ( D @ 'fun_app$au' ) ) ) )
            & ( D @ ( 'preregister$i' @ 'fun_app$j' ) )
            & ( C @ ( 'preregister$i' @ 'fun_app$j' ) ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).

thf(1304,plain,
    ! [A: 'A_itself$',B: 'D_update_set$'] :
      ( ( ! [C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
            ( ( ! [E: 'D_update$'] :
                  ( ( B @ ( E @ 'member$a' ) )
                 => ( ( E @ ( C @ 'fun_app$au' ) )
                    = ( E @ ( D @ 'fun_app$au' ) ) ) )
              & ( D @ ( 'preregister$i' @ 'fun_app$j' ) )
              & ( C @ ( 'preregister$i' @ 'fun_app$j' ) ) )
           => ( C = D ) )
       => ( B @ ( A @ 'separating$' ) ) )
      & ( ( B @ ( A @ 'separating$' ) )
       => ! [C: 'D_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
            ( ( ! [E: 'D_update$'] :
                  ( ( B @ ( E @ 'member$a' ) )
                 => ( ( E @ ( C @ 'fun_app$au' ) )
                    = ( E @ ( D @ 'fun_app$au' ) ) ) )
              & ( D @ ( 'preregister$i' @ 'fun_app$j' ) )
              & ( C @ ( 'preregister$i' @ 'fun_app$j' ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(379,axiom,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( 'uvu$' @ 'pred_fun$b' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvu$' @ 'pred_fun$c' ) @ 'fun_app$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).

thf(1873,plain,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvu$' @ 'pred_fun$c' ) @ 'fun_app$i' ) )
       => ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( 'uvu$' @ 'pred_fun$b' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( 'uvu$' @ 'pred_fun$b' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvu$' @ 'pred_fun$c' ) @ 'fun_app$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(141,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).

thf(1018,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(496,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$' ) @ 'fun_app$bl' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$d' @ 'fun_app$h' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).

thf(2256,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$' ) @ 'fun_app$bl' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$d' @ 'fun_app$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(286,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$as' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( G @ ( E @ ( B @ 'comp$as' ) @ 'comp$x' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom692) ).

thf(1547,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'D_update_a_update_fun$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_d_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$as' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) )
        = ( G @ ( E @ ( B @ 'comp$as' ) @ 'comp$x' ) @ ( A @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(356,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$g' ) )
      = ( D @ ( B @ 'map_prod$h' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bx' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).

thf(1798,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$g' ) )
      = ( D @ ( B @ 'map_prod$h' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bx' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(348,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$e' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).

thf(1770,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( A @ 'comp$e' ) @ 'compatible$' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(53,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uuo$' @ 'fun_app$n' ) )
      = ( 'id_update$c' @ ( B @ ( A @ 'fun_app$m' ) @ 'tensor_update$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).

thf(690,plain,
    ! [A: 'D_update_b_update_fun$',B: 'D_update$'] :
      ( ( B @ ( A @ 'uuo$' @ 'fun_app$n' ) )
      = ( 'id_update$c' @ ( B @ ( A @ 'fun_app$m' ) @ 'tensor_update$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(106,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_c_update_fun$',F: 'C_update_c_update_fun$',G: 'C_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'C_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$y' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$y' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom681) ).

thf(872,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'C_update_c_update_fun$',F: 'C_update_c_update_fun$',G: 'C_update_a_update_fun$',H: 'D_update_a_update_fun$',I: 'C_update_d_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$y' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( I @ ( H @ 'comp$y' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(109,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$c' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom636) ).

thf(887,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$a' @ ( B @ 'image$a' ) @ ( F @ 'member$c' ) )
              & ( 'top$a' @ ( A @ 'image$a' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(130,axiom,
    ! [A: 'B_update$',B: 'B_update$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$a' @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) )
      = ( C @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( A @ 'comp_update$a' @ 'fun_app$x' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).

thf(971,plain,
    ! [A: 'B_update$',B: 'B_update$',C: 'B_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$a' @ 'fun_app$x' ) @ 'comp_update$a' @ 'fun_app$x' ) )
      = ( C @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( A @ 'comp_update$a' @ 'fun_app$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(461,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).

thf(2143,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(303,axiom,
    ! [A: 'D_update_d_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( 'preregister$i' @ 'fun_app$j' ) )
        & ( A @ 'preregister$m' ) )
     => ( A @ ( B @ 'comp$x' ) @ ( 'preregister$i' @ 'fun_app$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom199) ).

thf(1605,plain,
    ! [A: 'D_update_d_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( 'preregister$i' @ 'fun_app$j' ) )
        & ( A @ 'preregister$m' ) )
     => ( A @ ( B @ 'comp$x' ) @ ( 'preregister$i' @ 'fun_app$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(401,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$ad' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'compatible$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).

thf(1941,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$ad' @ 'fun_app$j' ) ) )
     => ( B @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'compatible$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(351,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$ca' ) )
        = ( C @ ( A @ 'fun_app$x' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).

thf(1780,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$j' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$ca' ) )
        = ( C @ ( A @ 'fun_app$x' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(341,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'preregister$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).

thf(1753,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'preregister$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(200,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).

thf(1225,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(436,axiom,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'uur$' @ 'register$ax' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).

thf(2060,plain,
    ! [A: 'C_update_b_update_fun$'] :
      ( ( A @ 'register$c' )
     => ( A @ 'uur$' @ 'register$ax' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(58,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$' @ ( A @ 'image$' ) @ ( D @ 'member$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom638) ).

thf(707,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ! [D: 'A_update$'] :
          ( ( 'top$' @ ( A @ 'image$' ) @ ( D @ 'member$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(151,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$e' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).

thf(1053,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$e' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(444,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvg$' @ ( A @ 'uvi$' @ 'compatible$ai' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).

thf(2092,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvg$' @ ( A @ 'uvi$' @ 'compatible$ai' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(83,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom642) ).

thf(791,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ! [E: 'A_update$'] :
            ( ( 'top$a' @ ( B @ 'image$a' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( B @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(190,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$y' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( G @ ( E @ ( B @ 'comp$y' ) @ 'comp$e' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom687) ).

thf(1188,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'C_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$y' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
        = ( G @ ( E @ ( B @ 'comp$y' ) @ 'comp$e' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(377,axiom,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$g' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$g' ) @ ( G @ ( C @ 'comp$cd' ) @ ( B @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( D @ 'conversep$a' @ ( E @ 'relcompp$f' ) @ ( D @ 'relcompp$e' ) @ 'quotient$i' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom673) ).

thf(1869,plain,
    ! [A: 'C_update_c_update_bool_fun_fun$',B: 'C_update_a_update_fun$',C: 'A_update_c_update_fun$',D: 'C_update_a_update_bool_fun_fun$',E: 'A_update_a_update_bool_fun_fun$',F: 'A_update_b_update_fun$',G: 'B_update_a_update_fun$',H: 'A_update_b_update_bool_fun_fun$'] :
      ( ( ( H @ ( G @ ( F @ ( E @ 'quotient$h' ) ) ) )
        & ( D @ ( C @ ( B @ ( A @ 'quotient$g' ) ) ) ) )
     => ( H @ ( D @ 'relcompp$g' ) @ ( G @ ( C @ 'comp$cd' ) @ ( B @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( D @ 'conversep$a' @ ( E @ 'relcompp$f' ) @ ( D @ 'relcompp$e' ) @ 'quotient$i' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(95,axiom,
    ! [A: 'D_update$',B: 'D_update$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'comp_update$b' @ 'fun_app$bg' ) )
      = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).

thf(840,plain,
    ! [A: 'D_update$',B: 'D_update$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'comp_update$b' @ 'fun_app$bg' ) )
      = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(203,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$n' ) ) )
        = ( C @ ( A @ 'fun_app$az' ) @ ( D @ ( B @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).

thf(1235,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$n' ) ) )
        = ( C @ ( A @ 'fun_app$az' ) @ ( D @ ( B @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(345,axiom,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register$g',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).

thf(1763,plain,
    'h$' @ ( 'f$' @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'register$g',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(21,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
      = ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).

thf(576,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
      = ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(295,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).

thf(1579,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$',F: 'C_d_prod_update$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(41,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$',C: 'B_update$'] :
      ( ( A @ 'register$f' )
     => ( ( C @ ( A @ 'fun_app$az' ) @ ( B @ ( A @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( A @ 'fun_app$az' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).

thf(643,plain,
    ! [A: 'B_update_a_update_fun$',B: 'B_update$',C: 'B_update$'] :
      ( ( A @ 'register$f' )
     => ( ( C @ ( A @ 'fun_app$az' ) @ ( B @ ( A @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( A @ 'fun_app$az' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(258,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uvw$' ) @ ( 'uvu$' @ 'pred_fun$c' ) @ 'fun_app$i' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).

thf(1432,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( D @ ( C @ 'uvw$' ) @ ( 'uvu$' @ 'pred_fun$c' ) @ 'fun_app$i' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
        = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(467,axiom,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( A @ 'uuq$' @ 'register$aw' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).

thf(2165,plain,
    ! [A: 'C_update_a_update_fun$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( A @ 'uuq$' @ 'register$aw' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(504,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_tensor$b' ) @ 'fun_app$bn' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).

thf(2276,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update$',D: 'A_update$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$m' ) @ ( B @ ( A @ 'register_tensor$b' ) @ 'fun_app$bn' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(414,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).

thf(1980,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(11,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$i' ) @ 'fun_app$dv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).

thf(544,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$g' ) @ 'fun_app$dt' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_fun$i' ) @ 'fun_app$dv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(113,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( C @ ( B @ 'comp$h' ) @ ( A @ 'compatible$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).

thf(907,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( C @ ( B @ 'comp$h' ) @ ( A @ 'compatible$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(327,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).

thf(1702,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(339,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$o' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).

thf(1749,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'compatible$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(278,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$bx' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).

thf(1504,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$bx' ) @ ( A @ 'fun_app$u' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$bd' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(318,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: 'B_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$g' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).

thf(1670,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: 'B_update_b_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ 'comp$g' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$g' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(428,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvp$' @ 'fun_app$t' ) )
      = ( 'id_update$c' @ ( B @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).

thf(2030,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvp$' @ 'fun_app$t' ) )
      = ( 'id_update$c' @ ( B @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(19,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
      = ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).

thf(571,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
      = ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(387,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bg' ) @ ( D @ 'fun_app$au' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).

thf(1898,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'D_update_a_update_fun$',E: 'D_update_d_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bg' ) @ ( D @ 'fun_app$au' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$ao' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(372,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( C @ ( B @ 'comp$ar' ) @ ( A @ 'compatible$ac' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).

thf(1849,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
     => ( C @ ( B @ 'comp$ar' ) @ ( A @ 'compatible$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(235,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$b' ) @ 'comp$bh' ) )
      = ( C @ ( B @ 'comp$e' ) @ ( C @ ( A @ 'comp$e' ) @ 'convol$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).

thf(1353,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'convol$b' ) @ 'comp$bh' ) )
      = ( C @ ( B @ 'comp$e' ) @ ( C @ ( A @ 'comp$e' ) @ 'convol$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(27,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update$',D: 'A_update$'] :
      ( ( ! [E: 'D_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$m' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( ( D @ ( C @ 'tensor_update$j' ) @ ( B @ ( A @ 'register_pair$f' ) @ 'fun_app$cl' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).

thf(600,plain,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'D_update$',D: 'A_update$'] :
      ( ( ! [E: 'D_update$',F: 'A_update$'] :
            ( ( F @ ( B @ 'fun_app$ae' ) @ ( E @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$m' ) @ ( F @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( ( D @ ( C @ 'tensor_update$j' ) @ ( B @ ( A @ 'register_pair$f' ) @ 'fun_app$cl' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(272,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_c_update_fun$',E: 'A_update_b_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$at' ) )
          = ( D @ ( C @ 'comp$as' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ 'comp$al' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).

thf(1485,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_c_update_fun$',E: 'A_update_b_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( C @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$at' ) )
          = ( D @ ( C @ 'comp$as' ) ) ) )
     => ( ( B @ ( A @ ( E @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( F @ 'comp$al' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(412,axiom,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'uva$' @ 'fun_app$' ) )
      = ( 'id_update$' @ ( A @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).

thf(1972,plain,
    ! [A: 'B_update$'] :
      ( ( A @ ( 'uva$' @ 'fun_app$' ) )
      = ( 'id_update$' @ ( A @ 'tensor_update$' @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(163,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$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).

thf(1094,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$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( F @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(177,axiom,
    ! [A: 'C_update$',B: 'C_update$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'comp_update$c' @ 'fun_app$bx' ) )
      = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).

thf(1140,plain,
    ! [A: 'C_update$',B: 'C_update$',C: 'C_update$'] :
      ( ( C @ ( B @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) @ 'comp_update$c' @ 'fun_app$bx' ) )
      = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'comp_update$c' @ 'fun_app$bx' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(368,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( A @ ( B @ 'compatible$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).

thf(1839,plain,
    ! [A: 'A_update_b_update_fun$',B: 'B_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( A @ ( B @ 'compatible$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(265,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$c' ) )
      = ( D @ ( B @ 'map_prod$d' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bv' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).

thf(1459,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$'] :
      ( ( D @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_prod$c' ) )
      = ( D @ ( B @ 'map_prod$d' ) @ ( C @ ( A @ 'map_prod$' ) @ 'comp$bv' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(15,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( ! [E: 'B_update_d_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
              = ( E @ ( D @ 'fun_app$cp' ) @ ( C @ 'fun_app$ct' ) ) )
         => $false )
        & ( ( B @ ( A @ 'comp$ax' ) )
          = ( D @ ( C @ 'comp$ax' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).

thf(556,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ~ ( ~ ! [E: 'B_update_d_update_fun$'] :
              ( ( E @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
              = ( E @ ( D @ 'fun_app$cp' ) @ ( C @ 'fun_app$ct' ) ) )
        & ( ( B @ ( A @ 'comp$ax' ) )
          = ( D @ ( C @ 'comp$ax' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(47,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uuy$' @ 'fun_app$bc' ) )
      = ( B @ ( A @ 'fun_app$bd' ) @ ( 'id_update$a' @ 'tensor_update$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).

thf(671,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update$'] :
      ( ( B @ ( A @ 'uuy$' @ 'fun_app$bc' ) )
      = ( B @ ( A @ 'fun_app$bd' ) @ ( 'id_update$a' @ 'tensor_update$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(513,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
    <=> ( ! [C: 'C_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$e' @ 'fun_app$j' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).

thf(2310,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( ( ! [C: 'C_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
              = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
          & ( B @ ( 'register$e' @ 'fun_app$j' ) )
          & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
       => ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) ) )
      & ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
       => ( ! [C: 'C_update$',D: 'D_update$'] :
              ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
              = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
          & ( B @ ( 'register$e' @ 'fun_app$j' ) )
          & ( A @ ( 'register$' @ 'fun_app$k' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(478,axiom,
    'h$' @ ( 'g$' @ 'compatible$' @ 'fun_app$j' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).

thf(2194,plain,
    'h$' @ ( 'g$' @ 'compatible$' @ 'fun_app$j' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(281,axiom,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$n' ) ) )
        = ( D @ ( B @ 'fun_app$bd' ) @ ( C @ ( A @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).

thf(1517,plain,
    ! [A: 'B_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update$',D: 'A_update$'] :
      ( ( B @ ( A @ 'compatible$l' ) )
     => ( ( D @ ( C @ 'tensor_update$' @ 'fun_app$a' ) @ ( B @ ( A @ 'register_pair$n' ) ) )
        = ( D @ ( B @ 'fun_app$bd' ) @ ( C @ ( A @ 'fun_app$az' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(173,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( C @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).

thf(1126,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update$',D: 'A_update_b_update_fun$',E: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$by' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$by' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) )
        = ( C @ ( E @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'fun_app$bz' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(475,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvn$' @ ( A @ 'uvi$' @ 'compatible$aj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).

thf(2187,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvn$' @ ( A @ 'uvi$' @ 'compatible$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(75,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
      = ( 'top$' @ ( B @ 'image$' ) @ ( A @ 'image$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom644) ).

thf(771,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'top$' @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) )
      = ( 'top$' @ ( B @ 'image$' ) @ ( A @ 'image$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(256,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$l' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bz' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom576) ).

thf(1421,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( D @ ( C @ 'map_prod$l' ) @ ( B @ ( A @ 'map_prod$' ) @ 'comp$bz' ) )
      = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'map_prod$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(423,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bh' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).

thf(2013,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'C_update_a_update_fun$',E: 'D_update_c_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$bh' ) @ ( D @ 'fun_app$u' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(121,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).

thf(931,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$f' ) )
     => ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
        = ( C @ ( A @ 'fun_app$q' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(10,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ax' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( D @ ( C @ 'fun_app$cv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).

thf(539,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun_c_update_b_update_fun_fun$',D: 'B_update_d_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$ax' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( D @ ( C @ 'fun_app$cv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(225,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).

thf(1321,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(366,axiom,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$x' ) )
     => ( A @ ( B @ 'comp$f' ) @ 'register$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).

thf(1834,plain,
    ! [A: 'C_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$x' ) )
     => ( A @ ( B @ 'comp$f' ) @ 'register$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(451,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) ) )
     => ( B @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$n' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).

thf(2110,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) ) )
     => ( B @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'compatible$n' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(139,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'D_update$',C: 'D_update$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( ( C @ ( A @ 'fun_app$au' ) @ ( B @ ( A @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'fun_app$au' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).

thf(1010,plain,
    ! [A: 'D_update_a_update_fun$',B: 'D_update$',C: 'D_update$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( ( C @ ( A @ 'fun_app$au' ) @ ( B @ ( A @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$b' @ 'fun_app$bg' ) @ ( A @ 'fun_app$au' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(511,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ 'uvi$' @ ( A @ 'uvm$' @ 'compatible$ah' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).

thf(2305,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$c' ) )
     => ( B @ 'uvi$' @ ( A @ 'uvm$' @ 'compatible$ah' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(298,axiom,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'uul$' @ 'register$ar' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).

thf(1590,plain,
    ! [A: 'A_update_c_update_fun$'] :
      ( ( A @ 'register$w' )
     => ( A @ 'uul$' @ 'register$ar' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(468,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$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ad' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).

thf(2167,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$' @ 'fun_app$k' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ad' ) )
        = ( D @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(506,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_tensor$h' ) @ 'fun_app$bt' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).

thf(2283,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'A_update$',D: 'C_update$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_update$b' @ 'fun_app$e' ) @ ( B @ ( A @ 'register_tensor$h' ) @ 'fun_app$bt' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'tensor_update$' @ 'fun_app$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(447,axiom,
    'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register$c',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).

thf(2098,plain,
    'g$' @ ( 'f$' @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register$c',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(319,axiom,
    'id_update$' @ 'tensor_update$c' @ 'register$bh',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).

thf(1674,plain,
    'id_update$' @ 'tensor_update$c' @ 'register$bh',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(279,axiom,
    ! [A: 'C_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$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).

thf(1508,plain,
    ! [A: 'C_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$c' ) )
         => ( ( D @ ( B @ 'fun_app$ae' ) )
            = ( D @ ( C @ 'fun_app$ae' ) ) ) )
     => ( ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(123,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$l' ) @ 'register$aa' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).

thf(946,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$l' ) @ 'register$aa' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(37,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).

thf(632,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(374,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$y' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( G @ ( E @ ( B @ 'comp$y' ) @ 'comp$as' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom689) ).

thf(1854,plain,
    ! [A: 'A_update_d_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$',G: 'D_update_c_update_fun$'] :
      ( ( ( C
          = ( E @ ( D @ 'comp$y' ) ) )
        & ( 'top$a' @ ( B @ ( A @ 'type_definition$h' ) ) ) )
     => ( ( G @ ( C @ ( F @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
        = ( G @ ( E @ ( B @ 'comp$y' ) @ 'comp$as' ) @ ( A @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$h' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(458,axiom,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( 'uvt$' @ 'pred_fun$' ) ) )
    <=> ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvt$' @ 'pred_fun$a' ) @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).

thf(2130,plain,
    ! [A: 'B_update_bool_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvt$' @ 'pred_fun$a' ) @ 'fun_app$k' ) )
       => ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( 'uvt$' @ 'pred_fun$' ) ) ) )
      & ( ( C @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ ( A @ ( 'uvt$' @ 'pred_fun$' ) ) )
       => ( C @ ( B @ ( A @ 'comp$bt' ) @ ( 'uvt$' @ 'pred_fun$a' ) @ 'fun_app$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(79,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$o' ) ) )
     => ( C @ ( B @ 'comp$h' ) @ ( A @ 'compatible$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).

thf(781,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update_d_update_fun$'] :
      ( ( ( C @ 'register$v' )
        & ( B @ ( A @ 'compatible$o' ) ) )
     => ( C @ ( B @ 'comp$h' ) @ ( A @ 'compatible$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(498,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_pair$s' ) @ 'register$af' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).

thf(2262,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ ( A @ 'register_pair$s' ) @ 'register$af' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(126,axiom,
    'uve$' @ 'register$bi',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).

thf(961,plain,
    'uve$' @ 'register$bi',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(88,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom647) ).

thf(813,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(18,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$ct' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$d' ) @ 'fun_app$cs' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).

thf(568,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'C_d_prod_update_a_update_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( E @ ( D @ ( C @ 'map_fun$c' ) @ 'fun_app$cu' ) @ ( B @ ( A @ 'map_fun$' ) @ 'fun_app$ct' ) )
      = ( E @ ( D @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'map_fun$d' ) @ 'fun_app$cs' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(260,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$y' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( E @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).

thf(1440,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$y' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
          = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) )
     => ( ( E @ ( B @ 'comp$y' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(480,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( A @ ( 'register$' @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).

thf(2198,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( A @ ( 'register$' @ 'fun_app$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(191,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$w' )
        & ( B @ ( A @ 'compatible$n' ) ) )
     => ( B @ ( C @ ( A @ 'comp$i' ) @ 'compatible$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).

thf(1193,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'A_update_c_update_fun$'] :
      ( ( ( C @ 'register$w' )
        & ( B @ ( A @ 'compatible$n' ) ) )
     => ( B @ ( C @ ( A @ 'comp$i' ) @ 'compatible$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(304,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).

thf(1607,plain,
    ! [A: 'D_update_a_update_fun$',B: 'C_update_d_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$y' ) )
        = C )
     => ( ( B @ ( A @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(385,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$b' )
        & ( A @ 'preregister$g' ) )
     => ( A @ ( B @ 'comp$i' ) @ 'preregister$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).

thf(1893,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$b' )
        & ( A @ 'preregister$g' ) )
     => ( A @ ( B @ 'comp$i' ) @ 'preregister$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(261,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$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).

thf(1444,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$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$ae' ) )
        = ( C @ ( E @ 'fun_app$u' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(9,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$',D: 'A_update_a_update_fun_c_update_b_update_fun_fun$',E: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( C @ ( E @ 'fun_app$cp' ) @ ( D @ 'fun_app$ct' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
        = ( C @ ( E @ ( D @ 'comp$ax' ) @ 'fun_app$cv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).

thf(536,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_d_update_fun_a_update_a_update_fun_fun$',C: 'B_update_d_update_fun$',D: 'A_update_a_update_fun_c_update_b_update_fun_fun$',E: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$cp' ) @ ( A @ 'fun_app$ct' ) )
        = ( C @ ( E @ 'fun_app$cp' ) @ ( D @ 'fun_app$ct' ) ) )
     => ( ( C @ ( B @ ( A @ 'comp$ax' ) @ 'fun_app$cv' ) )
        = ( C @ ( E @ ( D @ 'comp$ax' ) @ 'fun_app$cv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(144,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_d_prod_update_a_update_fun$',F: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$bd' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).

thf(1030,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_d_prod_update_a_update_fun$',F: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$bd' ) )
          = F )
        & ( ( B @ ( A @ 'comp$g' ) )
          = ( D @ ( C @ 'comp$am' ) ) ) )
     => ( ( E @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ ( A @ 'comp$v' ) )
        = ( F @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(274,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: 'D_update_c_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$as' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( E @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).

thf(1491,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: 'D_update_c_update_fun$',F: 'D_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$as' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( E @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( F @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(473,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$a' @ 'fun_app$k' ) ) )
     => ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'preregister$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).

thf(2183,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$a' @ 'fun_app$k' ) ) )
     => ( A @ ( B @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'preregister$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(197,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).

thf(1212,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_a_update_fun$',C: 'C_update_a_update_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
      = ( C @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(60,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).

thf(716,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update_set$'] :
      ( ( C @ ( B @ 'image$a' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'image$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(306,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ! [E: 'C_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$q' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'fun_app$cg' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).

thf(1614,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ! [E: 'C_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$q' ) @ ( E @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( E @ ( A @ 'fun_app$q' ) @ ( F @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'fun_app$cg' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(495,axiom,
    'h$' @ ( 'g$' @ 'register_pair$' ) @ ( 'f$' @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'preregister$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).

thf(2255,plain,
    'h$' @ ( 'g$' @ 'register_pair$' ) @ ( 'f$' @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'preregister$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(164,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$j' @ 'fun_app$i' ) ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'preregister$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).

thf(1097,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$j' @ 'fun_app$i' ) ) )
     => ( A @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'preregister$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(309,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).

thf(1625,plain,
    ! [A: 'B_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'A_update_b_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$g' ) )
        = C )
     => ( ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( A @ 'comp$p' ) )
        = ( D @ ( C @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(90,axiom,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) @ ( A @ 'fun_app$dy' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom650) ).

thf(818,plain,
    ! [A: 'B_update_set_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$'] :
      ( ( D @ ( C @ 'image$' ) @ ( B @ 'image$f' ) @ ( A @ 'fun_app$dy' ) )
      = ( D @ ( C @ ( B @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) @ ( A @ 'fun_app$dy' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(100,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$j' ) @ 'register$z' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).

thf(854,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'D_update$'] :
            ( ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$j' ) @ 'register$z' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(284,axiom,
    ! [A: 'B_itself$',B: 'A_update_set$'] :
      ( ( B @ ( A @ 'separating$d' ) )
    <=> ! [C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
          ( ( ! [E: 'A_update$'] :
                ( ( B @ ( E @ 'member$c' ) )
               => ( ( E @ ( C @ 'fun_app$ae' ) )
                  = ( E @ ( D @ 'fun_app$ae' ) ) ) )
            & ( D @ 'preregister$c' )
            & ( C @ 'preregister$c' ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).

thf(1527,plain,
    ! [A: 'B_itself$',B: 'A_update_set$'] :
      ( ( ! [C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
            ( ( ! [E: 'A_update$'] :
                  ( ( B @ ( E @ 'member$c' ) )
                 => ( ( E @ ( C @ 'fun_app$ae' ) )
                    = ( E @ ( D @ 'fun_app$ae' ) ) ) )
              & ( D @ 'preregister$c' )
              & ( C @ 'preregister$c' ) )
           => ( C = D ) )
       => ( B @ ( A @ 'separating$d' ) ) )
      & ( ( B @ ( A @ 'separating$d' ) )
       => ! [C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
            ( ( ! [E: 'A_update$'] :
                  ( ( B @ ( E @ 'member$c' ) )
                 => ( ( E @ ( C @ 'fun_app$ae' ) )
                    = ( E @ ( D @ 'fun_app$ae' ) ) ) )
              & ( D @ 'preregister$c' )
              & ( C @ 'preregister$c' ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(433,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$g' ) @ 'register$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).

thf(2050,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$c' ) )
     => ( B @ ( A @ 'register_tensor$g' ) @ 'register$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(270,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( B @ ( C @ ( A @ 'comp$f' ) @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).

thf(1480,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( ( C @ 'register$x' )
        & ( B @ ( A @ 'compatible$f' ) ) )
     => ( B @ ( C @ ( A @ 'comp$f' ) @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(488,axiom,
    ! [A: 'A_itself$',B: 'C_update_set$'] :
      ( ( B @ ( A @ 'separating$b' ) )
    <=> ! [C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
          ( ( ! [E: 'C_update$'] :
                ( ( B @ ( E @ 'member$b' ) )
               => ( ( E @ ( C @ 'fun_app$u' ) )
                  = ( E @ ( D @ 'fun_app$u' ) ) ) )
            & ( D @ ( 'preregister$a' @ 'fun_app$k' ) )
            & ( C @ ( 'preregister$a' @ 'fun_app$k' ) ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).

thf(2218,plain,
    ! [A: 'A_itself$',B: 'C_update_set$'] :
      ( ( ! [C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
            ( ( ! [E: 'C_update$'] :
                  ( ( B @ ( E @ 'member$b' ) )
                 => ( ( E @ ( C @ 'fun_app$u' ) )
                    = ( E @ ( D @ 'fun_app$u' ) ) ) )
              & ( D @ ( 'preregister$a' @ 'fun_app$k' ) )
              & ( C @ ( 'preregister$a' @ 'fun_app$k' ) ) )
           => ( C = D ) )
       => ( B @ ( A @ 'separating$b' ) ) )
      & ( ( B @ ( A @ 'separating$b' ) )
       => ! [C: 'C_update_a_update_fun$',D: 'C_update_a_update_fun$'] :
            ( ( ! [E: 'C_update$'] :
                  ( ( B @ ( E @ 'member$b' ) )
                 => ( ( E @ ( C @ 'fun_app$u' ) )
                    = ( E @ ( D @ 'fun_app$u' ) ) ) )
              & ( D @ ( 'preregister$a' @ 'fun_app$k' ) )
              & ( C @ ( 'preregister$a' @ 'fun_app$k' ) ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(175,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'C_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$e' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$e' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom682) ).

thf(1133,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_a_update_fun$',C: 'B_update_a_update_fun$',D: 'A_update_b_update_fun$',E: 'D_update_c_update_fun$',F: 'C_update_d_update_fun$',G: 'C_update_a_update_fun$',H: 'C_update_a_update_fun$',I: 'C_update_c_update_fun$'] :
      ( ( ( ( E @ ( G @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$al' ) )
          = ( E @ ( I @ ( B @ 'comp$e' ) @ 'comp$as' ) @ ( A @ ( H @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$i' ) @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$d' ) ) )
        & ( 'top$c' @ ( D @ ( C @ 'type_definition$g' ) ) )
        & ( 'top$b' @ ( B @ ( A @ 'type_definition$f' ) ) ) )
     => ( ( I @ ( H @ 'comp$e' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(507,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) )
    <=> ( ! [C: 'C_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).

thf(2287,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( ! [C: 'C_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
              = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
          & ( B @ ( 'register$' @ 'fun_app$k' ) )
          & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
       => ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) ) )
      & ( ( B @ ( A @ 'compatible$m' @ 'fun_app$k' ) )
       => ( ! [C: 'C_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
              = ( C @ ( A @ 'fun_app$u' ) @ ( D @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
          & ( B @ ( 'register$' @ 'fun_app$k' ) )
          & ( A @ ( 'register$' @ 'fun_app$k' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(33,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_set$'] :
      ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).

thf(620,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_d_prod_update_set$'] :
      ( ( C @ ( B @ 'image$' ) @ ( A @ 'image$f' ) )
      = ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(449,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$a' ) @ 'fun_app$bm' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).

thf(2102,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$a' ) @ 'fun_app$bm' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'tensor_update$c' @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(70,axiom,
    ! [A: 'A_update_d_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$v' )
     => ( ( C @ ( A @ 'fun_app$aa' ) @ ( B @ ( A @ 'fun_app$aa' ) @ 'comp_update$b' @ 'fun_app$bg' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$aa' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).

thf(752,plain,
    ! [A: 'A_update_d_update_fun$',B: 'A_update$',C: 'A_update$'] :
      ( ( A @ 'register$v' )
     => ( ( C @ ( A @ 'fun_app$aa' ) @ ( B @ ( A @ 'fun_app$aa' ) @ 'comp_update$b' @ 'fun_app$bg' ) )
        = ( C @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( A @ 'fun_app$aa' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(238,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'register_tensor$o' ) )
      = ( B @ 'uvh$' @ ( A @ 'uvg$' @ 'register_pair$u' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).

thf(1363,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'register_tensor$o' ) )
      = ( B @ 'uvh$' @ ( A @ 'uvg$' @ 'register_pair$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(275,axiom,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'register$b' )
     => ( A @ 'preregister$h' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).

thf(1495,plain,
    ! [A: 'A_update_a_update_fun$'] :
      ( ( A @ 'register$b' )
     => ( A @ 'preregister$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(86,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$ac' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).

thf(807,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ! [C: 'A_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_pair$b' ) @ 'register$ac' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(253,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
      = ( C @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).

thf(1410,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_c_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'comp$f' ) )
      = ( C @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(353,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).

thf(1789,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$',D: 'A_update_b_update_fun$',E: 'D_update_a_update_fun$',F: 'D_update$'] :
      ( ( ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) )
        = ( F @ ( E @ 'fun_app$au' ) @ ( D @ 'fun_app$ae' ) ) )
     => ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
        = ( F @ ( E @ ( D @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(218,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_tensor$g' ) @ 'fun_app$bs' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).

thf(1288,plain,
    ! [A: 'C_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_tensor$g' ) @ 'fun_app$bs' ) )
        = ( D @ ( B @ 'fun_app$m' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(38,axiom,
    ! [A: 'D_update$',B: 'A_update$',C: 'D_update$',D: 'A_update$'] :
      ( ( D @ ( C @ 'tensor_update$j' ) @ ( B @ ( A @ 'tensor_update$j' ) @ 'comp_update$h' ) )
      = ( D @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( C @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'tensor_update$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).

thf(635,plain,
    ! [A: 'D_update$',B: 'A_update$',C: 'D_update$',D: 'A_update$'] :
      ( ( D @ ( C @ 'tensor_update$j' ) @ ( B @ ( A @ 'tensor_update$j' ) @ 'comp_update$h' ) )
      = ( D @ ( B @ 'comp_update$' @ 'fun_app$bd' ) @ ( C @ ( A @ 'comp_update$b' @ 'fun_app$bg' ) @ 'tensor_update$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(8,axiom,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aw' ) )
        = ( D @ ( C @ 'comp$aw' ) ) )
     => ( ( E @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( E @ ( D @ 'fun_app$cu' ) @ ( C @ 'fun_app$ct' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).

thf(532,plain,
    ! [A: 'A_update_a_update_fun_c_update_b_update_fun_fun$',B: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',C: 'A_update_a_update_fun_c_update_b_update_fun_fun$',D: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',E: 'B_update_c_d_prod_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$aw' ) )
        = ( D @ ( C @ 'comp$aw' ) ) )
     => ( ( E @ ( B @ 'fun_app$cu' ) @ ( A @ 'fun_app$ct' ) )
        = ( E @ ( D @ 'fun_app$cu' ) @ ( C @ 'fun_app$ct' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(55,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).

thf(696,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_b_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$o' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$j' ) @ 'fun_app$cd' ) )
        = ( C @ ( A @ 'fun_app$ae' ) @ ( D @ ( B @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(183,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'fun_app$cc' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).

thf(1165,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$a' @ 'fun_app$c' ) @ ( B @ ( A @ 'register_pair$k' ) @ 'fun_app$cc' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(259,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_c_update_fun$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$e' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( E @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).

thf(1436,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_c_update_fun$',F: 'C_update_a_update_fun$'] :
      ( ( ( ( E @ ( D @ 'comp$e' ) )
          = F )
        & ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = ( D @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) )
     => ( ( E @ ( B @ 'comp$e' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(375,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'D_update_c_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ 'comp$al' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).

thf(1859,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_b_update_fun$',D: 'D_update_c_update_fun$'] :
      ( ( ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = C )
     => ( ( D @ ( B @ 'comp$as' ) @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) )
        = ( D @ ( C @ 'comp$al' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(481,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvq$' @ ( A @ 'uvp$' @ 'compatible$aq' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).

thf(2201,plain,
    ! [A: 'C_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( B @ 'uvq$' @ ( A @ 'uvp$' @ 'compatible$aq' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(117,axiom,
    ! [A: 'B_update$'] :
      ( ( 'id_update$c' @ ( A @ 'comp_update$a' @ 'fun_app$x' ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).

thf(918,plain,
    ! [A: 'B_update$'] :
      ( ( 'id_update$c' @ ( A @ 'comp_update$a' @ 'fun_app$x' ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(417,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$p' ) )
    <=> ( ! [C: 'D_update$',D: 'A_update$'] :
            ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).

thf(1989,plain,
    ! [A: 'D_update_b_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( ! [C: 'D_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$g' ) )
       => ( B @ ( A @ 'compatible$p' ) ) )
      & ( ( B @ ( A @ 'compatible$p' ) )
       => ( ! [C: 'D_update$',D: 'A_update$'] :
              ( ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$ae' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$a' )
          & ( A @ 'register$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(67,axiom,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$m' ) )
        = 'id_update$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).

thf(740,plain,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$m' ) )
        = 'id_update$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(134,axiom,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( B @ ( A @ 'compatible$h' ) )
    <=> ( ! [C: 'D_update$',D: 'C_update$'] :
            ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
            = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
        & ( B @ 'register$c' )
        & ( A @ 'register$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).

thf(987,plain,
    ! [A: 'D_update_b_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( ! [C: 'D_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$g' ) )
       => ( B @ ( A @ 'compatible$h' ) ) )
      & ( ( B @ ( A @ 'compatible$h' ) )
       => ( ! [C: 'D_update$',D: 'C_update$'] :
              ( ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$m' ) @ 'comp_update$a' @ 'fun_app$x' ) )
              = ( C @ ( A @ 'fun_app$m' ) @ ( D @ ( B @ 'fun_app$q' ) @ 'comp_update$a' @ 'fun_app$x' ) ) )
          & ( B @ 'register$c' )
          & ( A @ 'register$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(212,axiom,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$u' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).

thf(1268,plain,
    ! [A: 'B_update_b_update_fun$',B: 'B_update_b_update_fun$',C: 'A_update_b_update_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$u' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(102,axiom,
    ! [A: 'B_update$',B: 'B_update$',C: 'B_update$',D: 'B_update$'] :
      ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'tensor_update$f' ) @ 'comp_update$d' ) )
      = ( D @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( C @ ( A @ 'comp_update$a' @ 'fun_app$x' ) @ 'tensor_update$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).

thf(860,plain,
    ! [A: 'B_update$',B: 'B_update$',C: 'B_update$',D: 'B_update$'] :
      ( ( D @ ( C @ 'tensor_update$f' ) @ ( B @ ( A @ 'tensor_update$f' ) @ 'comp_update$d' ) )
      = ( D @ ( B @ 'comp_update$a' @ 'fun_app$x' ) @ ( C @ ( A @ 'comp_update$a' @ 'fun_app$x' ) @ 'tensor_update$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(137,axiom,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( ( 'id_update$' @ ( A @ 'fun_app$ae' ) )
        = 'id_update$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).

thf(1004,plain,
    ! [A: 'A_update_b_update_fun$'] :
      ( ( A @ 'register$a' )
     => ( ( 'id_update$' @ ( A @ 'fun_app$ae' ) )
        = 'id_update$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(222,axiom,
    ! [A: 'D_update_a_update_fun$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$au' ) )
        = 'id_update$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).

thf(1299,plain,
    ! [A: 'D_update_a_update_fun$'] :
      ( ( A @ ( 'register$e' @ 'fun_app$j' ) )
     => ( ( 'id_update$a' @ ( A @ 'fun_app$au' ) )
        = 'id_update$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(388,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvo$' @ 'fun_app$t' ) )
      = ( B @ ( A @ 'fun_app$q' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).

thf(1902,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update$'] :
      ( ( B @ ( A @ 'uvo$' @ 'fun_app$t' ) )
      = ( B @ ( A @ 'fun_app$q' ) @ ( 'id_update$' @ 'tensor_update$c' @ 'fun_app$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(382,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( B @ ( A @ 'register_pair$k' ) @ 'register$y' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).

thf(1885,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( B @ ( A @ 'register_pair$k' ) @ 'register$y' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(171,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).

thf(1120,plain,
    ! [A: 'A_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'A_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$d' @ 'fun_app$j' ) )
     => ( ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$bd' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( A @ 'fun_app$bd' ) @ ( D @ ( B @ 'fun_app$au' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(364,axiom,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$w' ) )
     => ( A @ ( B @ 'comp$i' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).

thf(1829,plain,
    ! [A: 'A_update_c_update_fun$',B: 'C_update_b_update_fun$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$w' ) )
     => ( A @ ( B @ 'comp$i' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(174,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$cx' ) @ ( D @ 'fun_app$au' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) @ 'fun_app$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).

thf(1129,plain,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'D_update_a_update_fun$',E: 'C_update_d_update_fun$',F: 'A_update_b_update_fun$'] :
      ( ( ( C @ ( B @ 'fun_app$u' ) @ ( A @ 'fun_app$bd' ) )
        = ( C @ ( E @ 'fun_app$cx' ) @ ( D @ 'fun_app$au' ) ) )
     => ( ( C @ ( B @ ( A @ ( F @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'fun_app$q' ) )
        = ( C @ ( E @ ( D @ ( F @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'comp$an' ) @ 'fun_app$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(363,axiom,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uut$' @ 'register$az' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).

thf(1827,plain,
    ! [A: 'D_update_b_update_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'uut$' @ 'register$az' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(209,axiom,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$i' @ 'fun_app$j' ) ) )
     => ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'preregister$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).

thf(1261,plain,
    ! [A: 'D_update_a_update_fun$',B: 'A_update_b_update_fun$'] :
      ( ( ( B @ 'preregister$c' )
        & ( A @ ( 'preregister$i' @ 'fun_app$j' ) ) )
     => ( A @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'preregister$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(296,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).

thf(1582,plain,
    ! [A: 'C_update_a_update_fun$',B: 'D_update_a_update_fun$',C: 'C_update$',D: 'D_update$'] :
      ( ( B @ ( A @ 'compatible$' @ 'fun_app$j' ) )
     => ( ( D @ ( C @ 'tensor_update$h' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$by' ) )
        = ( D @ ( B @ 'fun_app$au' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(499,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ 'uvi$' @ ( A @ 'uvg$' @ 'compatible$as' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).

thf(2265,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ 'register$a' ) )
     => ( B @ 'uvi$' @ ( A @ 'uvg$' @ 'compatible$as' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(248,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom643) ).

thf(1399,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_update_a_update_fun$'] :
      ( ( 'top$b' @ ( B @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
      = ( 'top$b' @ ( B @ 'image$b' ) @ ( A @ 'image$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(308,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).

thf(1621,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_set$',C: 'C_d_prod_update_a_update_fun$',D: 'C_d_prod_update_set$',E: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'image$b' ) )
        = ( D @ ( C @ 'image$' ) ) )
     => ( ( B @ ( A @ ( E @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'image$c' ) )
        = ( D @ ( C @ ( E @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'image$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(317,axiom,
    ! [A: 'B_itself$',B: 'C_update_set$'] :
      ( ( B @ ( A @ 'separating$a' ) )
    <=> ! [C: 'C_update_b_update_fun$',D: 'C_update_b_update_fun$'] :
          ( ( ! [E: 'C_update$'] :
                ( ( B @ ( E @ 'member$b' ) )
               => ( ( E @ ( C @ 'fun_app$q' ) )
                  = ( E @ ( D @ 'fun_app$q' ) ) ) )
            & ( D @ 'preregister$b' )
            & ( C @ 'preregister$b' ) )
         => ( C = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).

thf(1653,plain,
    ! [A: 'B_itself$',B: 'C_update_set$'] :
      ( ( ! [C: 'C_update_b_update_fun$',D: 'C_update_b_update_fun$'] :
            ( ( ! [E: 'C_update$'] :
                  ( ( B @ ( E @ 'member$b' ) )
                 => ( ( E @ ( C @ 'fun_app$q' ) )
                    = ( E @ ( D @ 'fun_app$q' ) ) ) )
              & ( D @ 'preregister$b' )
              & ( C @ 'preregister$b' ) )
           => ( C = D ) )
       => ( B @ ( A @ 'separating$a' ) ) )
      & ( ( B @ ( A @ 'separating$a' ) )
       => ! [C: 'C_update_b_update_fun$',D: 'C_update_b_update_fun$'] :
            ( ( ! [E: 'C_update$'] :
                  ( ( B @ ( E @ 'member$b' ) )
                 => ( ( E @ ( C @ 'fun_app$q' ) )
                    = ( E @ ( D @ 'fun_app$q' ) ) ) )
              & ( D @ 'preregister$b' )
              & ( C @ 'preregister$b' ) )
           => ( C = D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(408,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).

thf(1962,plain,
    ! [A: 'A_update_b_update_fun$',B: 'D_update_a_update_fun$',C: 'D_update$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ 'fun_app$m' ) )
      = ( C @ ( B @ 'fun_app$au' ) @ ( A @ 'fun_app$ae' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(122,axiom,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$' @ ( B @ 'image$' ) @ ( F @ 'member$c' ) )
              & ( 'top$' @ ( A @ 'image$' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom635) ).

thf(935,plain,
    ! [A: 'C_d_prod_update_a_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'A_update_b_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( ( A @ ( C @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) )
          = ( B @ ( D @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) ) )
        & ! [E: 'A_update$',F: 'A_update$'] :
            ( ( ( ( E @ ( C @ 'fun_app$ae' ) )
                = ( F @ ( D @ 'fun_app$ae' ) ) )
              & ( 'top$' @ ( B @ 'image$' ) @ ( F @ 'member$c' ) )
              & ( 'top$' @ ( A @ 'image$' ) @ ( E @ 'member$c' ) ) )
           => ( E = F ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(119,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$d' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$b' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = G ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom676) ).

thf(923,plain,
    ! [A: 'A_update_a_update_fun$',B: 'A_update_a_update_fun$',C: 'B_update_b_update_fun$',D: 'B_update_b_update_fun$',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$'] :
      ( ( ( ( E @ ( G @ ( D @ 'comp$d' ) @ 'comp$f' ) )
          = ( E @ ( I @ ( B @ 'comp$b' ) @ 'comp$e' ) @ ( A @ ( H @ ( D @ 'comp$g' ) @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) )
        & ( 'top$b' @ ( F @ ( E @ 'type_definition$b' ) ) )
        & ( 'top$d' @ ( D @ ( C @ 'type_definition$a' ) ) )
        & ( 'top$c' @ ( B @ ( A @ 'type_definition$' ) ) ) )
     => ( ( I @ ( H @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = G ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(189,axiom,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$e' ) @ 'fun_app$bq' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom142) ).

thf(1184,plain,
    ! [A: 'C_update_b_update_fun$',B: 'C_update_b_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ( B @ 'register$c' )
        & ( A @ 'register$c' ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_tensor$e' ) @ 'fun_app$bq' ) )
        = ( D @ ( B @ 'fun_app$q' ) @ ( C @ ( A @ 'fun_app$q' ) @ 'tensor_update$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(255,axiom,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$b' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).

thf(1416,plain,
    ! [A: 'A_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update_a_update_fun$',D: 'A_update_b_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$b' ) )
        = C )
     => ( ( B @ ( A @ ( D @ 'comp$am' ) @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( C @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(393,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) )
      = ( C @ ( B @ 'comp$az' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).

thf(1917,plain,
    ! [A: 'A_update_b_update_fun$',B: 'C_d_prod_update_a_update_fun$',C: 'C_update_c_d_prod_update_fun$'] :
      ( ( C @ ( B @ ( A @ ( 'comp$a' @ 'fun_app$bk' ) @ 'fun_app$bj' ) @ 'comp$ba' ) )
      = ( C @ ( B @ 'comp$az' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(469,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun_bool_fun$'] :
      ( ( B @ 'collect$f' @ ( A @ 'member$f' ) )
    <=> ( A @ ( B @ 'fun_app$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).

thf(2170,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun_bool_fun$'] :
      ( ( ( A @ ( B @ 'fun_app$k' ) )
       => ( B @ 'collect$f' @ ( A @ 'member$f' ) ) )
      & ( ( B @ 'collect$f' @ ( A @ 'member$f' ) )
       => ( A @ ( B @ 'fun_app$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(450,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$',C: 'C_update$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( ( C @ ( A @ 'fun_app$u' ) @ ( B @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'fun_app$u' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).

thf(2106,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update$',C: 'C_update$'] :
      ( ( A @ ( 'register$' @ 'fun_app$k' ) )
     => ( ( C @ ( A @ 'fun_app$u' ) @ ( B @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
        = ( C @ ( B @ 'comp_update$c' @ 'fun_app$bx' ) @ ( A @ 'fun_app$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(140,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: 'C_update_a_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ 'comp$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).

thf(1014,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: 'C_update_a_update_fun$',F: 'C_update_b_update_fun$'] :
      ( ( ( ( E @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
          = F )
        & ( ( B @ ( A @ 'comp$am' ) )
          = ( D @ ( C @ 'comp$g' ) ) ) )
     => ( ( E @ ( B @ 'comp$b' ) @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( F @ ( C @ 'comp$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(490,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 @ 'uvw$' ) @ ( 'uvt$' @ 'pred_fun$a' ) @ 'fun_app$k' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).

thf(2238,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 @ 'uvw$' ) @ ( 'uvt$' @ 'pred_fun$a' ) @ 'fun_app$k' ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(508,axiom,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ! [E: 'C_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$u' ) @ ( E @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( E @ ( A @ 'fun_app$u' ) @ ( F @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_pair$s' ) @ 'fun_app$cf' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).

thf(2297,plain,
    ! [A: 'C_update_a_update_fun$',B: 'C_update_a_update_fun$',C: 'C_update$',D: 'C_update$'] :
      ( ( ! [E: 'C_update$',F: 'C_update$'] :
            ( ( F @ ( B @ 'fun_app$u' ) @ ( E @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) )
            = ( E @ ( A @ 'fun_app$u' ) @ ( F @ ( B @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) )
        & ( B @ ( 'register$' @ 'fun_app$k' ) )
        & ( A @ ( 'register$' @ 'fun_app$k' ) ) )
     => ( ( D @ ( C @ 'tensor_update$l' ) @ ( B @ ( A @ 'register_pair$s' ) @ 'fun_app$cf' ) )
        = ( D @ ( B @ 'fun_app$u' ) @ ( C @ ( A @ 'fun_app$u' ) @ 'comp_update$' @ 'fun_app$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(16,axiom,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$av' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( D @ ( C @ 'fun_app$cq' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).

thf(560,plain,
    ! [A: 'A_update_a_update_fun_d_update_b_update_fun_fun$',B: 'B_update_c_update_fun_a_update_a_update_fun_fun$',C: 'B_update_c_update_fun_d_update_b_update_fun_fun$',D: 'B_update_c_update_fun$'] :
      ( ( ( B @ ( A @ 'comp$av' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'fun_app$co' ) )
        = ( D @ ( C @ 'fun_app$cq' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(477,axiom,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$s' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ac' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).

thf(2191,plain,
    ! [A: 'A_update_b_update_fun$',B: 'A_update_b_update_fun$',C: 'C_update_a_update_fun$',D: 'D_update_a_update_fun$'] :
      ( ( ( D @ ( 'register$e' @ 'fun_app$j' ) )
        & ( C @ ( 'register$' @ 'fun_app$k' ) )
        & ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$s' ) @ ( B @ ( A @ 'register_tensor$p' ) @ 'comp$ac' ) )
        = ( D @ ( B @ ( 'comp$j' @ 'fun_app$bw' ) @ 'fun_app$bv' ) @ ( C @ ( A @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) @ 'register_tensor$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(360,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$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom640) ).

thf(1812,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$'] :
            ( ( 'top$b' @ ( B @ 'image$b' ) @ ( E @ 'member$c' ) )
           => ( ( E @ ( C @ 'fun_app$ae' ) )
              = ( E @ ( D @ 'fun_app$ae' ) ) ) )
        & ( A = B ) )
     => ( ( A @ ( C @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) )
        = ( B @ ( D @ ( 'comp$' @ 'fun_app$bf' ) @ 'fun_app$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(2359,plain,
    $false,
    inference(e,[status(thm)],[2163,2094,1369,846,518,962,1179,777,1295,2250,1586,1501,1879,1337,1718,909,628,1956,1950,2280,1110,977,1068,2062,1618,2248,1544,2099,2114,614,1158,762,1924,2210,730,1882,550,1999,1327,1640,1063,2042,2146,1497,2195,1705,898,2216,1914,2020,1046,1935,1359,1386,2082,1887,651,1391,1576,1650,1645,1724,1475,565,1366,2136,1265,1228,1482,1409,1709,1792,1985,1760,719,785,2269,1871,1907,1330,587,1462,949,2185,1455,638,1379,1514,1890,1347,1568,2301,1232,1847,2007,1489,789,591,623,1334,514,2017,1302,756,1714,2027,1040,1632,1136,834,1864,2122,1383,574,1051,821,1843,1215,1447,866,774,2002,2242,1405,1943,1521,2205,1975,981,766,1169,687,1104,1242,849,2011,678,661,1199,1153,810,2047,2307,1768,529,1691,1274,1343,1174,693,1560,746,1091,1824,2150,1938,1602,1920,1968,852,1687,583,2179,1210,1195,1281,2112,1910,974,1836,2181,1079,1027,1402,1350,1592,1089,1983,1143,1794,1970,725,869,783,857,1270,1851,1772,1259,610,1755,1683,1292,554,1424,526,1612,1082,2023,901,1075,1207,2085,1155,547,1744,837,1099,1297,1451,1831,654,1552,1932,1002,779,2272,1324,1114,647,1776,1263,997,515,1249,2052,1599,1246,2203,1086,2208,921,2076,1286,1071,674,2089,1895,2189,926,1563,657,2235,1278,1648,965,1764,2176,1680,1747,1595,1374,733,2260,1698,1959,2253,2033,2149,1219,824,904,1007,843,1752,1929,743,875,579,1965,1124,1784,1389,713,1239,2055,804,704,1356,1675,641,2161,1635,1733,1058,1107,604,2079,2119,1117,1574,1524,1048,1722,2116,737,1571,681,1408,1043,1801,863,2065,816,1630,2267,700,1556,1022,1177,1952,1820,1731,594,799,1162,626,915,1926,768,1066,608,1477,1726,2303,1694,1805,912,685,521,1171,1841,1396,2212,959,2139,883,1034,1809,2096,1758,1203,2271,1905,2037,2124,617,1340,1472,968,2005,1413,722,1948,1304,1873,1018,2256,1547,1798,1770,690,872,887,971,2143,1605,1941,1780,1753,1225,2060,707,1053,2092,791,1188,1869,840,1235,1763,576,1579,643,1432,2165,2276,1980,544,907,1702,1749,1504,1670,2030,571,1898,1849,1353,600,1485,1972,1094,1140,1839,1459,556,671,2310,2194,1517,1126,2187,771,1421,2013,931,539,1321,1834,2110,1010,2305,1590,2167,2283,2098,1674,1508,946,632,1854,2130,781,2262,961,813,568,1440,2198,1193,1607,1893,1444,536,1030,1491,2183,1212,716,1614,2255,1097,1625,818,854,1527,2050,1480,2218,1133,2287,620,2102,752,1363,1495,807,1410,1789,1288,635,532,696,1165,1436,1859,2201,918,1989,740,987,1268,860,1004,1299,1902,1885,1120,1829,1129,1827,1261,1582,2265,1399,1621,1653,1962,935,923,1184,1416,1917,2170,2106,1014,2238,2297,560,2191,1812]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ITP383_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.36  % Computer : n008.cluster.edu
% 0.11/0.36  % Model    : x86_64 x86_64
% 0.11/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36  % Memory   : 8046.5625MB
% 0.11/0.36  % OS       : Linux 6.8.0-71-generic
% 0.11/0.36  % CPULimit : 300
% 0.11/0.36  % WCLimit  : 300
% 0.11/0.36  % DateTime : Fri Sep 25 19:10:09 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.37  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.81  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 3.06/1.33  % [INFO] 	 Parsing done (525ms). 
% 3.06/1.34  % [INFO] 	 Running in sequential loop mode. 
% 3.98/1.58  % [INFO] 	 eprover registered as external prover. 
% 3.98/1.59  % [INFO] 	 Scanning for conjecture ... 
% 5.10/1.82  % [INFO] 	 Found a conjecture (or negated_conjecture) and 695 axioms. Running axiom selection ... 
% 6.89/2.22  % [INFO] 	 Axiom selection finished. Selected 511 axioms (removed 184 axioms). 
% 8.59/2.70  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 8.59/2.74  % [INFO] 	 Type checking passed. 
% 8.59/2.75  % [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 ... 
% 23.47/6.60  % External prover 'e' found a proof!
% 23.47/6.60  % [INFO] 	 Killing All external provers ... 
% 23.47/6.60  % Time passed: 6037ms (effective reasoning time: 5251ms)
% 23.47/6.60  % 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)>
% 23.90/6.60  % Axioms used in derivation (511): axiom326, axiom635, axiom260, axiom280, axiom127, axiom315, axiom546, axiom116, axiom452, axiom491, axiom681, axiom241, axiom76, axiom273, axiom61, axiom230, axiom100, axiom6, axiom503, axiom485, axiom54, axiom549, axiom369, axiom404, axiom14, axiom333, axiom214, axiom322, axiom307, axiom203, axiom284, axiom423, axiom65, axiom142, axiom311, axiom169, axiom622, axiom531, axiom291, axiom441, axiom507, axiom430, axiom158, axiom131, axiom10, axiom580, axiom344, axiom138, axiom508, axiom392, axiom597, axiom337, axiom119, axiom210, axiom407, axiom692, axiom477, axiom673, axiom401, axiom257, axiom22, axiom397, axiom460, axiom354, axiom619, axiom412, axiom172, axiom147, axiom434, axiom341, axiom504, axiom173, axiom638, axiom109, axiom348, axiom184, axiom329, axiom376, axiom684, axiom266, axiom445, axiom524, axiom695, axiom42, axiom513, axiom239, axiom300, axiom350, axiom372, axiom195, axiom162, axiom358, axiom161, axiom632, axiom616, axiom150, axiom542, axiom2, axiom134, axiom104, axiom456, axiom87, axiom572, axiom130, axiom98, axiom112, axiom304, axiom643, axiom473, axiom365, axiom39, axiom499, axiom330, axiom650, axiom418, axiom251, axiom687, axiom64, axiom682, axiom247, axiom676, axiom578, axiom636, axiom352, axiom126, axiom539, axiom427, axiom625, axiom642, axiom217, axiom343, axiom411, axiom294, axiom179, axiom363, axiom314, axiom289, axiom437, axiom236, axiom151, axiom115, axiom623, axiom94, axiom83, axiom101, axiom336, axiom321, axiom647, axiom78, axiom278, axiom272, axiom228, axiom405, axiom455, axiom121, axiom137, axiom206, axiom318, axiom60, axiom631, axiom0, axiom574, axiom490, axiom240, axiom290, axiom13, axiom53, axiom433, axiom143, axiom359, axiom416, axiom545, axiom108, axiom395, axiom258, axiom75, axiom325, axiom448, axiom552, axiom385, axiom157, axiom90, axiom168, axiom332, axiom9, axiom478, axiom693, axiom303, axiom366, axiom207, axiom538, axiom80, axiom252, axiom422, axiom185, axiom472, axiom146, axiom97, axiom192, axiom355, axiom263, axiom415, axiom398, axiom254, axiom444, axiom82, axiom694, axiom45, axiom679, axiom229, axiom541, axiom360, axiom174, axiom556, axiom639, axiom319, axiom347, axiom646, axiom180, axiom67, axiom213, axiom683, axiom450, axiom196, axiom523, axiom615, axiom629, axiom310, axiom243, axiom426, axiom72, axiom461, axiom449, axiom438, axiom91, axiom105, axiom267, axiom89, axiom111, axiom512, axiom224, axiom122, axiom38, axiom419, axiom377, axiom218, axiom86, axiom163, axiom408, axiom297, axiom447, axiom52, axiom432, axiom156, axiom511, axiom279, axiom641, axiom501, axiom342, axiom193, axiom630, axiom544, axiom152, axiom425, axiom167, axiom454, axiom205, axiom364, axiom628, axiom79, axiom190, axiom573, axiom443, axiom96, axiom149, axiom189, axiom394, axiom560, axiom93, axiom216, axiom595, axiom227, axiom182, axiom409, axiom286, axiom428, axiom618, axiom118, axiom275, axiom63, axiom19, axiom458, axiom613, axiom102, axiom410, axiom320, axiom201, axiom178, axiom259, axiom74, axiom276, axiom451, axiom85, axiom145, axiom509, axiom233, axiom598, axiom302, axiom367, axiom378, axiom599, axiom471, axiom506, axiom186, axiom497, axiom164, axiom374, axiom614, axiom440, axiom678, axiom581, axiom282, axiom271, axiom4, axiom255, axiom153, axiom324, axiom71, axiom462, axiom15, axiom129, axiom114, axiom244, axiom620, axiom594, axiom136, axiom414, axiom106, axiom533, axiom170, axiom268, axiom181, axiom403, axiom522, axiom436, axiom555, axiom486, axiom346, axiom645, axiom262, axiom68, axiom686, axiom335, axiom175, axiom237, axiom356, axiom439, axiom634, axiom110, axiom125, axiom675, axiom49, axiom577, axiom690, axiom298, axiom248, axiom421, axiom226, axiom521, axiom338, axiom242, axiom558, axiom691, axiom510, axiom199, axiom547, axiom166, axiom559, axiom651, axiom88, axiom442, axiom92, axiom399, axiom66, axiom204, axiom296, axiom141, axiom576, axiom596, axiom274, axiom117, axiom621, axiom44, axiom222, axiom323, axiom446, axiom84, axiom554, axiom155, axiom269, axiom453, axiom81, axiom103, axiom7, axiom515, axiom231, axiom306, axiom253, axiom640, axiom249, axiom368, axiom680, axiom689, axiom550, axiom99, axiom148, axiom128, axiom316, axiom285, axiom540, axiom537, axiom183, axiom301, axiom649, axiom211, axiom29, axiom361, axiom429, axiom188, axiom532, axiom177, axiom264, axiom431, axiom208, axiom159, axiom487, axiom519, axiom402, axiom551, axiom73, axiom107, axiom417, axiom339, axiom154, axiom265, axiom165, axiom270, axiom113, axiom176, axiom171, axiom3, axiom305, axiom187, axiom288, axiom644, axiom317, axiom198, axiom529, axiom144, axiom55, axiom281, axiom424, axiom633, axiom593, axiom245, axiom685, axiom135, axiom536, axiom373, axiom435, axiom312, axiom95, axiom70, axiom238, axiom617, axiom465, axiom299, axiom351, axiom261, axiom77, axiom413, axiom256, axiom334, axiom406, axiom160, axiom514, axiom43, axiom677, axiom582, axiom637, axiom420, axiom470, axiom139, axiom200, axiom624, axiom525, axiom234, axiom362, axiom548, axiom674, axiom62, axiom648, axiom209, axiom468, axiom492, axiom328, axiom140, axiom250, axiom688, axiom340, axiom194
% 23.90/6.60  % No. of inferences in proof: 1026
% 23.90/6.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6037 ms resp. 5251 ms w/o parsing
% 25.05/7.03  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.60/7.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------