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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP399_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 : n001.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 07:37:49 AM UTC 2026

% Result   : Theorem 23.40s 7.47s
% Output   : Refutation 25.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  521
% Syntax   : Number of formulae    : 1044 ( 120 unt;   0 typ;   0 def)
%            Number of atoms       : 3024 ( 788 equ;   0 cnn)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 11556 (  28   ~;   0   |; 853   &;9548   @)
%                                         (  68 <=>;1059  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :  282 ( 281 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  627 ( 625 usr;  63 con; 0-3 aty)
%            Number of variables   : 2536 (   0   ^;2416   !; 120   ?;2536   :)

% Comments : 
%------------------------------------------------------------------------------
thf('A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun$_type',type,
    'A_ell2_a_ell2_cblinfun$': $tType ).

thf('A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_a_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_a_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun$_type',type,
    'B_ell2_b_ell2_cblinfun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$_type',type,
    'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_c_prod_ell2_a_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_c_prod_ell2_a_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_b_prod_ell2_c_a_c_prod_b_complement_domain_prod_b_prod_ell2_cblinfun_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_b_prod_ell2_c_a_c_prod_b_complement_domain_prod_b_prod_ell2_cblinfun_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_b_a_a_b_complement_domain_prod_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_b_a_a_b_complement_domain_prod_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_b_a_a_b_complement_domain_prod_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_b_a_a_b_complement_domain_prod_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$_type',type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

thf('C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_prod_ell2_a_a_prod_ell2_cblinfun$_type',type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun$': $tType ).

thf('A_c_prod_ell2$_type',type,
    'A_c_prod_ell2$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_a_b_complement_domain_prod_ell2_c_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_a_b_complement_domain_prod_ell2_c_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_ell2_c_ell2_cblinfun$_type',type,
    'C_ell2_c_ell2_cblinfun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_a_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_a_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_bool_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_bool_fun$': $tType ).

thf('A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$_type',type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$': $tType ).

thf('C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$_type',type,
    'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_c_complement_domain_prod_ell2_b_b_c_complement_domain_prod_ell2_cblinfun$_type',type,
    'B_b_c_complement_domain_prod_ell2_b_b_c_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$_type',type,
    'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$': $tType ).

thf('C_a_prod_ell2_c_a_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$_type',type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$_type',type,
    'C_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

thf('C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$_type',type,
    'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$_type',type,
    'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$': $tType ).

thf('A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_a_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_a_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_fun$': $tType ).

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

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$': $tType ).

thf('B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$_type',type,
    'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$': $tType ).

thf('A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_cblinfun_fun$_type',type,
    'B_c_a_c_prod_b_complement_domain_prod_prod_ell2_b_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

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

thf('A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$': $tType ).

thf('A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_c_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_c_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_ell2$_type',type,
    'C_ell2$': $tType ).

thf('A_a_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_a_a_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_a_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_a_a_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_b_complement_domain_ell2_a_b_complement_domain_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_b_complement_domain_ell2_a_b_complement_domain_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$_type',type,
    'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('B_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_a_complement_domain_prod_ell2_c_c_a_complement_domain_prod_ell2_cblinfun$_type',type,
    'C_c_a_complement_domain_prod_ell2_c_c_a_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$_type',type,
    'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$': $tType ).

thf('A_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$_type',type,
    'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_prod_ell2_c_a_prod_ell2_cblinfun$_type',type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_prod_ell2_c_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_prod_ell2_c_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_c_prod_ell2_a_c_prod_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_c_prod_ell2_a_c_prod_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_b_prod_ell2_c_a_c_prod_b_complement_domain_prod_b_prod_ell2_cblinfun_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_b_prod_ell2_c_a_c_prod_b_complement_domain_prod_b_prod_ell2_cblinfun_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_b_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$_type',type,
    'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_set$_type',type,
    'B_ell2_b_ell2_cblinfun_set$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_prod_ell2_c_c_prod_ell2_cblinfun$_type',type,
    'C_c_prod_ell2_c_c_prod_ell2_cblinfun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_complement_domain_prod_ell2_a_a_c_complement_domain_prod_ell2_cblinfun$_type',type,
    'A_a_c_complement_domain_prod_ell2_a_a_c_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_set$_type',type,
    'A_ell2_a_ell2_cblinfun_set$': $tType ).

thf('A_c_prod_a_prod_ell2_a_c_prod_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_prod_ell2_a_c_prod_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_ell2$_type',type,
    'A_ell2$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

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

thf('C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_c_b_complement_domain_prod_ell2_c_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_c_b_complement_domain_prod_ell2_c_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

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

thf('B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('B_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'B_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_a_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_a_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_c_complement_domain_prod_ell2_c_c_c_complement_domain_prod_ell2_cblinfun$_type',type,
    'C_c_c_complement_domain_prod_ell2_c_c_c_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun$': $tType ).

thf('A_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun$_type',type,
    'A_b_complement_domain_b_prod_ell2_a_b_complement_domain_b_prod_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_c_b_complement_domain_prod_ell2_a_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_c_b_complement_domain_prod_ell2_a_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_c_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_b_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_a_b_complement_domain_b_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_b_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_a_b_complement_domain_b_complement_domain_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$_type',type,
    'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$': $tType ).

thf('A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_a_b_complement_domain_prod_ell2_b_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_bool_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_bool_fun$': $tType ).

thf('A_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_c_prod_prod_ell2_a_a_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_ell2_a_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_ell2_a_a_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_complement_domain_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$_type',type,
    'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$': $tType ).

thf('A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('A_c_prod_a_c_prod_prod_ell2_a_c_prod_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_a_c_prod_prod_ell2_a_c_prod_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$_type',type,
    'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$': $tType ).

thf('B_ell2_b_ell2_cblinfun_bool_fun$_type',type,
    'B_ell2_b_ell2_cblinfun_bool_fun$': $tType ).

thf('B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_c_prod_ell2_a_a_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_a_b_complement_domain_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('B_a_a_b_complement_domain_prod_complement_domain_ell2_b_a_a_b_complement_domain_prod_complement_domain_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'B_a_a_b_complement_domain_prod_complement_domain_ell2_b_a_a_b_complement_domain_prod_complement_domain_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$_type',type,
    'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$': $tType ).

thf('C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$_type',type,
    'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$': $tType ).

thf('C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$': $tType ).

thf('C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$': $tType ).

thf('C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('B_ell2$_type',type,
    'B_ell2$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('B_a_a_b_complement_domain_prod_complement_domain_ell2_b_a_a_b_complement_domain_prod_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'B_a_a_b_complement_domain_prod_complement_domain_ell2_b_a_a_b_complement_domain_prod_complement_domain_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$_type',type,
    'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$': $tType ).

thf('A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$_type',type,
    'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$_type',type,
    'A_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$': $tType ).

thf('C_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun$_type',type,
    'C_b_complement_domain_c_prod_ell2_c_b_complement_domain_c_prod_ell2_cblinfun$': $tType ).

thf('C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$_type',type,
    'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$': $tType ).

thf('A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$_type',type,
    'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$': $tType ).

thf('A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$_type',type,
    'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$': $tType ).

thf('comp$dd_decl',type,
    'comp$dd': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$q_decl',type,
    'equivalent_registers$q': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$an_decl',type,
    'register_pair$an': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$h_decl',type,
    'comp$h': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('t3$_decl',type,
    't3$': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('inv_into$aq_decl',type,
    'inv_into$aq': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$v_decl',type,
    'comp$v': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('bij_betw$l_decl',type,
    'bij_betw$l': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('comp$ae_decl',type,
    'comp$ae': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$a_decl',type,
    'iso_register$a': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$aq_decl',type,
    'register$aq': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('complements$y_decl',type,
    'complements$y': 'A_c_prod_a_prod_ell2_a_c_prod_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$am_decl',type,
    'register_tensor$am': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_c_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$ad_decl',type,
    'register_tensor$ad': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_a_b_complement_domain_prod_ell2_c_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('complements$r_decl',type,
    'complements$r': 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('register$o_decl',type,
    'register$o': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$_decl',type,
    'comp$': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$am_decl',type,
    'equivalent_registers$am': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$dp_decl',type,
    'comp$dp': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('complements$ah_decl',type,
    'complements$ah': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('iso_register$ad_decl',type,
    'iso_register$ad': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('member$b_decl',type,
    'member$b': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('register_tensor$t_decl',type,
    'register_tensor$t': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$c_decl',type,
    'register_tensor$c': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$bf_decl',type,
    'register_tensor$bf': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ba_decl',type,
    'equivalent_registers$ba': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$_decl',type,
    'complements$': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$q_decl',type,
    'comp$q': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$w_decl',type,
    'comp$w': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ar_decl',type,
    'equivalent_registers$ar': 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$d_decl',type,
    'equivalent_registers$d': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$ac_decl',type,
    'equivalent_registers$ac': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$y_decl',type,
    'compatible$y': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('inv_into$m_decl',type,
    'inv_into$m': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('collect$b_decl',type,
    'collect$b': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_bool_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('fun_app$i_decl',type,
    'fun_app$i': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

thf('bij_betw$q_decl',type,
    'bij_betw$q': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > $o ).

thf('register_tensor$w_decl',type,
    'register_tensor$w': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$f_decl',type,
    'register_tensor$f': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ah_decl',type,
    'equivalent_registers$ah': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$k_decl',type,
    'tensor_op$k': 'C_ell2_c_ell2_cblinfun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register_tensor$x_decl',type,
    'register_tensor$x': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('compatible$ar_decl',type,
    'compatible$ar': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('butterfly$a_decl',type,
    'butterfly$a': 'A_ell2$' > 'A_ell2$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('comp$z_decl',type,
    'comp$z': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$e_decl',type,
    'fun_app$e': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('inv_into$o_decl',type,
    'inv_into$o': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('regular_register$b_decl',type,
    'regular_register$b': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$az_decl',type,
    'compatible$az': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complement$f_decl',type,
    'complement$f': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$bj_decl',type,
    'comp$bj': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$g_decl',type,
    'register_pair$g': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complement$l_decl',type,
    'complement$l': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_tensor$e_decl',type,
    'register_tensor$e': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('top$m_decl',type,
    'top$m': 'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$' ).

thf('register_tensor$ah_decl',type,
    'register_tensor$ah': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('fun_app$ae_decl',type,
    'fun_app$ae': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' ).

thf('compatible$av_decl',type,
    'compatible$av': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complement$o_decl',type,
    'complement$o': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('compatible$l_decl',type,
    'compatible$l': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$w_decl',type,
    'complements$w': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_b_complement_domain_a_b_complement_domain_prod_ell2_c_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('compatible$m_decl',type,
    'compatible$m': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$am_decl',type,
    'register_pair$am': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_tensor$m_decl',type,
    'register_tensor$m': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$dq_decl',type,
    'comp$dq': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$cb_decl',type,
    'comp$cb': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$y_decl',type,
    'fun_app$y': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

thf('comp$dh_decl',type,
    'comp$dh': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$u_decl',type,
    'compatible$u': 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('compatible$aw_decl',type,
    'compatible$aw': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('register$g_decl',type,
    'register$g': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('id$a_decl',type,
    'id$a': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$ac_decl',type,
    'register_tensor$ac': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_c_b_complement_domain_prod_ell2_a_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$at_decl',type,
    'equivalent_registers$at': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('bij_betw$c_decl',type,
    'bij_betw$c': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('compatible$f_decl',type,
    'compatible$f': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('collect$c_decl',type,
    'collect$c': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('default$_decl',type,
    'default$': 'B$' ).

thf('compatible$x_decl',type,
    'compatible$x': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('comp$cg_decl',type,
    'comp$cg': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$u_decl',type,
    'register_pair$u': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('assoc$b_decl',type,
    'assoc$b': 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$' ).

thf('register_pair$b_decl',type,
    'register_pair$b': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$ad_decl',type,
    'register$ad': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('bij_betw$p_decl',type,
    'bij_betw$p': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('comp$cr_decl',type,
    'comp$cr': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$j_decl',type,
    'iso_register$j': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('comp$at_decl',type,
    'comp$at': 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_a_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_fun$' > 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('tensor_op$d_decl',type,
    'tensor_op$d': 'A_ell2_a_ell2_cblinfun$' > 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$' > 'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$' ).

thf('fun_app$am_decl',type,
    'fun_app$am': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('comp$j_decl',type,
    'comp$j': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$t_decl',type,
    'register_pair$t': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('comp$ce_decl',type,
    'comp$ce': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$ba_decl',type,
    'register_pair$ba': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('ket$_decl',type,
    'ket$': 'B$' > 'B_ell2$' ).

thf('register_pair$be_decl',type,
    'register_pair$be': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$g_decl',type,
    'inv_into$g': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complements$z_decl',type,
    'complements$z': 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('regular_register$h_decl',type,
    'regular_register$h': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('comp$df_decl',type,
    'comp$df': 'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('complement$q_decl',type,
    'complement$q': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('compatible$ay_decl',type,
    'compatible$ay': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('bij_betw$t_decl',type,
    'bij_betw$t': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('bij_betw$ae_decl',type,
    'bij_betw$ae': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_ell2_a_ell2_cblinfun_set$' > $o ).

thf('compatible$o_decl',type,
    'compatible$o': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$bj_decl',type,
    'register_tensor$bj': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('bij_betw$f_decl',type,
    'bij_betw$f': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('comp$ct_decl',type,
    'comp$ct': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$e_decl',type,
    'comp$e': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('tensor_op$p_decl',type,
    'tensor_op$p': 'A_ell2_a_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun$' ).

thf('fun_app$c_decl',type,
    'fun_app$c': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register$w_decl',type,
    'register$w': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('comp$aw_decl',type,
    'comp$aw': 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complement$i_decl',type,
    'complement$i': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_b_complement_domain_ell2_a_b_complement_domain_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$d_decl',type,
    'register_pair$d': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$z_decl',type,
    'fun_app$z': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

thf('register_pair$av_decl',type,
    'register_pair$av': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_a_complement_domain_prod_ell2_a_a_a_complement_domain_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('comp$ag_decl',type,
    'comp$ag': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_pair$ak_decl',type,
    'register_pair$ak': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$k_decl',type,
    'comp$k': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$d_decl',type,
    'register$d': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('regular_register$g_decl',type,
    'regular_register$g': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('id$c_decl',type,
    'id$c': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$ag_decl',type,
    'compatible$ag': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$c_decl',type,
    'equivalent_registers$c': 'A_b_complement_domain_b_complement_domain_ell2_a_b_complement_domain_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$g_decl',type,
    'register_tensor$g': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('member$c_decl',type,
    'member$c': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('comp$cy_decl',type,
    'comp$cy': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('inv_into$z_decl',type,
    'inv_into$z': 'A_ell2_a_ell2_cblinfun_set$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('register_pair$aq_decl',type,
    'register_pair$aq': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$ac_decl',type,
    'compatible$ac': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$x_decl',type,
    'complements$x': 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_b_complement_domain_c_b_complement_domain_prod_ell2_c_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$ao_decl',type,
    'register_tensor$ao': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('comp$ch_decl',type,
    'comp$ch': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_tensor$v_decl',type,
    'register_tensor$v': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('compatible$as_decl',type,
    'compatible$as': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$ah_decl',type,
    'fun_app$ah': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('compatible$ae_decl',type,
    'compatible$ae': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$u_decl',type,
    'tensor_op$u': 'A_ell2_a_ell2_cblinfun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('tensor_op$e_decl',type,
    'tensor_op$e': 'A_ell2_a_ell2_cblinfun$' > 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$' > 'A_a_c_complement_domain_prod_ell2_a_a_c_complement_domain_prod_ell2_cblinfun$' ).

thf('comp$bp_decl',type,
    'comp$bp': 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('iso_register$z_decl',type,
    'iso_register$z': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('f$_decl',type,
    'f$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('top$f_decl',type,
    'top$f': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('register_pair$bb_decl',type,
    'register_pair$bb': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('equivalent_registers$j_decl',type,
    'equivalent_registers$j': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('swap$d_decl',type,
    'swap$d': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_prod_ell2_c_a_prod_ell2_cblinfun_fun$' ).

thf('comp$do_decl',type,
    'comp$do': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$an_decl',type,
    'equivalent_registers$an': 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$q_decl',type,
    'iso_register$q': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > $o ).

thf('regular_register$f_decl',type,
    'regular_register$f': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('top$n_decl',type,
    'top$n': 'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$' ).

thf('register_tensor$u_decl',type,
    'register_tensor$u': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('comp$co_decl',type,
    'comp$co': 'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$ar_decl',type,
    'fun_app$ar': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('fun_app$be_decl',type,
    'fun_app$be': 'B_ell2_b_ell2_cblinfun_bool_fun$' > 'B_ell2_b_ell2_cblinfun$' > $o ).

thf('tensor_op$c_decl',type,
    'tensor_op$c': 'A_ell2_a_ell2_cblinfun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register_tensor$p_decl',type,
    'register_tensor$p': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('swap$f_decl',type,
    'swap$f': 'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$_decl',type,
    'equivalent_registers$': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$b_decl',type,
    'compatible$b': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('ket$c_decl',type,
    'ket$c': 'A_c_prod$' > 'A_c_prod_ell2$' ).

thf('bij_betw$ac_decl',type,
    'bij_betw$ac': 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('register_pair$at_decl',type,
    'register_pair$at': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('inv_into$c_decl',type,
    'inv_into$c': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$ca_decl',type,
    'comp$ca': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$aw_decl',type,
    'register_pair$aw': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_c_complement_domain_prod_ell2_a_a_c_complement_domain_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('compatible$j_decl',type,
    'compatible$j': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('assoc$g_decl',type,
    'assoc$g': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('comp$l_decl',type,
    'comp$l': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complements$ae_decl',type,
    'complements$ae': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('register$ak_decl',type,
    'register$ak': 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('register_pair$aj_decl',type,
    'register_pair$aj': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$ad_decl',type,
    'comp$ad': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$bk_decl',type,
    'register_tensor$bk': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' ).

thf('comp$cd_decl',type,
    'comp$cd': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complements$o_decl',type,
    'complements$o': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$w_decl',type,
    'iso_register$w': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$p_decl',type,
    'equivalent_registers$p': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$i_decl',type,
    'comp$i': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$r_decl',type,
    'register$r': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('fun_app$k_decl',type,
    'fun_app$k': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('fun_app$_decl',type,
    'fun_app$': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('comp$bh_decl',type,
    'comp$bh': 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$m_decl',type,
    'equivalent_registers$m': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$x_decl',type,
    'fun_app$x': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('top$d_decl',type,
    'top$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('fun_app$ap_decl',type,
    'fun_app$ap': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('comp$ap_decl',type,
    'comp$ap': 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('assoc$a_decl',type,
    'assoc$a': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('fun_app$o_decl',type,
    'fun_app$o': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

thf('comp$bc_decl',type,
    'comp$bc': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$e_decl',type,
    'register$e': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('g$_decl',type,
    'g$': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$bd_decl',type,
    'comp$bd': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$cv_decl',type,
    'comp$cv': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ay_decl',type,
    'equivalent_registers$ay': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$aj_decl',type,
    'comp$aj': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$ac_decl',type,
    'register$ac': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('iso_register$b_decl',type,
    'iso_register$b': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$al_decl',type,
    'register$al': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$s_decl',type,
    'register_tensor$s': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('iso_register$_decl',type,
    'iso_register$': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$aj_decl',type,
    'register_tensor$aj': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('top$r_decl',type,
    'top$r': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$' ).

thf('compatible$a_decl',type,
    'compatible$a': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$ah_decl',type,
    'compatible$ah': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$ba_decl',type,
    'compatible$ba': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('assoc$_decl',type,
    'assoc$': 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_a_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_fun$' ).

thf('inv_into$ag_decl',type,
    'inv_into$ag': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('top$q_decl',type,
    'top$q': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_bool_fun$' ).

thf('comp$di_decl',type,
    'comp$di': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('fun_app$ao_decl',type,
    'fun_app$ao': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('register_tensor$l_decl',type,
    'register_tensor$l': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register$ao_decl',type,
    'register$ao': 'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('id$g_decl',type,
    'id$g': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('inv_into$k_decl',type,
    'inv_into$k': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('bij_betw$i_decl',type,
    'bij_betw$i': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > $o ).

thf('id$d_decl',type,
    'id$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register$ah_decl',type,
    'register$ah': 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$o_decl',type,
    'register_tensor$o': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('complement$d_decl',type,
    'complement$d': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$aq_decl',type,
    'comp$aq': 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$z_decl',type,
    'register_pair$z': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_c_prod_ell2_a_c_prod_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('aG$_decl',type,
    'aG$': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' ).

thf('equivalent_registers$au_decl',type,
    'equivalent_registers$au': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$as_decl',type,
    'register_tensor$as': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('compatible$ab_decl',type,
    'compatible$ab': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$g_decl',type,
    'complements$g': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$aq_decl',type,
    'equivalent_registers$aq': 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$aa_decl',type,
    'register_pair$aa': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_c_prod_ell2_a_c_prod_b_complement_domain_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$ba_decl',type,
    'fun_app$ba': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_bool_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > $o ).

thf('collect$_decl',type,
    'collect$': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_bool_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('comp$bv_decl',type,
    'comp$bv': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('register_tensor$_decl',type,
    'register_tensor$': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('complements$v_decl',type,
    'complements$v': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_c_b_complement_domain_prod_ell2_a_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('compatible$_decl',type,
    'compatible$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$au_decl',type,
    'register_pair$au': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'B_b_c_complement_domain_prod_ell2_b_b_c_complement_domain_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('register_tensor$bl_decl',type,
    'register_tensor$bl': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('complements$f_decl',type,
    'complements$f': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$a_decl',type,
    'top$a': 'B_ell2_b_ell2_cblinfun_set$' ).

thf('complement$m_decl',type,
    'complement$m': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('register$ai_decl',type,
    'register$ai': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('inv_into$i_decl',type,
    'inv_into$i': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('bij_betw$e_decl',type,
    'bij_betw$e': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('top$e_decl',type,
    'top$e': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' ).

thf('compatible$ai_decl',type,
    'compatible$ai': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$ad_decl',type,
    'fun_app$ad': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('register_pair$w_decl',type,
    'register_pair$w': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('register_tensor$af_decl',type,
    'register_tensor$af': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_prod_ell2_a_c_prod_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('complements$af_decl',type,
    'complements$af': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$an_decl',type,
    'register_tensor$an': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_prod_ell2_a_c_prod_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('comp$ah_decl',type,
    'comp$ah': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complements$aa_decl',type,
    'complements$aa': 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('comp$n_decl',type,
    'comp$n': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$d_decl',type,
    'comp$d': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$j_decl',type,
    'register$j': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$t_decl',type,
    'comp$t': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$az_decl',type,
    'fun_app$az': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register_tensor$r_decl',type,
    'register_tensor$r': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('compatible$d_decl',type,
    'compatible$d': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$ai_decl',type,
    'complements$ai': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('register$k_decl',type,
    'register$k': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$o_decl',type,
    'equivalent_registers$o': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$cw_decl',type,
    'comp$cw': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$x_decl',type,
    'comp$x': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$ap_decl',type,
    'compatible$ap': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$p_decl',type,
    'top$p': 'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('register_tensor$b_decl',type,
    'register_tensor$b': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('bij_betw$_decl',type,
    'bij_betw$': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('register$am_decl',type,
    'register$am': 'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('complements$j_decl',type,
    'complements$j': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$bl_decl',type,
    'comp$bl': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('iso_register$g_decl',type,
    'iso_register$g': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('assoc$h_decl',type,
    'assoc$h': 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_a_a_c_prod_b_complement_domain_c_prod_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$bi_decl',type,
    'register_tensor$bi': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' ).

thf('compatible$al_decl',type,
    'compatible$al': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$_decl',type,
    'tensor_op$': 'B_ell2_b_ell2_cblinfun$' > 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$' > 'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$' ).

thf('comp$bi_decl',type,
    'comp$bi': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$an_decl',type,
    'compatible$an': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$bd_decl',type,
    'register_pair$bd': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('top$c_decl',type,
    'top$c': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('comp$de_decl',type,
    'comp$de': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('comp$ab_decl',type,
    'comp$ab': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$ab_decl',type,
    'inv_into$ab': 'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$x_decl',type,
    'register_pair$x': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('bij_betw$x_decl',type,
    'bij_betw$x': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('swap$g_decl',type,
    'swap$g': 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$w_decl',type,
    'equivalent_registers$w': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$f_decl',type,
    'inv_into$f': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('inv_into$y_decl',type,
    'inv_into$y': 'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('iso_register$ag_decl',type,
    'iso_register$ag': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('id$i_decl',type,
    'id$i': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('tensor_op$n_decl',type,
    'tensor_op$n': 'B_ell2_b_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

thf('iso_register$ae_decl',type,
    'iso_register$ae': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('complements$ac_decl',type,
    'complements$ac': 'A_c_prod_a_c_prod_prod_ell2_a_c_prod_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('fun_app$f_decl',type,
    'fun_app$f': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' ).

thf('complements$d_decl',type,
    'complements$d': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$v_decl',type,
    'equivalent_registers$v': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$e_decl',type,
    'complements$e': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$b_decl',type,
    'complements$b': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('bij_betw$w_decl',type,
    'bij_betw$w': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > $o ).

thf('comp$dc_decl',type,
    'comp$dc': 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('complements$t_decl',type,
    'complements$t': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complement$c_decl',type,
    'complement$c': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('bij_betw$n_decl',type,
    'bij_betw$n': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('fun_app$as_decl',type,
    'fun_app$as': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('equivalent_registers$e_decl',type,
    'equivalent_registers$e': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$af_decl',type,
    'comp$af': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('top$l_decl',type,
    'top$l': 'A_ell2_a_ell2_cblinfun_set$' ).

thf('id$f_decl',type,
    'id$f': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complements$i_decl',type,
    'complements$i': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$cj_decl',type,
    'comp$cj': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('regular_register$d_decl',type,
    'regular_register$d': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$h_decl',type,
    'register_tensor$h': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('top$g_decl',type,
    'top$g': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('register$u_decl',type,
    'register$u': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('comp$cm_decl',type,
    'comp$cm': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$s_decl',type,
    'fun_app$s': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register$m_decl',type,
    'register$m': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$q_decl',type,
    'register_tensor$q': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$v_decl',type,
    'compatible$v': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('default$b_decl',type,
    'default$b': 'C$' ).

thf('swap$i_decl',type,
    'swap$i': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' ).

thf('register$t_decl',type,
    'register$t': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('register$a_decl',type,
    'register$a': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$s_decl',type,
    'register_pair$s': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('fun_app$t_decl',type,
    'fun_app$t': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('top$s_decl',type,
    'top$s': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_bool_fun$' ).

thf('top$i_decl',type,
    'top$i': 'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('register_tensor$bp_decl',type,
    'register_tensor$bp': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register$aa_decl',type,
    'register$aa': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('swap$_decl',type,
    'swap$': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$k_decl',type,
    'equivalent_registers$k': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$az_decl',type,
    'register_pair$az': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ai_decl',type,
    'equivalent_registers$ai': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('compatible$aq_decl',type,
    'compatible$aq': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$ae_decl',type,
    'inv_into$ae': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('butterfly$b_decl',type,
    'butterfly$b': 'C_ell2$' > 'C_ell2$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('complements$ab_decl',type,
    'complements$ab': 'C_a_c_prod_prod_ell2_c_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_c_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$y_decl',type,
    'equivalent_registers$y': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$aj_decl',type,
    'equivalent_registers$aj': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('inv_into$ad_decl',type,
    'inv_into$ad': 'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$v_decl',type,
    'register_pair$v': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('inv_into$t_decl',type,
    'inv_into$t': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('comp$y_decl',type,
    'comp$y': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$ac_decl',type,
    'comp$ac': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$k_decl',type,
    'compatible$k': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$i_decl',type,
    'equivalent_registers$i': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$f_decl',type,
    'register_pair$f': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('assoc$e_decl',type,
    'assoc$e': 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_a_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_fun$' ).

thf('comp$r_decl',type,
    'comp$r': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$e_decl',type,
    'iso_register$e': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$ar_decl',type,
    'inv_into$ar': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$af_decl',type,
    'compatible$af': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$n_decl',type,
    'register_tensor$n': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$ai_decl',type,
    'register_tensor$ai': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register$z_decl',type,
    'register$z': 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('iso_register$af_decl',type,
    'iso_register$af': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('compatible$c_decl',type,
    'compatible$c': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$l_decl',type,
    'register_pair$l': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$b_decl',type,
    'equivalent_registers$b': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complement$n_decl',type,
    'complement$n': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('bij_betw$a_decl',type,
    'bij_betw$a': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('inv_into$ai_decl',type,
    'inv_into$ai': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('complement$e_decl',type,
    'complement$e': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$h_decl',type,
    'inv_into$h': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$aq_decl',type,
    'fun_app$aq': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('equivalent_registers$n_decl',type,
    'equivalent_registers$n': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('assoc$n_decl',type,
    'assoc$n': 'C_a_prod_a_c_prod_b_complement_domain_prod_ell2_c_a_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('iso_register$m_decl',type,
    'iso_register$m': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('complement$a_decl',type,
    'complement$a': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$ai_decl',type,
    'fun_app$ai': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' ).

thf('assoc$k_decl',type,
    'assoc$k': 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_a_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_fun$' ).

thf('compatible$n_decl',type,
    'compatible$n': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$i_decl',type,
    'compatible$i': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$k_decl',type,
    'iso_register$k': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('aF$_decl',type,
    'aF$': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

thf('comp$db_decl',type,
    'comp$db': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('comp$s_decl',type,
    'comp$s': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$ao_decl',type,
    'compatible$ao': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$s_decl',type,
    'register$s': 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('compatible$z_decl',type,
    'compatible$z': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('bij_betw$m_decl',type,
    'bij_betw$m': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('iso_register$s_decl',type,
    'iso_register$s': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('register_pair$bc_decl',type,
    'register_pair$bc': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('fun_app$al_decl',type,
    'fun_app$al': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('inv_into$ao_decl',type,
    'inv_into$ao': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$ag_decl',type,
    'register_tensor$ag': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register_pair$ax_decl',type,
    'register_pair$ax': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_c_a_complement_domain_prod_ell2_c_c_a_complement_domain_prod_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('comp$dk_decl',type,
    'comp$dk': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('default$c_decl',type,
    'default$c': 'A_c_prod$' ).

thf('register_tensor$ak_decl',type,
    'register_tensor$ak': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_a_b_complement_domain_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('t2$_decl',type,
    't2$': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('fun_app$h_decl',type,
    'fun_app$h': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('id$e_decl',type,
    'id$e': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$bx_decl',type,
    'comp$bx': 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$ad_decl',type,
    'compatible$ad': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$ab_decl',type,
    'equivalent_registers$ab': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$ci_decl',type,
    'comp$ci': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$by_decl',type,
    'comp$by': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$a_decl',type,
    'equivalent_registers$a': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$ai_decl',type,
    'register_pair$ai': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$e_decl',type,
    'inv_into$e': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_tensor$bo_decl',type,
    'register_tensor$bo': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$bb_decl',type,
    'equivalent_registers$bb': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$b_decl',type,
    'top$b': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('equivalent_registers$u_decl',type,
    'equivalent_registers$u': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$ao_decl',type,
    'register_pair$ao': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$x_decl',type,
    'inv_into$x': 'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$i_decl',type,
    'register_pair$i': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$ax_decl',type,
    'compatible$ax': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('swap$e_decl',type,
    'swap$e': 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('iso_register$f_decl',type,
    'iso_register$f': 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$o_decl',type,
    'tensor_op$o': 'C_ell2_c_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun$' ).

thf('tensor_op$m_decl',type,
    'tensor_op$m': 'C_ell2_c_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun$' ).

thf('complement$r_decl',type,
    'complement$r': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('top$j_decl',type,
    'top$j': 'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('fun_app$an_decl',type,
    'fun_app$an': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('comp$dg_decl',type,
    'comp$dg': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('regular_register$a_decl',type,
    'regular_register$a': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$bf_decl',type,
    'register_pair$bf': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$ag_decl',type,
    'fun_app$ag': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$' ).

thf('ket$a_decl',type,
    'ket$a': 'A$' > 'A_ell2$' ).

thf('comp$u_decl',type,
    'comp$u': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('bij_betw$h_decl',type,
    'bij_betw$h': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('register_pair$ap_decl',type,
    'register_pair$ap': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$g_decl',type,
    'compatible$g': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$j_decl',type,
    'fun_app$j': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('iso_register$v_decl',type,
    'iso_register$v': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$h_decl',type,
    'top$h': 'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('register$_decl',type,
    'register$': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$b_decl',type,
    'tensor_op$b': 'B_ell2_b_ell2_cblinfun$' > 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$' > 'B_b_c_complement_domain_prod_ell2_b_b_c_complement_domain_prod_ell2_cblinfun$' ).

thf('inv_into$s_decl',type,
    'inv_into$s': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('member$d_decl',type,
    'member$d': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > $o ).

thf('bij_betw$g_decl',type,
    'bij_betw$g': 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > $o ).

thf('complements$h_decl',type,
    'complements$h': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$ak_decl',type,
    'compatible$ak': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$r_decl',type,
    'equivalent_registers$r': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$bb_decl',type,
    'register_tensor$bb': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$g_decl',type,
    'equivalent_registers$g': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('butterfly$_decl',type,
    'butterfly$': 'B_ell2$' > 'B_ell2$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('inv_into$b_decl',type,
    'inv_into$b': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$ak_decl',type,
    'comp$ak': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('complement$p_decl',type,
    'complement$p': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('bij_betw$o_decl',type,
    'bij_betw$o': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('equivalent_registers$f_decl',type,
    'equivalent_registers$f': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$bn_decl',type,
    'register_tensor$bn': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$d_decl',type,
    'register_tensor$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('register_pair$c_decl',type,
    'register_pair$c': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$r_decl',type,
    'iso_register$r': 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$a_decl',type,
    'register_tensor$a': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('complement$k_decl',type,
    'complement$k': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_c_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$af_decl',type,
    'inv_into$af': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('tensor_op$a_decl',type,
    'tensor_op$a': 'B_ell2_b_ell2_cblinfun$' > 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$' > 'B_b_a_complement_domain_prod_ell2_b_b_a_complement_domain_prod_ell2_cblinfun$' ).

thf('assoc$o_decl',type,
    'assoc$o': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$au_decl',type,
    'comp$au': 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$cf_decl',type,
    'comp$cf': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('bij_betw$d_decl',type,
    'bij_betw$d': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('register_tensor$j_decl',type,
    'register_tensor$j': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('bij_betw$b_decl',type,
    'bij_betw$b': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('compatible$s_decl',type,
    'compatible$s': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_b_complement_domain_ell2_a_a_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$bc_decl',type,
    'fun_app$bc': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_bool_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > $o ).

thf('register_tensor$k_decl',type,
    'register_tensor$k': 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' ).

thf('iso_register$u_decl',type,
    'iso_register$u': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$b_decl',type,
    'fun_app$b': 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('collect$a_decl',type,
    'collect$a': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('swap$a_decl',type,
    'swap$a': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_b_complement_domain_a_prod_ell2_a_c_prod_b_complement_domain_a_prod_ell2_cblinfun_fun$' ).

thf('regular_register$i_decl',type,
    'regular_register$i': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$l_decl',type,
    'inv_into$l': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('comp$ai_decl',type,
    'comp$ai': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$ac_decl',type,
    'inv_into$ac': 'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$ab_decl',type,
    'register_pair$ab': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$v_decl',type,
    'register$v': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('inv_into$n_decl',type,
    'inv_into$n': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$bz_decl',type,
    'comp$bz': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$v_decl',type,
    'fun_app$v': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('register_pair$ay_decl',type,
    'register_pair$ay': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_c_c_complement_domain_prod_ell2_c_c_c_complement_domain_prod_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' ).

thf('register_pair$e_decl',type,
    'register_pair$e': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_c_prod_b_complement_domain_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$c_decl',type,
    'iso_register$c': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$m_decl',type,
    'comp$m': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$ak_decl',type,
    'inv_into$ak': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$as_decl',type,
    'register_pair$as': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_b_b_complement_domain_prod_ell2_b_b_b_complement_domain_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('compatible$r_decl',type,
    'compatible$r': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$cs_decl',type,
    'comp$cs': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$p_decl',type,
    'compatible$p': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$j_decl',type,
    'tensor_op$j': 'A_ell2_a_ell2_cblinfun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$' ).

thf('assoc$m_decl',type,
    'assoc$m': 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_a_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_fun$' ).

thf('inv_into$w_decl',type,
    'inv_into$w': 'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('collect$d_decl',type,
    'collect$d': 'B_ell2_b_ell2_cblinfun_bool_fun$' > 'B_ell2_b_ell2_cblinfun_set$' ).

thf('register$y_decl',type,
    'register$y': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$bc_decl',type,
    'equivalent_registers$bc': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$_decl',type,
    'register_pair$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('top$t_decl',type,
    'top$t': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_bool_fun$' ).

thf('register$ap_decl',type,
    'register$ap': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('default$a_decl',type,
    'default$a': 'A$' ).

thf('comp$cl_decl',type,
    'comp$cl': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$l_decl',type,
    'equivalent_registers$l': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$dj_decl',type,
    'comp$dj': 'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$h_decl',type,
    'equivalent_registers$h': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$t_decl',type,
    'iso_register$t': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$x_decl',type,
    'equivalent_registers$x': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$ak_decl',type,
    'equivalent_registers$ak': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$aj_decl',type,
    'compatible$aj': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('compatible$w_decl',type,
    'compatible$w': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('complements$u_decl',type,
    'complements$u': 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > $o ).

thf('comp$f_decl',type,
    'comp$f': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('regular_register$_decl',type,
    'regular_register$': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$u_decl',type,
    'top$u': 'B_ell2_b_ell2_cblinfun_bool_fun$' ).

thf('swap$h_decl',type,
    'swap$h': 'C_a_c_prod_b_complement_domain_prod_a_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('fun_app$d_decl',type,
    'fun_app$d': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('inv_into$_decl',type,
    'inv_into$': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$t_decl',type,
    'equivalent_registers$t': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$p_decl',type,
    'iso_register$p': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('ket$b_decl',type,
    'ket$b': 'C$' > 'C_ell2$' ).

thf('compatible$q_decl',type,
    'compatible$q': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('fun_app$g_decl',type,
    'fun_app$g': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun$' ).

thf('compatible$aa_decl',type,
    'compatible$aa': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$av_decl',type,
    'equivalent_registers$av': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('top$_decl',type,
    'top$': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' ).

thf('comp$az_decl',type,
    'comp$az': 'A_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_a_c_c_prod_prod_ell2_a_c_c_prod_prod_ell2_cblinfun_fun$' > 'A_c_prod_c_prod_ell2_a_c_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$m_decl',type,
    'fun_app$m': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' ).

thf('bij_betw$u_decl',type,
    'bij_betw$u': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$' > $o ).

thf('iso_register$n_decl',type,
    'iso_register$n': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('register_pair$j_decl',type,
    'register_pair$j': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_c_a_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$j_decl',type,
    'inv_into$j': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_pair$a_decl',type,
    'register_pair$a': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$be_decl',type,
    'comp$be': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$q_decl',type,
    'register_pair$q': 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('fun_app$w_decl',type,
    'fun_app$w': 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

thf('compatible$am_decl',type,
    'compatible$am': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$az_decl',type,
    'equivalent_registers$az': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$f_decl',type,
    'tensor_op$f': 'C_ell2_c_ell2_cblinfun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' ).

thf('register_pair$n_decl',type,
    'register_pair$n': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$a_decl',type,
    'inv_into$a': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('t1$_decl',type,
    't1$': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('butterfly$c_decl',type,
    'butterfly$c': 'A_c_prod_ell2$' > 'A_c_prod_ell2$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun$' ).

thf('equivalent_registers$ax_decl',type,
    'equivalent_registers$ax': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('tensor_op$i_decl',type,
    'tensor_op$i': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('complements$a_decl',type,
    'complements$a': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$as_decl',type,
    'register$as': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$al_decl',type,
    'equivalent_registers$al': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$v_decl',type,
    'inv_into$v': 'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_c_c_b_complement_domain_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('comp$al_decl',type,
    'comp$al': 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$an_decl',type,
    'register$an': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('top$k_decl',type,
    'top$k': 'A_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_a_a_b_complement_domain_prod_a_a_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('bij_betw$k_decl',type,
    'bij_betw$k': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('fun_app$af_decl',type,
    'fun_app$af': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun$' > 'A_ell2_a_ell2_cblinfun$' ).

thf('complements$c_decl',type,
    'complements$c': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$r_decl',type,
    'register_pair$r': 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' ).

thf('comp$cc_decl',type,
    'comp$cc': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_tensor$ab_decl',type,
    'register_tensor$ab': 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('comp$bf_decl',type,
    'comp$bf': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$al_decl',type,
    'register_pair$al': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$i_decl',type,
    'register$i': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$y_decl',type,
    'register_tensor$y': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('fun_app$a_decl',type,
    'fun_app$a': 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$' ).

thf('assoc$f_decl',type,
    'assoc$f': 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_pair$ar_decl',type,
    'register_pair$ar': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_prod_ell2_c_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('fun_app$u_decl',type,
    'fun_app$u': 'C_c_prod_ell2_c_c_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'C_c_prod_ell2_c_c_prod_ell2_cblinfun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun$' ).

thf('comp$p_decl',type,
    'comp$p': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('id$_decl',type,
    'id$': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' ).

thf('complement$b_decl',type,
    'complement$b': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('tensor_op$l_decl',type,
    'tensor_op$l': 'A_ell2_a_ell2_cblinfun$' > 'C_ell2_c_ell2_cblinfun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun$' ).

thf('tensor_op$h_decl',type,
    'tensor_op$h': 'C_ell2_c_ell2_cblinfun$' > 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$' > 'C_c_c_complement_domain_prod_ell2_c_c_c_complement_domain_prod_ell2_cblinfun$' ).

thf('fun_app$n_decl',type,
    'fun_app$n': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$' ).

thf('comp$o_decl',type,
    'comp$o': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$bb_decl',type,
    'comp$bb': 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_a_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_fun$' > 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$a_decl',type,
    'comp$a': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$as_decl',type,
    'equivalent_registers$as': 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('iso_register$aa_decl',type,
    'iso_register$aa': 'C_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_c_prod_b_complement_domain_prod_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_b_complement_domain_a_b_complement_domain_prod_ell2_a_b_complement_domain_a_b_complement_domain_prod_ell2_cblinfun_fun$' > $o ).

thf('regular_register$c_decl',type,
    'regular_register$c': 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('comp$bt_decl',type,
    'comp$bt': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('complements$s_decl',type,
    'complements$s': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$i_decl',type,
    'register_tensor$i': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('comp$dl_decl',type,
    'comp$dl': 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('complement$_decl',type,
    'complement$': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$s_decl',type,
    'equivalent_registers$s': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$l_decl',type,
    'register$l': 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$h_decl',type,
    'register$h': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register$q_decl',type,
    'register$q': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('assoc$l_decl',type,
    'assoc$l': 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' ).

thf('member$a_decl',type,
    'member$a': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('inv_into$aa_decl',type,
    'inv_into$aa': 'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' > 'B_b_prod_ell2_b_b_prod_ell2_cblinfun_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_c_c_b_complement_domain_prod_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$al_decl',type,
    'register_tensor$al': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_prod_ell2_c_a_c_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$z_decl',type,
    'equivalent_registers$z': 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$u_decl',type,
    'inv_into$u': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('equivalent_registers$aw_decl',type,
    'equivalent_registers$aw': 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$bm_decl',type,
    'register_tensor$bm': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_c_prod_ell2_a_c_prod_ell2_cblinfun_fun$' ).

thf('iso_register$o_decl',type,
    'iso_register$o': 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > $o ).

thf('top$o_decl',type,
    'top$o': 'C_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_c_c_b_complement_domain_prod_prod_ell2_cblinfun_set$' ).

thf('register_tensor$bq_decl',type,
    'register_tensor$bq': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_a_prod_ell2_a_a_prod_ell2_cblinfun_a_a_prod_ell2_a_a_prod_ell2_cblinfun_fun$' ).

thf('register$x_decl',type,
    'register$x': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('equivalent_registers$aa_decl',type,
    'equivalent_registers$aa': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$ba_decl',type,
    'comp$ba': 'A_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_a_c_a_a_c_prod_b_complement_domain_prod_prod_prod_ell2_cblinfun_fun$' > 'A_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_prod_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('iso_register$d_decl',type,
    'iso_register$d': 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('comp$cn_decl',type,
    'comp$cn': 'A_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_a_a_c_prod_b_complement_domain_prod_c_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('compatible$t_decl',type,
    'compatible$t': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_pair$m_decl',type,
    'register_pair$m': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('inv_into$p_decl',type,
    'inv_into$p': 'B_ell2_b_ell2_cblinfun_set$' > 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register$n_decl',type,
    'register$n': 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('complements$p_decl',type,
    'complements$p': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('register_tensor$bg_decl',type,
    'register_tensor$bg': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('comp$ck_decl',type,
    'comp$ck': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$ao_decl',type,
    'comp$ao': 'A_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_a_a_prod_c_prod_ell2_a_a_prod_c_prod_ell2_cblinfun_fun$' > 'A_a_c_prod_prod_ell2_a_a_c_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('tensor_op$g_decl',type,
    'tensor_op$g': 'C_ell2_c_ell2_cblinfun$' > 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$' > 'C_c_a_complement_domain_prod_ell2_c_c_a_complement_domain_prod_ell2_cblinfun$' ).

thf('bij_betw$j_decl',type,
    'bij_betw$j': 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_set$' > 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$' > $o ).

thf('inv_into$r_decl',type,
    'inv_into$r': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('comp$g_decl',type,
    'comp$g': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('register_pair$k_decl',type,
    'register_pair$k': 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_a_a_c_prod_b_complement_domain_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_a_a_a_c_prod_b_complement_domain_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('i$_decl',type,
    'i$': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' ).

thf('comp$cu_decl',type,
    'comp$cu': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_b_complement_domain_a_prod_ell2_a_b_complement_domain_a_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('equivalent_registers$ae_decl',type,
    'equivalent_registers$ae': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$' > $o ).

thf('register$p_decl',type,
    'register$p': 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$' > $o ).

thf('comp$av_decl',type,
    'comp$av': 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('regular_register$e_decl',type,
    'regular_register$e': 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf('complements$q_decl',type,
    'complements$q': 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$ap_decl',type,
    'inv_into$ap': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('register_pair$h_decl',type,
    'register_pair$h': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' ).

thf('comp$bk_decl',type,
    'comp$bk': 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$' > 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$' ).

thf('register_tensor$ae_decl',type,
    'register_tensor$ae': 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'C_b_complement_domain_c_b_complement_domain_prod_ell2_c_b_complement_domain_c_b_complement_domain_prod_ell2_cblinfun_b_b_prod_ell2_b_b_prod_ell2_cblinfun_fun$' ).

thf('member$_decl',type,
    'member$': 'B_ell2_b_ell2_cblinfun$' > 'B_ell2_b_ell2_cblinfun_set$' > $o ).

thf('complements$k_decl',type,
    'complements$k': 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'A_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_a_a_c_a_c_prod_b_complement_domain_prod_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > $o ).

thf('inv_into$d_decl',type,
    'inv_into$d': 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$' > 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$' > 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$' ).

thf('complements$ag_decl',type,
    'complements$ag': 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$' > $o ).

thf(462,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ao' )
        & ( C @ 'register$t' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bn' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$cf' ) )
        = ( D @ ( B @ 'comp$cg' ) @ ( C @ ( A @ 'comp$d' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).

thf(2199,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ao' )
        & ( C @ 'register$t' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bn' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$cf' ) )
        = ( D @ ( B @ 'comp$cg' ) @ ( C @ ( A @ 'comp$d' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(66,axiom,
    'id$' @ 'iso_register$z',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).

thf(809,plain,
    'id$' @ 'iso_register$z',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(338,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$e' )
        & ( A @ 'register$q' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$ai' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).

thf(1823,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$e' )
        & ( A @ 'register$q' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'register$ai' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(293,axiom,
    'i$' @ 'iso_register$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).

thf(1633,plain,
    'i$' @ 'iso_register$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(316,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$f' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$f' ) ) ) )
           => $false )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).

thf(1729,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ~ ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ~ ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$f' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$f' ) ) ) )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(181,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$g' ) @ ( A @ ( B @ 'inv_into$f' ) @ 'fun_app$f' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).

thf(1237,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$g' ) @ ( A @ ( B @ 'inv_into$f' ) @ 'fun_app$f' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(516,axiom,
    ( 't3$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'f$' @ 'register_pair$' ) @ ( 'g$' @ 'register_pair$d' ) @ ( 'top$b' @ 'inv_into$' ) @ 'fun_app$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).

thf(2331,plain,
    ( 't3$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'f$' @ 'register_pair$' ) @ ( 'g$' @ 'register_pair$d' ) @ ( 'top$b' @ 'inv_into$' ) @ 'fun_app$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(34,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$be' ) @ 'bij_betw$' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).

thf(666,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$be' ) @ 'bij_betw$' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$a' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$be' ) @ 'bij_betw$' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(268,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$f' ) @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom184) ).

thf(1549,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$f' ) @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(270,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$q' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$g' ) @ ( A @ 'comp$r' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).

thf(1554,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$c' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$q' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$g' ) @ ( A @ 'comp$r' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(450,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$v' ) )
        & ( B @ ( A @ 'complements$' ) ) )
     => ( C @ ( A @ 'complements$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).

thf(2163,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$v' ) )
        & ( B @ ( A @ 'complements$' ) ) )
     => ( C @ ( A @ 'complements$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(33,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
    <=> ? [D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
          ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( C @ ( E @ 'member$' ) )
             => ( ( ( E @ ( D @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) )
                  = E )
                & ( B @ ( E @ ( D @ 'fun_app$f' ) @ 'member$a' ) ) ) )
          & ! [E: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( B @ ( E @ 'member$a' ) )
             => ( ( ( E @ ( A @ 'fun_app$g' ) @ ( D @ 'fun_app$f' ) )
                  = E )
                & ( C @ ( E @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).

thf(645,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ? [D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$f' ) @ 'member$a' ) ) ) )
            & ! [E: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$a' ) )
               => ( ( ( E @ ( A @ 'fun_app$g' ) @ ( D @ 'fun_app$f' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ) ) )
       => ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
      & ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
       => ? [D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$f' ) @ ( A @ 'fun_app$g' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$f' ) @ 'member$a' ) ) ) )
            & ! [E: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$a' ) )
               => ( ( ( E @ ( A @ 'fun_app$g' ) @ ( D @ 'fun_app$f' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(82,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$f' )
        & ( A @ 'iso_register$q' ) )
     => ( B @ ( A @ 'comp$a' ) @ 'iso_register$r' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).

thf(892,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$f' )
        & ( A @ 'iso_register$q' ) )
     => ( B @ ( A @ 'comp$a' ) @ 'iso_register$r' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(354,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( A @ ( 'top$b' @ 'inv_into$' ) @ 'iso_register$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom135) ).

thf(1879,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( A @ ( 'top$b' @ 'inv_into$' ) @ 'iso_register$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(312,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( B @ 'compatible$n' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).

thf(1718,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( B @ 'compatible$n' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(121,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$db' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$dc' ) )
          = 'id$d' ) )
     => ( 'top$l' @ ( 'top$d' @ ( B @ 'bij_betw$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).

thf(1024,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$db' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$dc' ) )
          = 'id$d' ) )
     => ( 'top$l' @ ( 'top$d' @ ( B @ 'bij_betw$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(242,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$j' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$a' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).

thf(1469,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'fun_app$j' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$a' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(507,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( C @ ( A @ 'compatible$d' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$ac' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).

thf(2306,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( C @ ( A @ 'compatible$d' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(520,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$a' ) )
        & ( C @ ( A @ 'compatible$ag' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) @ ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) @ 'equivalent_registers$ar' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).

thf(2341,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$a' ) )
        & ( C @ ( A @ 'compatible$ag' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) @ ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) @ 'equivalent_registers$ar' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(518,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$y' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).

thf(2336,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$y' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(435,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$am' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bl' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$cb' ) )
        = ( D @ ( B @ 'comp$cc' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).

thf(2131,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$am' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bl' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$cb' ) )
        = ( D @ ( B @ 'comp$cc' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(385,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$x' )
        & ( A @ 'register$u' ) )
     => ( ( D @ ( C @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'fun_app$o' ) )
        = ( D @ ( B @ 'fun_app$ag' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'tensor_op$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).

thf(1995,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$x' )
        & ( A @ 'register$u' ) )
     => ( ( D @ ( C @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_tensor$x' ) @ 'fun_app$o' ) )
        = ( D @ ( B @ 'fun_app$ag' ) @ ( C @ ( A @ 'fun_app$af' ) @ 'tensor_op$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(489,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$j' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$e' @ 'equivalent_registers$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).

thf(2263,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$j' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$e' @ 'equivalent_registers$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(89,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$j' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).

thf(909,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(31,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$o' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$o' ) )
              = ( C @ ( A @ 'fun_app$o' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom636) ).

thf(628,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$o' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$o' ) )
                = ( C @ ( A @ 'fun_app$o' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$o' ) )
                = ( C @ ( A @ 'fun_app$o' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(107,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).

thf(962,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(382,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$x' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$cm' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).

thf(1982,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$x' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$cm' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(175,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( B @ ( A @ 'complements$p' ) ) )
     => ( C @ ( A @ 'complements$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).

thf(1200,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( B @ ( A @ 'complements$p' ) ) )
     => ( C @ ( A @ 'complements$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(1,conjecture,
    'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'f$' @ 'register_pair$' ) @ ( 'g$' @ 'complements$' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture0) ).

thf(2,negated_conjecture,
    ~ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'f$' @ 'register_pair$' ) @ ( 'g$' @ 'complements$' ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(523,plain,
    ~ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'f$' @ 'register_pair$' ) @ ( 'g$' @ 'complements$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(466,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'register$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).

thf(2210,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(40,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$u' ) @ 'register$ad' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).

thf(683,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$u' ) @ 'register$ad' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(474,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( B @ 'register_pair$b' ) @ ( A @ 'complements$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).

thf(2231,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( B @ 'register_pair$b' ) @ ( A @ 'complements$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(231,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$e' ) @ ( 'top$d' @ 'inv_into$f' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).

thf(1443,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$e' ) @ ( 'top$d' @ 'inv_into$f' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(220,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( A @ ( B @ 'equivalent_registers$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).

thf(1401,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( A @ ( B @ 'equivalent_registers$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(177,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$' @ 'inv_into$a' ) @ 'fun_app$a' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$k' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom246) ).

thf(1205,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$k' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$' @ 'inv_into$a' ) @ 'fun_app$a' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$' @ 'inv_into$a' ) @ 'fun_app$a' ) ) )
         => ( ( B @ ( A @ 'fun_app$k' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(419,axiom,
    ( 't1$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'register_pair$n' ) @ ( 'top$' @ 'inv_into$a' ) @ 'fun_app$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).

thf(2099,plain,
    ( 't1$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'register_pair$n' ) @ ( 'top$' @ 'inv_into$a' ) @ 'fun_app$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(191,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$b' ) @ ( B @ 'fun_app$j' ) )
            = C )
        & ! [C: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$j' ) @ ( A @ 'fun_app$b' ) )
            = C ) )
     => ( ( B @ ( 'top$g' @ 'inv_into$o' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom180) ).

thf(1269,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$b' ) @ ( B @ 'fun_app$j' ) )
            = C )
        & ! [C: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$j' ) @ ( A @ 'fun_app$b' ) )
            = C ) )
     => ( ( B @ ( 'top$g' @ 'inv_into$o' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(28,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$o' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$n' ) @ 'fun_app$h' ) @ ( A @ 'fun_app$i' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom185) ).

thf(614,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$o' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$n' ) @ 'fun_app$h' ) @ ( A @ 'fun_app$i' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(229,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$t' ) )
     => ( A @ ( B @ 'comp$d' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).

thf(1437,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$t' ) )
     => ( A @ ( B @ 'comp$d' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(166,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$f' )
    <=> ( ? [B: 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$e' ) @ ( A @ 'complement$p' @ ( A @ 'register_pair$aw' ) ) )
            = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( A @ 'register$t' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).

thf(1173,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$e' ) @ ( A @ 'complement$p' @ ( A @ 'register_pair$aw' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$t' ) )
       => ( A @ 'regular_register$f' ) )
      & ( ( A @ 'regular_register$f' )
       => ( ? [B: 'A_c_complement_domain_ell2_a_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$e' ) @ ( A @ 'complement$p' @ ( A @ 'register_pair$aw' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$t' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(428,axiom,
    'top$a' @ ( 'top$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'register_pair$n' ) @ 'bij_betw$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).

thf(2117,plain,
    'top$a' @ ( 'top$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'register_pair$n' ) @ 'bij_betw$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(421,axiom,
    'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'complement$e' @ 'equivalent_registers$' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).

thf(2104,plain,
    'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'complement$e' @ 'equivalent_registers$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(226,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$aq' ) ) )
     => ( C @ ( B @ 'comp$k' ) @ ( A @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).

thf(1422,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$aq' ) ) )
     => ( C @ ( B @ 'comp$k' ) @ ( A @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(370,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ ( C @ 'compatible$ar' ) )
        & ( B @ ( A @ 'compatible$ax' ) ) )
     => ( D @ ( B @ 'register_tensor$i' ) @ ( C @ ( A @ 'register_tensor$i' ) @ 'compatible$ay' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).

thf(1939,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ ( C @ 'compatible$ar' ) )
        & ( B @ ( A @ 'compatible$ax' ) ) )
     => ( D @ ( B @ 'register_tensor$i' ) @ ( C @ ( A @ 'register_tensor$i' ) @ 'compatible$ay' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(196,axiom,
    'id$' @ 'register$q',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).

thf(1305,plain,
    'id$' @ 'register$q',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(23,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$h' ) @ ( B @ 'fun_app$i' ) )
            = C )
        & ! [C: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$i' ) @ ( A @ 'fun_app$h' ) )
            = C ) )
     => ( ( B @ ( 'top$g' @ 'inv_into$n' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom179) ).

thf(597,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$h' ) @ ( B @ 'fun_app$i' ) )
            = C )
        & ! [C: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$i' ) @ ( A @ 'fun_app$h' ) )
            = C ) )
     => ( ( B @ ( 'top$g' @ 'inv_into$n' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(253,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$b' ) )
     => ( ( B @ ( A @ 'register_tensor$d' ) @ ( 'top$j' @ 'inv_into$x' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'register_tensor$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).

thf(1497,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$b' ) )
     => ( ( B @ ( A @ 'register_tensor$d' ) @ ( 'top$j' @ 'inv_into$x' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'register_tensor$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(228,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$c' ) ) )
        & ! [B: 'B_ell2_b_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$c' ) )
              = ( C @ ( A @ 'fun_app$c' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).

thf(1426,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$c' ) ) )
        & ! [B: 'B_ell2_b_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$c' ) )
                = ( C @ ( A @ 'fun_app$c' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$c' ) )
                = ( C @ ( A @ 'fun_app$c' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(5,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( 'top$c' @ ( 'top$c' @ ( A @ ( 'top$c' @ 'inv_into$s' ) @ 'bij_betw$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).

thf(533,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( 'top$c' @ ( 'top$c' @ ( A @ ( 'top$c' @ 'inv_into$s' ) @ 'bij_betw$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(349,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( B @ 'register_pair$h' ) @ ( A @ 'complements$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).

thf(1867,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( B @ 'register_pair$h' ) @ ( A @ 'complements$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(386,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( ( 'swap$e' @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$cs' ) )
        = ( A @ ( B @ 'register_pair$ab' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).

thf(1999,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( ( 'swap$e' @ ( B @ ( A @ 'register_pair$d' ) @ 'comp$cs' ) )
        = ( A @ ( B @ 'register_pair$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(440,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$x' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).

thf(2141,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(69,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
    <=> ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ( ( A @ ( B @ 'comp$do' ) )
              = 'id$i' )
            & ( ( B @ ( A @ 'comp$dp' ) )
              = 'id$g' )
            & ( B @ 'register$as' ) )
        & ( A @ 'register$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom590) ).

thf(814,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$do' ) )
                = 'id$i' )
              & ( ( B @ ( A @ 'comp$dp' ) )
                = 'id$g' )
              & ( B @ 'register$as' ) )
          & ( A @ 'register$e' ) )
       => ( A @ 'iso_register$' ) )
      & ( ( A @ 'iso_register$' )
       => ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$do' ) )
                = 'id$i' )
              & ( ( B @ ( A @ 'comp$dp' ) )
                = 'id$g' )
              & ( B @ 'register$as' ) )
          & ( A @ 'register$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(188,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ag' )
     => ( ( A @ ( 'top$g' @ 'inv_into$ar' ) @ ( A @ 'comp$di' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom605) ).

thf(1260,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ag' )
     => ( ( A @ ( 'top$g' @ 'inv_into$ar' ) @ ( A @ 'comp$di' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(91,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dc' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$db' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$ap' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).

thf(913,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dc' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$db' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$ap' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(297,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( B @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).

thf(1640,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( B @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(102,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$c' ) )
     => ( 'top$c' = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).

thf(945,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$c' ) )
     => ( 'top$c' = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(398,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom125) ).

thf(2042,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(257,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$x' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$m' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$t' ) @ ( A @ 'comp$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).

thf(1507,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$x' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$m' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$t' ) @ ( A @ 'comp$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(7,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$bv' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$bv' ) )
          = 'id$' )
        & ( B @ 'register$q' )
        & ( A @ 'register$q' ) )
     => ( A @ 'iso_register$z' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).

thf(538,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$bv' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$bv' ) )
          = 'id$' )
        & ( B @ 'register$q' )
        & ( A @ 'register$q' ) )
     => ( A @ 'iso_register$z' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(209,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$p' )
     => ( A @ ( 'top$g' @ 'inv_into$n' ) @ 'iso_register$q' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).

thf(1354,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$p' )
     => ( A @ ( 'top$g' @ 'inv_into$n' ) @ 'iso_register$q' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(442,axiom,
    'g$' @ 'regular_register$a',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).

thf(2146,plain,
    'g$' @ 'regular_register$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(173,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( A @ 'register$j' ) )
     => ( C @ ( A @ 'comp$al' ) @ ( B @ ( A @ 'comp$q' ) @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).

thf(1196,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( A @ 'register$j' ) )
     => ( C @ ( A @ 'comp$al' ) @ ( B @ ( A @ 'comp$q' ) @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(85,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$j' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$m' ) @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).

thf(898,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$j' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$m' ) @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(400,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ 'register$h' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).

thf(2046,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ 'register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(275,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$a' )
    <=> ( ? [B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( A @ 'complement$f' @ ( A @ 'register_pair$x' ) @ 'fun_app$d' ) )
            = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( A @ 'register$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).

thf(1576,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( A @ 'complement$f' @ ( A @ 'register_pair$x' ) @ 'fun_app$d' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$' ) )
       => ( A @ 'regular_register$a' ) )
      & ( ( A @ 'regular_register$a' )
       => ( ? [B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( A @ 'complement$f' @ ( A @ 'register_pair$x' ) @ 'fun_app$d' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(126,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dp' ) )
          = 'id$g' )
        & ( ( B @ ( A @ 'comp$do' ) )
          = 'id$i' )
        & ( B @ 'register$e' )
        & ( A @ 'register$as' ) )
     => ( A @ 'iso_register$s' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).

thf(1046,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dp' ) )
          = 'id$g' )
        & ( ( B @ ( A @ 'comp$do' ) )
          = 'id$i' )
        & ( B @ 'register$e' )
        & ( A @ 'register$as' ) )
     => ( A @ 'iso_register$s' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(368,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( B @ ( A @ 'complements$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).

thf(1935,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( B @ ( A @ 'complements$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(244,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$d' ) @ 'register$k' )
     => ( A @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).

thf(1475,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$d' ) @ 'register$k' )
     => ( A @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(333,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$g' )
    <=> ( ? [B: 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$g' ) @ ( A @ 'complement$q' @ ( A @ 'register_pair$ax' ) ) )
            = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( A @ 'register$u' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).

thf(1803,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$g' ) @ ( A @ 'complement$q' @ ( A @ 'register_pair$ax' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$u' ) )
       => ( A @ 'regular_register$g' ) )
      & ( ( A @ 'regular_register$g' )
       => ( ? [B: 'C_a_complement_domain_ell2_c_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$g' ) @ ( A @ 'complement$q' @ ( A @ 'register_pair$ax' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(437,axiom,
    'f$' @ 'register$a',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).

thf(2136,plain,
    'f$' @ 'register$a',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(358,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( 'top$e' @ ( 'top$f' @ ( B @ 'bij_betw$i' ) ) )
        & ( 'top$a' @ ( 'top$e' @ ( A @ 'bij_betw$h' ) ) ) )
     => ( ( B @ ( A @ 'comp$' ) @ ( 'top$f' @ 'inv_into$j' ) )
        = ( A @ ( 'top$e' @ 'inv_into$l' ) @ ( B @ ( 'top$f' @ 'inv_into$k' ) @ 'comp$ag' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).

thf(1904,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( 'top$e' @ ( 'top$f' @ ( B @ 'bij_betw$i' ) ) )
        & ( 'top$a' @ ( 'top$e' @ ( A @ 'bij_betw$h' ) ) ) )
     => ( ( B @ ( A @ 'comp$' ) @ ( 'top$f' @ 'inv_into$j' ) )
        = ( A @ ( 'top$e' @ 'inv_into$l' ) @ ( B @ ( 'top$f' @ 'inv_into$k' ) @ 'comp$ag' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(180,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$b' )
    <=> ( ? [B: 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$' ) @ ( A @ 'complement$l' @ ( A @ 'register_pair$as' ) ) )
            = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( A @ 'register$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).

thf(1228,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$' ) @ ( A @ 'complement$l' @ ( A @ 'register_pair$as' ) ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$j' ) )
       => ( A @ 'regular_register$b' ) )
      & ( ( A @ 'regular_register$b' )
       => ( ? [B: 'B_b_complement_domain_ell2_b_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$' ) @ ( A @ 'complement$l' @ ( A @ 'register_pair$as' ) ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(291,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$c' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$c' ) ) ) )
           => $false )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).

thf(1623,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ~ ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ~ ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$c' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$c' ) ) ) )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(247,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$a' ) @ 'fun_app$a' ) @ ( A @ 'fun_app$k' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom181) ).

thf(1482,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$a' ) @ 'fun_app$a' ) @ ( A @ 'fun_app$k' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(130,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$d' ) @ ( C @ 'inv_into$c' ) @ 'fun_app$d' ) )
        = ( D @ ( A @ 'fun_app$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom193) ).

thf(1055,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$d' ) @ ( C @ 'inv_into$c' ) @ 'fun_app$d' ) )
        = ( D @ ( A @ 'fun_app$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(515,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$k' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'comp$l' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).

thf(2328,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$k' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'comp$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(331,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$h' )
    <=> ( ? [B: 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$h' ) @ ( A @ 'complement$r' @ ( A @ 'register_pair$ay' ) ) )
            = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( A @ 'register$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).

thf(1792,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$h' ) @ ( A @ 'complement$r' @ ( A @ 'register_pair$ay' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$p' ) )
       => ( A @ 'regular_register$h' ) )
      & ( ( A @ 'regular_register$h' )
       => ( ? [B: 'C_c_complement_domain_ell2_c_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$h' ) @ ( A @ 'complement$r' @ ( A @ 'register_pair$ay' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$p' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(397,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$k' ) @ ( A @ ( B @ 'inv_into$a' ) @ 'fun_app$a' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).

thf(2039,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$k' ) @ ( A @ ( B @ 'inv_into$a' ) @ 'fun_app$a' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(351,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$' ) @ ( 'top$h' @ 'inv_into$v' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).

thf(1871,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$' ) @ ( 'top$h' @ 'inv_into$v' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(359,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$l' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$e' @ 'equivalent_registers$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).

thf(1907,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$l' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$e' @ 'equivalent_registers$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(202,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'fun_app$' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$e' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).

thf(1330,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$e' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'fun_app$' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'fun_app$' ) ) )
         => ( ( B @ ( A @ 'fun_app$e' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(236,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$y' )
        & ( A @ 'register$p' ) )
     => ( ( D @ ( C @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_tensor$y' ) @ 'fun_app$m' ) )
        = ( D @ ( B @ 'fun_app$ai' ) @ ( C @ ( A @ 'fun_app$ah' ) @ 'tensor_op$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).

thf(1455,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$y' )
        & ( A @ 'register$p' ) )
     => ( ( D @ ( C @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_tensor$y' ) @ 'fun_app$m' ) )
        = ( D @ ( B @ 'fun_app$ai' ) @ ( C @ ( A @ 'fun_app$ah' ) @ 'tensor_op$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(171,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).

thf(1191,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(433,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$l' @ ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) @ 'comp$ba' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).

thf(2126,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$l' @ ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) @ 'comp$ba' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(8,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$t' ) @ ( 'top$d' @ 'inv_into$u' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom258) ).

thf(542,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$t' ) @ ( 'top$d' @ 'inv_into$u' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(323,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$p' ) )
     => ( A @ ( B @ 'comp$e' ) @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).

thf(1760,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$p' ) )
     => ( A @ ( B @ 'comp$e' ) @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(303,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$e' )
        & ( C @ 'register$q' )
        & ( B @ 'register$d' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$i' ) @ ( B @ ( A @ 'register_tensor$bf' ) @ 'comp$bt' ) )
        = ( D @ ( B @ 'comp$' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_tensor$bg' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).

thf(1660,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$e' )
        & ( C @ 'register$q' )
        & ( B @ 'register$d' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'register_tensor$i' ) @ ( B @ ( A @ 'register_tensor$bf' ) @ 'comp$bt' ) )
        = ( D @ ( B @ 'comp$' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_tensor$bg' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(19,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$c' @ ( 'top$a' @ ( B @ 'bij_betw$c' ) ) )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( B @ ( A @ 'comp$ab' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( B @ ( 'top$a' @ 'inv_into$c' ) @ 'comp$ab' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).

thf(587,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$c' @ ( 'top$a' @ ( B @ 'bij_betw$c' ) ) )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( B @ ( A @ 'comp$ab' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( B @ ( 'top$a' @ 'inv_into$c' ) @ 'comp$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(30,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$d' @ 'inv_into$u' ) @ 'fun_app$o' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$n' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).

thf(619,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$n' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$d' @ 'inv_into$u' ) @ 'fun_app$o' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$d' @ 'inv_into$u' ) @ 'fun_app$o' ) ) )
         => ( ( B @ ( A @ 'fun_app$n' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(494,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( A @ 'compatible$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).

thf(2274,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( A @ 'compatible$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(44,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$q' ) @ 'iso_register$' )
        & ( B @ ( A @ 'compatible$u' ) ) )
     => ( B @ ( A @ 'complements$r' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).

thf(702,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$q' ) @ 'iso_register$' )
        & ( B @ ( A @ 'compatible$u' ) ) )
     => ( B @ ( A @ 'complements$r' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(266,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
     => ( 'top$a' @ ( 'top$' @ ( A @ ( B @ 'comp$be' ) @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).

thf(1545,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
     => ( 'top$a' @ ( 'top$' @ ( A @ ( B @ 'comp$be' ) @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(11,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$u' ) @ ( 'top$c' @ 'inv_into$t' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).

thf(559,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$u' ) @ ( 'top$c' @ 'inv_into$t' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(73,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).

thf(853,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(356,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$j' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ 'comp$j' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).

thf(1892,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$j' )
        & ( A @ 'register$a' ) )
     => ( A @ ( B @ 'comp$j' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(453,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$k' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$ba' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).

thf(2169,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$k' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$ba' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(311,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
    <=> ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
        ? [C: 'B_ell2_b_ell2_cblinfun$'] :
          ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$f' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$f' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).

thf(1704,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$f' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$f' ) )
              = B ) )
       => ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
      & ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
       => ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$f' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$f' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(285,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$f' @ 'register_tensor$ae' ) @ ( B @ ( A @ 'register_tensor$r' ) @ 'complements$x' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).

thf(1609,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$f' @ 'register_tensor$ae' ) @ ( B @ ( A @ 'register_tensor$r' ) @ 'complements$x' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(26,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( A @ ( 'top$q' @ 'fun_app$ba' ) )
    <=> ( 'top$c' @ ( A @ 'member$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).

thf(606,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( 'top$c' @ ( A @ 'member$c' ) )
       => ( A @ ( 'top$q' @ 'fun_app$ba' ) ) )
      & ( ( A @ ( 'top$q' @ 'fun_app$ba' ) )
       => ( 'top$c' @ ( A @ 'member$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(59,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( A @ ( 'top$s' @ 'fun_app$bc' ) )
    <=> ( 'top$d' @ ( A @ 'member$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom626) ).

thf(770,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( 'top$d' @ ( A @ 'member$a' ) )
       => ( A @ ( 'top$s' @ 'fun_app$bc' ) ) )
      & ( ( A @ ( 'top$s' @ 'fun_app$bc' ) )
       => ( 'top$d' @ ( A @ 'member$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(79,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).

thf(881,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(148,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).

thf(1115,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(448,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( A @ 'compatible$r' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).

thf(2158,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( A @ 'compatible$r' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(393,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ! [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$e' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$e' ) ) ) )
           => $false )
        & ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).

thf(2024,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ~ ( ! [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$e' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$e' ) ) ) )
        & ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(505,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( 'assoc$h' @ ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) @ 'comp$aw' ) )
        = ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).

thf(2301,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( 'assoc$h' @ ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) @ 'comp$aw' ) )
        = ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(335,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ ( B @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).

thf(1815,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ ( B @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(477,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$aa' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$ay' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).

thf(2237,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$aa' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$ay' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(240,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'iso_register$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).

thf(1465,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'iso_register$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(195,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$c' ) @ ( B @ 'fun_app$d' ) )
            = C )
        & ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$c' ) )
            = C ) )
     => ( ( B @ ( 'top$c' @ 'inv_into$d' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).

thf(1302,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$c' ) @ ( B @ 'fun_app$d' ) )
            = C )
        & ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$d' ) @ ( A @ 'fun_app$c' ) )
            = C ) )
     => ( ( B @ ( 'top$c' @ 'inv_into$d' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(422,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$e' @ 'register_tensor$ak' ) @ ( B @ ( A @ 'register_tensor$aj' ) @ 'complements$aa' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).

thf(2105,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$e' @ 'register_tensor$ak' ) @ ( B @ ( A @ 'register_tensor$aj' ) @ 'complements$aa' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(361,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( A @ 'register_pair$l' ) @ ( B @ 'complements$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).

thf(1911,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( A @ 'register_pair$l' ) @ ( B @ 'complements$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(146,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dc' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$db' ) )
          = 'id$' ) )
     => ( 'top$d' @ ( 'top$l' @ ( B @ 'bij_betw$ac' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).

thf(1109,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dc' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$db' ) )
          = 'id$' ) )
     => ( 'top$d' @ ( 'top$l' @ ( B @ 'bij_betw$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(487,axiom,
    ( 't2$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'register_pair$i' ) @ ( 'top$g' @ 'inv_into$o' ) @ 'fun_app$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).

thf(2259,plain,
    ( 't2$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'register_pair$i' ) @ ( 'top$g' @ 'inv_into$o' ) @ 'fun_app$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(99,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [B: 'B_ell2_b_ell2_cblinfun$'] : ( A @ ( B @ 'member$' ) )
     => ( 'top$a' = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).

thf(937,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [B: 'B_ell2_b_ell2_cblinfun$'] : ( A @ ( B @ 'member$' ) )
     => ( 'top$a' = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(395,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ad' )
     => ( ( A @ ( 'top$c' @ 'inv_into$ao' ) @ ( A @ 'comp$cy' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).

thf(2034,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ad' )
     => ( ( A @ ( 'top$c' @ 'inv_into$ao' ) @ ( A @ 'comp$cy' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(65,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$d' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$e' ) @ ( A @ ( B @ 'inv_into$' ) @ 'fun_app$' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).

thf(806,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$d' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$e' ) @ ( A @ ( B @ 'inv_into$' ) @ 'fun_app$' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(109,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
    <=> ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
        ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$o' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$o' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).

thf(966,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$o' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$o' ) )
              = B ) )
       => ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) )
      & ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
       => ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$o' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$o' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(409,axiom,
    ( ! [A: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
        ( ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) )
          = ( A @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) ) )
       => $false )
   => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).

thf(2073,plain,
    ~ ! [A: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
        ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) )
       != ( A @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(128,axiom,
    ? [A: 'B_ell2_b_ell2_cblinfun$'] : ( 'top$a' @ ( A @ 'member$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).

thf(1051,plain,
    ? [A: 'B_ell2_b_ell2_cblinfun$'] : ( 'top$a' @ ( A @ 'member$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(390,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).

thf(2017,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(57,axiom,
    'top$g' @ ( 'top$g' @ ( 'id$e' @ 'bij_betw$w' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).

thf(766,plain,
    'top$g' @ ( 'top$g' @ ( 'id$e' @ 'bij_betw$w' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(403,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$' ) @ 'compatible$am' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).

thf(2058,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$' ) @ 'compatible$am' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(458,axiom,
    ! [A: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ba' ) )
     => ( ( 'swap$a' @ ( B @ ( A @ 'register_pair$bd' ) @ 'comp$co' ) )
        = ( A @ ( B @ 'register_pair$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).

thf(2190,plain,
    ! [A: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ba' ) )
     => ( ( 'swap$a' @ ( B @ ( A @ 'register_pair$bd' ) @ 'comp$co' ) )
        = ( A @ ( B @ 'register_pair$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(136,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$p' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$o' ) @ 'fun_app$b' ) @ ( A @ 'fun_app$j' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom186) ).

thf(1072,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$p' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$o' ) @ 'fun_app$b' ) @ ( A @ 'fun_app$j' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(150,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$e' @ 'register_tensor$ac' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'complements$v' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).

thf(1119,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$e' @ 'register_tensor$ac' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'complements$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(208,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$d' ) )
     => ( ( B @ ( A @ 'register_tensor$n' ) @ ( 'top$o' @ 'inv_into$ac' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'register_tensor$o' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).

thf(1351,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$g' )
        & ( A @ 'iso_register$d' ) )
     => ( ( B @ ( A @ 'register_tensor$n' ) @ ( 'top$o' @ 'inv_into$ac' ) )
        = ( B @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'register_tensor$o' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(387,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = ( D @ ( C @ 'comp$a' ) ) )
     => ( ( E @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( E @ ( D @ 'fun_app$f' ) @ ( C @ 'fun_app$h' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).

thf(2002,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = ( D @ ( C @ 'comp$a' ) ) )
     => ( ( E @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( E @ ( D @ 'fun_app$f' ) @ ( C @ 'fun_app$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(222,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( A @ 'register_pair$m' ) @ ( B @ 'complements$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).

thf(1405,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( A @ 'register_pair$m' ) @ ( B @ 'complements$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(379,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( A @ 'compatible$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).

thf(1975,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( A @ 'compatible$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(262,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'compatible$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).

thf(1526,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'compatible$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(438,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( A @ 'complements$s' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).

thf(2137,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( A @ 'complements$s' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(479,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( ( 'swap$f' @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ct' ) )
        = ( A @ ( B @ 'register_pair$bd' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).

thf(2242,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( ( 'swap$f' @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ct' ) )
        = ( A @ ( B @ 'register_pair$bd' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(497,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$' ) )
     => ( A @ 'complement$f' @ ( B @ 'equivalent_registers$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).

thf(2286,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$' ) )
     => ( A @ 'complement$f' @ ( B @ 'equivalent_registers$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(144,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$q' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$p' ) @ ( C @ 'inv_into$' ) @ 'fun_app$' ) )
        = ( D @ ( A @ 'fun_app$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).

thf(1104,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$q' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$p' ) @ ( C @ 'inv_into$' ) @ 'fun_app$' ) )
        = ( D @ ( A @ 'fun_app$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(310,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$p' ) )
    <=> ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).

thf(1697,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
          & ( B @ ( A @ 'compatible$c' ) ) )
       => ( B @ ( A @ 'complements$p' ) ) )
      & ( ( B @ ( A @ 'complements$p' ) )
       => ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
          & ( B @ ( A @ 'compatible$c' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(183,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$d' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom182) ).

thf(1242,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$d' ) @ 'fun_app$c' ) @ ( A @ 'fun_app$d' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(347,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$w' ) ) )
     => ( B @ ( C @ 'comp$h' ) @ ( A @ ( C @ 'comp$g' ) @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom266) ).

thf(1863,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$w' ) ) )
     => ( B @ ( C @ 'comp$h' ) @ ( A @ ( C @ 'comp$g' ) @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(299,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$u' ) )
        & ( A @ 'register$d' ) )
     => ( ( C @ ( A @ 'comp$z' ) @ ( B @ ( A @ 'comp$y' ) @ 'register_pair$b' ) )
        = ( C @ ( B @ 'register_pair$q' ) @ ( A @ 'comp$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).

thf(1651,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$u' ) )
        & ( A @ 'register$d' ) )
     => ( ( C @ ( A @ 'comp$z' ) @ ( B @ ( A @ 'comp$y' ) @ 'register_pair$b' ) )
        = ( C @ ( B @ 'register_pair$q' ) @ ( A @ 'comp$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(283,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( A @ ( 'top$g' @ 'inv_into$o' ) @ 'iso_register$r' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).

thf(1604,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( A @ ( 'top$g' @ 'inv_into$o' ) @ 'iso_register$r' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(94,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$i' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$h' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$' ) @ 'bij_betw$t' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).

thf(920,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$i' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$' ) @ 'bij_betw$t' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$h' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$h' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$' ) @ 'bij_betw$t' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(464,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( ( 'assoc$' @ ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) @ 'comp$ao' ) )
        = ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).

thf(2204,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( ( 'assoc$' @ ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) @ 'comp$ao' ) )
        = ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(197,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$y' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$o' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$u' ) @ ( A @ 'comp$p' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).

thf(1306,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$y' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$o' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$g' ) )
        = ( C @ ( B @ 'register_pair$u' ) @ ( A @ 'comp$p' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(55,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
     => ( ( B @ ( A @ 'comp$af' ) @ ( 'top$a' @ 'inv_into$e' ) )
        = ( A @ ( 'top$a' @ 'inv_into$e' ) @ ( B @ ( 'top$a' @ 'inv_into$b' ) @ 'comp$r' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).

thf(761,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
     => ( ( B @ ( A @ 'comp$af' ) @ ( 'top$a' @ 'inv_into$e' ) )
        = ( A @ ( 'top$a' @ 'inv_into$e' ) @ ( B @ ( 'top$a' @ 'inv_into$b' ) @ 'comp$r' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(429,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$d' ) @ 'iso_register$d' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( B @ ( A @ 'complements$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).

thf(2118,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$d' ) @ 'iso_register$d' )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( B @ ( A @ 'complements$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(67,axiom,
    ( ( 'id$e' @ ( 'top$g' @ 'inv_into$ai' ) )
    = 'id$e' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).

thf(810,plain,
    ( ( 'id$e' @ ( 'top$g' @ 'inv_into$ai' ) )
    = 'id$e' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(416,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$' ) )
     => ( A @ ( B @ 'complements$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).

thf(2093,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$' ) )
     => ( A @ ( B @ 'complements$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(502,axiom,
    'g$' @ 'register$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).

thf(2296,plain,
    'g$' @ 'register$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(412,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ ( A @ 'complement$' @ 'compatible$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).

thf(2083,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ ( A @ 'complement$' @ 'compatible$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(327,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$n' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$n' ) ) ) )
           => $false )
        & ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).

thf(1768,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ~ ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$n' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$n' ) ) ) )
        & ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(295,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( B @ ( C @ 'register_pair$i' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$am' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).

thf(1636,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( B @ ( C @ 'register_pair$i' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$am' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(164,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$o' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$o' ) ) ) )
           => $false )
        & ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).

thf(1163,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ~ ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$o' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$o' ) ) ) )
        & ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(52,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$c' ) )
         => ( ( E @ ( B @ 'fun_app$d' ) )
            = ( E @ ( C @ 'fun_app$d' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'bij_betw$b' ) ) )
      <=> ( D @ ( A @ ( C @ 'bij_betw$b' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).

thf(746,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$c' ) )
         => ( ( E @ ( B @ 'fun_app$d' ) )
            = ( E @ ( C @ 'fun_app$d' ) ) ) )
     => ( ( ( D @ ( A @ ( C @ 'bij_betw$b' ) ) )
         => ( D @ ( A @ ( B @ 'bij_betw$b' ) ) ) )
        & ( ( D @ ( A @ ( B @ 'bij_betw$b' ) ) )
         => ( D @ ( A @ ( C @ 'bij_betw$b' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(205,axiom,
    ! [A: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$am' ) )
     => ( ( 'swap$' @ ( B @ ( A @ 'register_pair$ab' ) @ 'comp$cn' ) )
        = ( A @ ( B @ 'register_pair$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom518) ).

thf(1343,plain,
    ! [A: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$am' ) )
     => ( ( 'swap$' @ ( B @ ( A @ 'register_pair$ab' ) @ 'comp$cn' ) )
        = ( A @ ( B @ 'register_pair$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(186,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( 'top$' @ ( 'top$a' @ ( A @ ( 'top$' @ 'inv_into$a' ) @ 'bij_betw$j' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).

thf(1255,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( 'top$' @ ( 'top$a' @ ( A @ ( 'top$' @ 'inv_into$a' ) @ 'bij_betw$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(273,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'fun_app$b' ) )
      = ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).

thf(1570,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'fun_app$b' ) )
      = ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(255,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'complements$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).

thf(1502,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'complements$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(305,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$ba' ) @ 'fun_app$aq' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ag' ) )
        & ( A @ 'register$u' ) )
     => ( A @ 'regular_register$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).

thf(1666,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$ba' ) @ 'fun_app$aq' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ag' ) )
        & ( A @ 'register$u' ) )
     => ( A @ 'regular_register$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(289,axiom,
    ( 'top$b'
    = ( 'top$r' @ 'collect$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).

thf(1619,plain,
    ( 'top$b'
    = ( 'top$r' @ 'collect$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(394,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$a' ) @ 'bij_betw$j' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).

thf(2032,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$a' ) @ 'bij_betw$j' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(50,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ 'comp$ab' ) )
        = 'id$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom600) ).

thf(729,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( A @ 'comp$ab' ) )
        = 'id$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(389,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$j' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ 'comp$k' ) @ ( A @ ( C @ 'comp$j' ) @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom267) ).

thf(2015,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$j' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ 'comp$k' ) @ ( A @ ( C @ 'comp$j' ) @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(214,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ 'comp$dg' ) )
        = 'id$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom604) ).

thf(1387,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( A @ 'comp$dg' ) )
        = 'id$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(314,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$e' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$l' ) @ ( 'top$n' @ 'inv_into$ab' ) )
        = ( B @ ( 'top$g' @ 'inv_into$o' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).

thf(1723,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$e' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$l' ) @ ( 'top$n' @ 'inv_into$ab' ) )
        = ( B @ ( 'top$g' @ 'inv_into$o' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(105,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( 'top$c' @ ( 'top$d' @ ( A @ ( 'top$c' @ 'inv_into$t' ) @ 'bij_betw$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).

thf(957,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( 'top$c' @ ( 'top$d' @ ( A @ ( 'top$c' @ 'inv_into$t' ) @ 'bij_betw$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(83,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$a' ) )
         => ( C @ ( D @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).

thf(894,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$a' ) )
         => ( C @ ( D @ ( A @ 'fun_app$g' ) @ 'member$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(482,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( C @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$v' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).

thf(2249,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( B @ ( C @ 'register_pair$' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$v' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(61,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$u' ) )
     => ( B @ ( A @ 'register_pair$q' ) @ 'register$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).

thf(778,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$u' ) )
     => ( B @ ( A @ 'register_pair$q' ) @ 'register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(179,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$b' ) )
         => ( ( E @ ( B @ 'fun_app$k' ) )
            = ( E @ ( C @ 'fun_app$k' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'bij_betw$' ) ) )
      <=> ( D @ ( A @ ( C @ 'bij_betw$' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).

thf(1217,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$b' ) )
         => ( ( E @ ( B @ 'fun_app$k' ) )
            = ( E @ ( C @ 'fun_app$k' ) ) ) )
     => ( ( ( D @ ( A @ ( C @ 'bij_betw$' ) ) )
         => ( D @ ( A @ ( B @ 'bij_betw$' ) ) ) )
        & ( ( D @ ( A @ ( B @ 'bij_betw$' ) ) )
         => ( D @ ( A @ ( C @ 'bij_betw$' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(443,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( C @ ( A @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) @ ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) @ 'equivalent_registers$at' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).

thf(2147,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( C @ ( A @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) @ ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) @ 'equivalent_registers$at' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(92,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$g' ) @ 'register$m' )
     => ( B @ 'register$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).

thf(916,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$g' ) @ 'register$m' )
     => ( B @ 'register$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(14,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$r' ) @ 'register$z' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).

thf(566,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$r' ) @ 'register$z' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(364,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$c' ) @ ( 'top$c' @ 'inv_into$d' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).

thf(1920,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$c' ) @ ( 'top$c' @ 'inv_into$d' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(407,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$aa' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$u' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$w' ) @ ( A @ 'comp$v' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).

thf(2068,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$aa' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$u' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$w' ) @ ( A @ 'comp$v' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(456,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$' ) )
    <=> ( ( B @ ( A @ 'register_pair$d' ) @ 'iso_register$d' )
        & ( B @ ( A @ 'compatible$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).

thf(2181,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$d' ) @ 'iso_register$d' )
          & ( B @ ( A @ 'compatible$a' ) ) )
       => ( B @ ( A @ 'complements$' ) ) )
      & ( ( B @ ( A @ 'complements$' ) )
       => ( ( B @ ( A @ 'register_pair$d' ) @ 'iso_register$d' )
          & ( B @ ( A @ 'compatible$a' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(301,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'complements$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).

thf(1656,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'complements$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(122,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$be' ) @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).

thf(1027,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$be' ) @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(53,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$d' @ ( A @ 'member$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).

thf(757,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$d' @ ( A @ 'member$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(223,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ae' )
     => ( ( A @ ( 'top$d' @ 'inv_into$ap' ) @ ( A @ 'comp$db' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom601) ).

thf(1407,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$ae' )
     => ( ( A @ ( 'top$d' @ 'inv_into$ap' ) @ ( A @ 'comp$db' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(47,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( B @ 'comp$ac' ) @ 'bij_betw$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).

thf(710,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) )
        & ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( B @ 'comp$ac' ) @ 'bij_betw$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(274,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( 'top$a' @ 'inv_into$e' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).

thf(1573,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( 'top$a' @ 'inv_into$e' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(124,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$n' ) ) )
        & ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$n' ) )
              = ( C @ ( A @ 'fun_app$n' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom638) ).

thf(1032,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$n' ) ) )
        & ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$n' ) )
                = ( C @ ( A @ 'fun_app$n' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$n' ) )
                = ( C @ ( A @ 'fun_app$n' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(282,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$z' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'iso_register$p' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).

thf(1602,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$z' ) )
     => ( B @ ( A @ 'register_tensor$i' ) @ 'iso_register$p' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(294,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$q' ) )
     => ( A @ ( B @ 'comp$g' ) @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).

thf(1634,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$q' ) )
     => ( A @ ( B @ 'comp$g' ) @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(216,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$v' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$v' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cd' ) )
        = ( D @ ( B @ 'comp$ai' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).

thf(1392,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$v' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$v' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cd' ) )
        = ( D @ ( B @ 'comp$ai' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(480,axiom,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$a' ) @ 'fun_app$b' ) )
    = ( 'aF$' @ ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ 'fun_app$az' ) @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).

thf(2245,plain,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$a' ) @ 'fun_app$b' ) )
    = ( 'aF$' @ ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ 'fun_app$az' ) @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(278,axiom,
    ( ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) )
    = ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ ( 'id$' @ 'register_tensor$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).

thf(1592,plain,
    ( ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) )
    = ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ ( 'id$' @ 'register_tensor$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(140,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( ( B @ ( A @ 'comp$r' ) @ ( 'top$d' @ 'inv_into$f' ) )
        = ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( B @ ( 'top$d' @ 'inv_into$f' ) @ 'comp$af' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).

thf(1089,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( ( B @ ( A @ 'comp$r' ) @ ( 'top$d' @ 'inv_into$f' ) )
        = ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( B @ ( 'top$d' @ 'inv_into$f' ) @ 'comp$af' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(427,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).

thf(2115,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(324,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( A @ 'complements$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).

thf(1762,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( A @ 'complements$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(103,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).

thf(948,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$ae' ) @ 'bij_betw$b' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$a' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(201,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$al' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).

thf(1328,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( B @ ( C @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(151,axiom,
    ! [A: 'A$',B: 'A$'] :
      ( ( ( A @ 'ket$a' )
        = ( B @ 'ket$a' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).

thf(1121,plain,
    ! [A: 'A$',B: 'A$'] :
      ( ( ( A = B )
       => ( ( A @ 'ket$a' )
          = ( B @ 'ket$a' ) ) )
      & ( ( ( A @ 'ket$a' )
          = ( B @ 'ket$a' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(133,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$c' @ ( A @ 'member$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).

thf(1064,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$c' @ ( A @ 'member$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(143,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$m' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$m' ) ) ) )
           => $false )
        & ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).

thf(1096,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ~ ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$m' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$m' ) ) ) )
        & ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(155,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$n' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$ck' ) @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).

thf(1138,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$n' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$ck' ) @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(21,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$k' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).

thf(593,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$k' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(63,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
    <=> ? [D: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
          ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( C @ ( E @ 'member$' ) )
             => ( ( ( E @ ( D @ 'fun_app$c' ) @ ( A @ 'fun_app$d' ) )
                  = E )
                & ( B @ ( E @ ( D @ 'fun_app$c' ) @ 'member$c' ) ) ) )
          & ! [E: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( B @ ( E @ 'member$c' ) )
             => ( ( ( E @ ( A @ 'fun_app$d' ) @ ( D @ 'fun_app$c' ) )
                  = E )
                & ( C @ ( E @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).

thf(783,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ? [D: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$c' ) @ ( A @ 'fun_app$d' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$c' ) @ 'member$c' ) ) ) )
            & ! [E: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$c' ) )
               => ( ( ( E @ ( A @ 'fun_app$d' ) @ ( D @ 'fun_app$c' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ) ) )
       => ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
      & ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
       => ? [D: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$c' ) @ ( A @ 'fun_app$d' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$c' ) @ 'member$c' ) ) ) )
            & ! [E: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$c' ) )
               => ( ( ( E @ ( A @ 'fun_app$d' ) @ ( D @ 'fun_app$c' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(113,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$j' )
     => ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom127) ).

thf(989,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$j' )
     => ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(265,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$d' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$d' ) )
              = ( C @ ( A @ 'fun_app$d' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).

thf(1534,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$d' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$d' ) )
                = ( C @ ( A @ 'fun_app$d' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$d' ) )
                = ( C @ ( A @ 'fun_app$d' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(374,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$d' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$l' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$cl' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).

thf(1953,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$d' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$l' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$cl' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(110,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$ac' ) )
          = 'id$f' )
        & ( ( B @ ( A @ 'comp$dd' ) )
          = 'id$d' ) )
     => ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).

thf(980,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$ac' ) )
          = 'id$f' )
        & ( ( B @ ( A @ 'comp$dd' ) )
          = 'id$d' ) )
     => ( 'top$a' @ ( 'top$d' @ ( B @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(277,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( D @ ( C @ 'fun_app$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).

thf(1587,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = C )
     => ( ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( D @ ( C @ 'fun_app$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(75,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).

thf(857,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( C @ ( D @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(218,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$j' )
        & ( A @ 'register$' ) )
     => ( A @ ( B @ 'comp$k' ) @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).

thf(1397,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$j' )
        & ( A @ 'register$' ) )
     => ( A @ ( B @ 'comp$k' ) @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(251,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$n' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$e' @ 'equivalent_registers$o' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).

thf(1493,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$n' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$e' @ 'equivalent_registers$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(163,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun$',B: 'C_ell2_c_ell2_cblinfun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'tensor_op$l' ) @ 'tensor_op$i' ) @ ( 'assoc$o' @ 'fun_app$t' ) )
      = ( C @ ( B @ 'tensor_op$k' ) @ ( A @ 'tensor_op$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).

thf(1160,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun$',B: 'C_ell2_c_ell2_cblinfun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'tensor_op$l' ) @ 'tensor_op$i' ) @ ( 'assoc$o' @ 'fun_app$t' ) )
      = ( C @ ( B @ 'tensor_op$k' ) @ ( A @ 'tensor_op$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(98,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$do' ) )
          = 'id$i' )
        & ( ( B @ ( A @ 'comp$dp' ) )
          = 'id$g' )
        & ( B @ 'register$as' )
        & ( A @ 'register$e' ) )
     => ( A @ 'iso_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).

thf(933,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$do' ) )
          = 'id$i' )
        & ( ( B @ ( A @ 'comp$dp' ) )
          = 'id$g' )
        & ( B @ 'register$as' )
        & ( A @ 'register$e' ) )
     => ( A @ 'iso_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(167,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'register$n' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).

thf(1182,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'register$n' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(238,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$' ) )
     => ( B @ ( A @ 'register_tensor$as' ) @ 'iso_register$aa' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).

thf(1461,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$' ) )
     => ( B @ ( A @ 'register_tensor$as' ) @ 'iso_register$aa' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(137,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$i' ) @ 'register$n' )
     => ( B @ 'register$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).

thf(1075,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$i' ) @ 'register$n' )
     => ( B @ 'register$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(411,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$aq' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bp' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cj' ) )
        = ( D @ ( B @ 'comp$z' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).

thf(2080,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$aq' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bp' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cj' ) )
        = ( D @ ( B @ 'comp$z' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(460,axiom,
    'g$' @ ( 'f$' @ 'compatible$' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).

thf(2196,plain,
    'g$' @ ( 'f$' @ 'compatible$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(369,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$t' ) @ 'register$ac' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).

thf(1937,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( B @ ( A @ 'register_tensor$t' ) @ 'register$ac' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(455,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$i' )
    <=> ( ? [B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$c' @ 'ket$c' @ ( 'default$c' @ 'ket$c' @ 'butterfly$c' ) @ 'tensor_op$i' ) @ ( A @ 'complement$' @ ( A @ 'register_pair$n' ) @ 'fun_app$k' ) )
            = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( A @ 'register$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).

thf(2172,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$c' @ 'ket$c' @ ( 'default$c' @ 'ket$c' @ 'butterfly$c' ) @ 'tensor_op$i' ) @ ( A @ 'complement$' @ ( A @ 'register_pair$n' ) @ 'fun_app$k' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$g' ) )
       => ( A @ 'regular_register$i' ) )
      & ( ( A @ 'regular_register$i' )
       => ( ? [B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$c' @ 'ket$c' @ ( 'default$c' @ 'ket$c' @ 'butterfly$c' ) @ 'tensor_op$i' ) @ ( A @ 'complement$' @ ( A @ 'register_pair$n' ) @ 'fun_app$k' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(178,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'top$a' @ 'inv_into$p' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).

thf(1214,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) @ ( 'top$a' @ 'inv_into$p' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(232,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$p' )
     => ( ( A @ ( A @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$dq' ) )
        = 'id$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).

thf(1446,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$p' )
     => ( ( A @ ( A @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$dq' ) )
        = 'id$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(38,axiom,
    'i$' @ 'register$e',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).

thf(679,plain,
    'i$' @ 'register$e',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(227,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$f' ) @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).

thf(1424,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$f' ) @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(510,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$x' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$av' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).

thf(2312,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$x' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$av' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(20,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( ( B @ ( A @ 'comp$ae' ) @ ( 'top$c' @ 'inv_into$d' ) )
        = ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( B @ ( 'top$c' @ 'inv_into$d' ) @ 'comp$ad' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).

thf(590,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( ( B @ ( A @ 'comp$ae' ) @ ( 'top$c' @ 'inv_into$d' ) )
        = ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( B @ ( 'top$c' @ 'inv_into$d' ) @ 'comp$ad' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(413,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$b' ) )
        & ( C @ ( B @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$g' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) @ 'comp$av' ) )
        = ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).

thf(2085,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$b' ) )
        & ( C @ ( B @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$g' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) @ 'comp$av' ) )
        = ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(161,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ae' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$i' ) @ 'compatible$ao' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).

thf(1155,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ae' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$i' ) @ 'compatible$ao' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(10,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$z' )
    <=> ( ? [B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
            ( ( ( A @ ( B @ 'comp$bv' ) )
              = 'id$' )
            & ( ( B @ ( A @ 'comp$bv' ) )
              = 'id$' )
            & ( B @ 'register$q' ) )
        & ( A @ 'register$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom584) ).

thf(547,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$bv' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$bv' ) )
                = 'id$' )
              & ( B @ 'register$q' ) )
          & ( A @ 'register$q' ) )
       => ( A @ 'iso_register$z' ) )
      & ( ( A @ 'iso_register$z' )
       => ( ? [B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$bv' ) )
                = 'id$' )
              & ( ( B @ ( A @ 'comp$bv' ) )
                = 'id$' )
              & ( B @ 'register$q' ) )
          & ( A @ 'register$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(318,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$z' ) )
     => ( ( B @ ( A @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) )
        = ( B @ ( 'top$f' @ 'inv_into$k' ) @ ( A @ ( 'top$l' @ 'inv_into$z' ) @ 'register_tensor$h' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).

thf(1744,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$z' ) )
     => ( ( B @ ( A @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) )
        = ( B @ ( 'top$f' @ 'inv_into$k' ) @ ( A @ ( 'top$l' @ 'inv_into$z' ) @ 'register_tensor$h' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(339,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ad' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$g' ) @ 'compatible$an' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).

thf(1825,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ad' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$g' ) @ 'compatible$an' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(506,axiom,
    ( 't2$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$a' ) @ 'fun_app$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).

thf(2304,plain,
    ( 't2$'
    = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ ( 'top$g' @ 'inv_into$n' ) @ 'comp$a' ) @ 'fun_app$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(152,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( B @ 'compatible$l' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).

thf(1131,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( B @ 'compatible$l' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(269,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).

thf(1552,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(127,axiom,
    'top$b' @ ( 'top$b' @ ( 'id$c' @ 'bij_betw$u' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).

thf(1050,plain,
    'top$b' @ ( 'top$b' @ ( 'id$c' @ 'bij_betw$u' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(90,axiom,
    ( ( 'swap$' @ ( 'top$b' @ 'inv_into$ak' ) )
    = 'swap$e' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).

thf(911,plain,
    ( ( 'swap$' @ ( 'top$b' @ 'inv_into$ak' ) )
    = 'swap$e' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(388,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$d' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).

thf(2006,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$d' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) ) )
         => ( ( B @ ( A @ 'fun_app$d' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(372,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$u' ) )
     => ( A @ ( B @ 'comp$h' ) @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).

thf(1947,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$u' ) )
     => ( A @ ( B @ 'comp$h' ) @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(383,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$c' )
    <=> ( ? [B: 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$a' ) @ ( A @ 'complement$m' @ ( A @ 'register_pair$at' ) ) )
            = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( A @ 'register$r' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).

thf(1984,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$a' ) @ ( A @ 'complement$m' @ ( A @ 'register_pair$at' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$r' ) )
       => ( A @ 'regular_register$c' ) )
      & ( ( A @ 'regular_register$c' )
       => ( ? [B: 'B_a_complement_domain_ell2_b_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$a' ) @ ( A @ 'complement$m' @ ( A @ 'register_pair$at' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$r' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(352,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$al' ) @ ( A @ 'fun_app$al' ) )
          = B )
     => ( 'top$b' @ ( 'top$b' @ ( A @ 'bij_betw$u' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).

thf(1874,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$al' ) @ ( A @ 'fun_app$al' ) )
          = B )
     => ( 'top$b' @ ( 'top$b' @ ( A @ 'bij_betw$u' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(281,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( 'top$a' @ 'inv_into$c' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).

thf(1599,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$d' ) @ ( 'top$a' @ 'inv_into$c' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(313,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$b' ) )
     => ( ( B @ ( A @ 'register_tensor$f' ) @ ( 'top$k' @ 'inv_into$y' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'register_tensor$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).

thf(1720,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$b' ) )
     => ( ( B @ ( A @ 'register_tensor$f' ) @ ( 'top$k' @ 'inv_into$y' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'register_tensor$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(493,axiom,
    ( ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) )
    = ( 'i$' @ ( 'f$' @ 'complement$e' @ 'comp$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).

thf(2272,plain,
    ( ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) )
    = ( 'i$' @ ( 'f$' @ 'complement$e' @ 'comp$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(328,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( ( 'swap$h' @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$cv' ) )
        = ( A @ ( B @ 'register_pair$bf' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom526) ).

thf(1776,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( ( 'swap$h' @ ( B @ ( A @ 'register_pair$i' ) @ 'comp$cv' ) )
        = ( A @ ( B @ 'register_pair$bf' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(189,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun$',B: 'C_ell2_c_ell2_cblinfun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( C @ ( B @ 'tensor_op$k' ) @ ( A @ 'tensor_op$j' ) @ ( 'assoc$g' @ 'fun_app$s' ) )
      = ( C @ ( B @ ( A @ 'tensor_op$l' ) @ 'tensor_op$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).

thf(1263,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun$',B: 'C_ell2_c_ell2_cblinfun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( C @ ( B @ 'tensor_op$k' ) @ ( A @ 'tensor_op$j' ) @ ( 'assoc$g' @ 'fun_app$s' ) )
      = ( C @ ( B @ ( A @ 'tensor_op$l' ) @ 'tensor_op$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(117,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).

thf(997,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(159,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ ( 'top$a' @ 'inv_into$e' ) @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).

thf(1150,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ ( 'top$a' @ 'inv_into$e' ) @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(245,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).

thf(1478,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ ( A @ 'comp$g' ) @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(190,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( ( A @ ( 'top$' @ 'inv_into$a' ) @ ( 'top$a' @ 'inv_into$m' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).

thf(1266,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
     => ( ( A @ ( 'top$' @ 'inv_into$a' ) @ ( 'top$a' @ 'inv_into$m' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(446,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ap' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bo' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ch' ) )
        = ( D @ ( B @ 'comp$ci' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).

thf(2153,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ap' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bo' ) @ ( B @ ( A @ 'register_pair$' ) @ 'comp$ch' ) )
        = ( D @ ( B @ 'comp$ci' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(344,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$v' ) )
     => ( B @ ( A @ 'comp$' ) @ 'iso_register$w' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).

thf(1857,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$' )
        & ( A @ 'iso_register$v' ) )
     => ( B @ ( A @ 'comp$' ) @ 'iso_register$w' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(176,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$bk' ) @ 'comp$a' ) )
      = ( C @ ( B @ 'comp$bl' ) @ ( A @ 'comp$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).

thf(1202,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$bk' ) @ 'comp$a' ) )
      = ( C @ ( B @ 'comp$bl' ) @ ( A @ 'comp$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(329,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$c' ) )
     => ( A @ ( B @ 'complements$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).

thf(1779,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$c' ) )
     => ( A @ ( B @ 'complements$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(193,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
    <=> ! [B: 'B_ell2_b_ell2_cblinfun$'] :
        ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$g' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$g' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).

thf(1286,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$g' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$g' ) )
              = B ) )
       => ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
      & ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
       => ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$g' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$g' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(36,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( D @ ( C @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( D @ ( B @ 'register_tensor$r' ) @ ( C @ ( A @ 'register_tensor$u' ) @ 'compatible$aw' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).

thf(674,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( D @ ( C @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( D @ ( B @ 'register_tensor$r' ) @ ( C @ ( A @ 'register_tensor$u' ) @ 'compatible$aw' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(304,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ 'comp$ac' ) )
        = 'id$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom602) ).

thf(1663,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ 'comp$ac' ) )
        = 'id$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(470,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$' ) @ 'register$l' )
     => ( B @ 'register$h' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).

thf(2221,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$' ) @ 'register$l' )
     => ( B @ 'register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(4,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$s' ) @ ( 'top$c' @ 'inv_into$s' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).

thf(530,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( ( A @ ( 'top$c' @ 'inv_into$s' ) @ ( 'top$c' @ 'inv_into$s' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(519,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$a' ) @ 'register$g' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom517) ).

thf(2338,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$a' ) @ 'register$g' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(95,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$d' )
        & ( A @ 'register$e' ) )
     => ( A @ ( B @ 'comp$' ) @ 'register$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).

thf(926,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$d' )
        & ( A @ 'register$e' ) )
     => ( A @ ( B @ 'comp$' ) @ 'register$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(154,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$af' )
     => ( ( A @ ( 'top$b' @ 'inv_into$aq' ) @ ( A @ 'comp$de' ) )
        = 'id$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).

thf(1135,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$af' )
     => ( ( A @ ( 'top$b' @ 'inv_into$aq' ) @ ( A @ 'comp$de' ) )
        = 'id$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(258,axiom,
    ( 'top$g'
    = ( 'top$t' @ 'collect$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).

thf(1510,plain,
    ( 'top$g'
    = ( 'top$t' @ 'collect$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(325,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$d' ) @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).

thf(1764,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$d' ) @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(500,axiom,
    ! [A: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$b' ) )
     => ( A @ ( B @ 'complements$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).

thf(2292,plain,
    ! [A: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$b' ) )
     => ( A @ ( B @ 'complements$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(307,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$d' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$d' ) ) ) )
           => $false )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).

thf(1680,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ~ ( ! [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$d' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$d' ) ) ) )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(377,axiom,
    ( ( 'assoc$a' @ ( 'top$b' @ 'inv_into$ae' ) )
    = 'assoc$n' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).

thf(1959,plain,
    ( ( 'assoc$a' @ ( 'top$b' @ 'inv_into$ae' ) )
    = 'assoc$n' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(319,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).

thf(1747,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(366,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( B @ 'register_pair$f' ) @ ( A @ 'complements$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).

thf(1927,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( B @ 'register_pair$f' ) @ ( A @ 'complements$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(292,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ab' ) )
     => ( A @ ( B @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).

thf(1631,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ab' ) )
     => ( A @ ( B @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(431,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$p' ) )
        & ( C @ ( B @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( ( 'assoc$a' @ ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) @ 'comp$ap' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom281) ).

thf(2121,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$p' ) )
        & ( C @ ( B @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( ( 'assoc$a' @ ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) @ 'comp$ap' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(476,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$f' @ 'register_tensor$am' ) @ ( B @ ( A @ 'register_tensor$al' ) @ 'complements$ab' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).

thf(2235,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$f' @ 'register_tensor$am' ) @ ( B @ ( A @ 'register_tensor$al' ) @ 'complements$ab' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(484,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom151) ).

thf(2253,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$l' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( C @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(444,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'compatible$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).

thf(2149,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'compatible$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(12,axiom,
    ? [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( 'top$b' @ ( A @ 'member$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).

thf(562,plain,
    ? [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( 'top$b' @ ( A @ 'member$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(342,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
    <=> ? [D: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
          ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( C @ ( E @ 'member$' ) )
             => ( ( ( E @ ( D @ 'fun_app$a' ) @ ( A @ 'fun_app$k' ) )
                  = E )
                & ( B @ ( E @ ( D @ 'fun_app$a' ) @ 'member$b' ) ) ) )
          & ! [E: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( B @ ( E @ 'member$b' ) )
             => ( ( ( E @ ( A @ 'fun_app$k' ) @ ( D @ 'fun_app$a' ) )
                  = E )
                & ( C @ ( E @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).

thf(1833,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ? [D: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$a' ) @ ( A @ 'fun_app$k' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$a' ) @ 'member$b' ) ) ) )
            & ! [E: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$b' ) )
               => ( ( ( E @ ( A @ 'fun_app$k' ) @ ( D @ 'fun_app$a' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ) ) )
       => ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
      & ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
       => ? [D: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
            ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( C @ ( E @ 'member$' ) )
               => ( ( ( E @ ( D @ 'fun_app$a' ) @ ( A @ 'fun_app$k' ) )
                    = E )
                  & ( B @ ( E @ ( D @ 'fun_app$a' ) @ 'member$b' ) ) ) )
            & ! [E: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( B @ ( E @ 'member$b' ) )
               => ( ( ( E @ ( A @ 'fun_app$k' ) @ ( D @ 'fun_app$a' ) )
                    = E )
                  & ( C @ ( E @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(42,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$k' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).

thf(694,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$k' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$bf' ) @ 'bij_betw$b' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$b' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$bf' ) @ 'bij_betw$b' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(401,axiom,
    ( ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
        ( ( ( ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) )
            = ( A @ ( 'f$' @ 'complement$e' @ 'comp$' ) ) )
          & ( A @ 'iso_register$' ) )
       => $false )
   => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).

thf(2048,plain,
    ~ ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
        ~ ( ( ( 'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) )
            = ( A @ ( 'f$' @ 'complement$e' @ 'comp$' ) ) )
          & ( A @ 'iso_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(51,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
    <=> ! [B: 'B_ell2_b_ell2_cblinfun$'] :
        ? [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
          ( ! [D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$e' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$e' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).

thf(732,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$e' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$e' ) )
              = B ) )
       => ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) )
      & ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
       => ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$e' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$e' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(287,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$m' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$al' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).

thf(1615,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$m' ) )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'equivalent_registers$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(457,axiom,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) )
    = ( 'aG$' @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom502) ).

thf(2188,plain,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ ( 'top$c' @ 'inv_into$d' ) @ 'fun_app$c' ) )
    = ( 'aG$' @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(367,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$n' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$ck' ) @ 'bij_betw$d' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).

thf(1929,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$n' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$ck' ) @ 'bij_betw$d' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$b' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$b' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$ck' ) @ 'bij_betw$d' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(70,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
    <=> ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
        ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$n' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$n' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).

thf(826,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$n' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$n' ) )
              = B ) )
       => ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) )
      & ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
       => ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$n' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$n' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(16,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$d' )
        & ( B @ ( A @ 'compatible$ar' ) ) )
     => ( B @ ( C @ 'comp$' ) @ ( A @ ( C @ 'comp$' ) @ 'compatible$as' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).

thf(579,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$d' )
        & ( B @ ( A @ 'compatible$ar' ) ) )
     => ( B @ ( C @ 'comp$' ) @ ( A @ ( C @ 'comp$' ) @ 'compatible$as' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(221,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).

thf(1403,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(436,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'compatible$ak' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).

thf(2134,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'compatible$ak' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(9,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( 'top$b' @ ( A @ 'member$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).

thf(545,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( 'top$b' @ ( A @ 'member$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(249,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).

thf(1488,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(459,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$an' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bm' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$ce' ) )
        = ( D @ ( B @ 'comp$s' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).

thf(2193,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$an' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bm' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$ce' ) )
        = ( D @ ( B @ 'comp$s' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(508,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$aa' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).

thf(2308,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$aa' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(199,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
    <=> ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
        ? [C: 'B_ell2_b_ell2_cblinfun$'] :
          ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$c' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$c' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).

thf(1312,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$c' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$c' ) )
              = B ) )
       => ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
      & ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
       => ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ! [D: 'B_ell2_b_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$c' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$c' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(348,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ 'register$i' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom34) ).

thf(1865,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ 'register$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(64,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$c' ) )
         => ( C @ ( D @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).

thf(804,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$b' ) ) )
     => ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$c' ) )
         => ( C @ ( D @ ( A @ 'fun_app$d' ) @ 'member$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(45,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
     => ( ( B @ ( A @ 'comp$ad' ) @ ( 'top$a' @ 'inv_into$c' ) )
        = ( A @ ( 'top$a' @ 'inv_into$c' ) @ ( B @ ( 'top$a' @ 'inv_into$b' ) @ 'comp$ae' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).

thf(704,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
     => ( ( B @ ( A @ 'comp$ad' ) @ ( 'top$a' @ 'inv_into$c' ) )
        = ( A @ ( 'top$a' @ 'inv_into$c' ) @ ( B @ ( 'top$a' @ 'inv_into$b' ) @ 'comp$ae' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(296,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( B @ 'compatible$o' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).

thf(1638,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( B @ 'compatible$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(210,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$f' ) ) )
        & ! [B: 'B_ell2_b_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$f' ) )
              = ( C @ ( A @ 'fun_app$f' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom633) ).

thf(1356,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$f' ) ) )
        & ! [B: 'B_ell2_b_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$f' ) )
                = ( C @ ( A @ 'fun_app$f' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$f' ) )
                = ( C @ ( A @ 'fun_app$f' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(35,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$e' )
        & ( A @ 'register$e' ) )
     => ( B @ ( A @ 'register_tensor$as' ) @ 'register$ah' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).

thf(672,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$e' )
        & ( A @ 'register$e' ) )
     => ( B @ ( A @ 'register_tensor$as' ) @ 'register$ah' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(131,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'A_ell2_a_ell2_cblinfun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_op$o' ) @ ( B @ ( A @ 'register_tensor$s' ) @ 'fun_app$w' ) )
        = ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$v' ) @ 'tensor_op$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).

thf(1058,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'A_ell2_a_ell2_cblinfun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_op$o' ) @ ( B @ ( A @ 'register_tensor$s' ) @ 'fun_app$w' ) )
        = ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$v' ) @ 'tensor_op$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(145,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ae' ) )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'comp$' ) @ ( B @ ( A @ 'comp$' ) @ 'equivalent_registers$w' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom141) ).

thf(1107,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ae' ) )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'comp$' ) @ ( B @ ( A @ 'comp$' ) @ 'equivalent_registers$w' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(402,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$w' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$h' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$s' ) @ ( A @ 'comp$i' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).

thf(2055,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$w' ) )
        & ( A @ 'register$a' ) )
     => ( ( C @ ( A @ 'comp$h' ) @ ( B @ ( A @ 'comp$g' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$s' ) @ ( A @ 'comp$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(141,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( 'top$d' @ ( 'top$c' @ ( A @ ( 'top$d' @ 'inv_into$u' ) @ 'bij_betw$l' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).

thf(1092,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) )
     => ( 'top$d' @ ( 'top$c' @ ( A @ ( 'top$d' @ 'inv_into$u' ) @ 'bij_betw$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(56,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$j' ) ) )
     => ? [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).

thf(764,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$j' ) ) )
     => ? [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(86,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$a' ) )
     => ( 'top$d' = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).

thf(900,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$a' ) )
     => ( 'top$d' = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(468,axiom,
    ( ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
        ( ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) )
          = ( A @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) ) )
       => $false )
   => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).

thf(2214,plain,
    ~ ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
        ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) )
       != ( A @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(357,axiom,
    ! [A: 'B$',B: 'B$'] :
      ( ( ( A @ 'ket$' )
        = ( B @ 'ket$' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).

thf(1894,plain,
    ! [A: 'B$',B: 'B$'] :
      ( ( ( A = B )
       => ( ( A @ 'ket$' )
          = ( B @ 'ket$' ) ) )
      & ( ( ( A @ 'ket$' )
          = ( B @ 'ket$' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(149,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'register$m' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).

thf(1117,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'register$m' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(261,axiom,
    ( 'top$c'
    = ( 'top$q' @ 'collect$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).

thf(1524,plain,
    ( 'top$c'
    = ( 'top$q' @ 'collect$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(207,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$d' ) @ 'register$k' )
     => ( B @ 'register$l' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).

thf(1349,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$d' ) @ 'register$k' )
     => ( B @ 'register$l' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(486,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$z' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$ax' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).

thf(2257,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$z' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$ax' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(504,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$' @ 'register_tensor$ai' ) @ ( B @ ( A @ 'register_tensor$ah' ) @ 'complements$z' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).

thf(2299,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$' @ 'register_tensor$ai' ) @ ( B @ ( A @ 'register_tensor$ah' ) @ 'complements$z' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(157,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$bb' ) ) )
          = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( B @ ( A @ 'complements$ah' ) )
        & ( A @ 'register$p' ) )
     => ( A @ 'regular_register$h' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).

thf(1144,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$bb' ) ) )
          = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( B @ ( A @ 'complements$ah' ) )
        & ( A @ 'register$p' ) )
     => ( A @ 'regular_register$h' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(461,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'complements$o' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).

thf(2197,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$g' )
     => ( A @ 'complement$' @ ( A @ 'complements$o' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(445,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( B @ 'compatible$m' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).

thf(2151,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( B @ 'compatible$m' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(473,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$' @ 'register_tensor$ao' ) @ ( B @ ( A @ 'register_tensor$an' ) @ 'complements$ac' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).

thf(2229,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$g' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$' @ 'register_tensor$ao' ) @ ( B @ ( A @ 'register_tensor$an' ) @ 'complements$ac' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(125,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$' ) @ 'fun_app$' ) @ ( A @ 'fun_app$e' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom183) ).

thf(1043,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( C @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$' ) @ 'fun_app$' ) @ ( A @ 'fun_app$e' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(332,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$t' ) )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( B @ ( C @ 'register_pair$d' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'equivalent_registers$ak' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).

thf(1801,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'equivalent_registers$t' ) )
        & ( B @ ( A @ 'compatible$a' ) ) )
     => ( B @ ( C @ 'register_pair$d' ) @ ( B @ ( A @ 'register_pair$d' ) @ 'equivalent_registers$ak' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(212,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$a' ) )
     => ( A @ 'complement$e' @ ( B @ 'equivalent_registers$b' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).

thf(1376,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$a' ) )
     => ( A @ 'complement$e' @ ( B @ 'equivalent_registers$b' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(230,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ! [E: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( E @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
              = ( E @ ( D @ 'fun_app$f' ) @ ( C @ 'fun_app$h' ) ) )
         => $false )
        & ( ( B @ ( A @ 'comp$a' ) )
          = ( D @ ( C @ 'comp$a' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).

thf(1439,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ~ ( ~ ! [E: 'B_ell2_b_ell2_cblinfun$'] :
              ( ( E @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
              = ( E @ ( D @ 'fun_app$f' ) @ ( C @ 'fun_app$h' ) ) )
        & ( ( B @ ( A @ 'comp$a' ) )
          = ( D @ ( C @ 'comp$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(81,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$d' @ ( 'top$a' @ ( B @ 'bij_betw$e' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ ( B @ 'comp$af' ) @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).

thf(890,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$d' @ ( 'top$a' @ ( B @ 'bij_betw$e' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( 'top$d' @ ( 'top$a' @ ( A @ ( B @ 'comp$af' ) @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(353,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$t' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$f' @ 'equivalent_registers$u' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).

thf(1877,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$t' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$f' @ 'equivalent_registers$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(139,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$a' @ 'inv_into$c' ) @ 'fun_app$d' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$c' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom244) ).

thf(1080,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$c' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$a' @ 'inv_into$c' ) @ 'fun_app$d' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$a' @ 'inv_into$c' ) @ 'fun_app$d' ) ) )
         => ( ( B @ ( A @ 'fun_app$c' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(203,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( 'top$a' @ 'inv_into$c' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).

thf(1339,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( 'top$a' @ 'inv_into$c' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(271,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$' )
    <=> ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( A @ 'complement$e' @ ( A @ 'register_pair$g' ) @ 'fun_app$g' ) )
            = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( A @ 'register$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).

thf(1557,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( A @ 'complement$e' @ ( A @ 'register_pair$g' ) @ 'fun_app$g' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$a' ) )
       => ( A @ 'regular_register$' ) )
      & ( ( A @ 'regular_register$' )
       => ( ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( A @ 'complement$e' @ ( A @ 'register_pair$g' ) @ 'fun_app$g' ) )
              = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
          & ( A @ 'register$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(425,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$' @ 'register_tensor$ag' ) @ ( B @ ( A @ 'register_tensor$af' ) @ 'complements$y' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).

thf(2111,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$g' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$' @ 'register_tensor$ag' ) @ ( B @ ( A @ 'register_tensor$af' ) @ 'complements$y' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(384,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$w' ) )
        & ( B @ ( A @ 'equivalent_registers$' ) ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).

thf(1993,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$w' ) )
        & ( B @ ( A @ 'equivalent_registers$' ) ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(491,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$' ) @ 'register$l' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).

thf(2267,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$' ) @ 'register$l' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(360,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( B @ 'complement$k' @ ( A @ 'complement$i' @ 'equivalent_registers$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).

thf(1909,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( B @ 'complement$k' @ ( A @ 'complement$i' @ 'equivalent_registers$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(43,axiom,
    ( ( 'id$f' @ ( 'top$a' @ 'inv_into$b' ) )
    = 'id$f' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).

thf(700,plain,
    ( ( 'id$f' @ ( 'top$a' @ 'inv_into$b' ) )
    = 'id$f' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(123,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$q' ) @ 'comp$' ) )
      = ( C @ ( B @ 'comp$' ) @ ( A @ 'comp$al' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).

thf(1029,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$q' ) @ 'comp$' ) )
      = ( C @ ( B @ 'comp$' ) @ ( A @ 'comp$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(108,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$h' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$i' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$' ) @ 'bij_betw$t' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).

thf(964,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_set$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$h' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$i' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$' ) @ 'bij_betw$t' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(101,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$e' @ ( B @ 'bij_betw$h' ) ) )
        & ( 'top$e' @ ( 'top$f' @ ( A @ 'bij_betw$i' ) ) ) )
     => ( 'top$a' @ ( 'top$f' @ ( A @ ( B @ 'comp$' ) @ 'bij_betw$t' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).

thf(943,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$e' @ ( B @ 'bij_betw$h' ) ) )
        & ( 'top$e' @ ( 'top$f' @ ( A @ 'bij_betw$i' ) ) ) )
     => ( 'top$a' @ ( 'top$f' @ ( A @ ( B @ 'comp$' ) @ 'bij_betw$t' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(511,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$u' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$ar' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$s' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).

thf(2314,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$u' ) @ ( B @ ( A @ 'register_pair$' ) @ 'fun_app$ar' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$s' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(434,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$d' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$' @ 'equivalent_registers$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).

thf(2129,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$d' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$' @ 'equivalent_registers$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(6,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$d' ) )
     => ( 'top$b' = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).

thf(535,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$'] :
      ( ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] : ( A @ ( B @ 'member$d' ) )
     => ( 'top$b' = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(521,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$s' ) )
    <=> ( ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).

thf(2343,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
          & ( B @ ( A @ 'compatible$b' ) ) )
       => ( B @ ( A @ 'complements$s' ) ) )
      & ( ( B @ ( A @ 'complements$s' ) )
       => ( ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
          & ( B @ ( A @ 'compatible$b' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(488,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$t' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).

thf(2261,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'equivalent_registers$t' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(337,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( A @ 'compatible$s' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).

thf(1821,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( B @ ( A @ 'register_pair$g' ) @ 'complement$c' @ ( A @ 'compatible$s' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(147,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$df' ) )
          = 'id$c' )
        & ( ( B @ ( A @ 'comp$de' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$aq' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).

thf(1112,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$df' ) )
          = 'id$c' )
        & ( ( B @ ( A @ 'comp$de' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$aq' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(308,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$l' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$d' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$cl' ) @ 'bij_betw$b' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).

thf(1688,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$l' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$cl' ) @ 'bij_betw$b' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$d' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$d' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$cl' ) @ 'bij_betw$b' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(111,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$bv' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$bv' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$l' @ 'inv_into$z' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).

thf(983,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$bv' ) )
          = 'id$' )
        & ( ( B @ ( A @ 'comp$bv' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$l' @ 'inv_into$z' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(174,axiom,
    ( 't2$'
    = ( 'aF$' @ ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ 'fun_app$az' ) @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom553) ).

thf(1198,plain,
    ( 't2$'
    = ( 'aF$' @ ( 'i$' @ ( 'top$f' @ 'inv_into$k' ) @ 'fun_app$az' ) @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(522,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$h' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$' @ 'equivalent_registers$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).

thf(2350,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$h' ) )
     => ( B @ 'complement$f' @ ( A @ 'complement$' @ 'equivalent_registers$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(279,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$g' ) @ 'register$m' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).

thf(1594,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$g' ) @ 'register$m' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(184,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$g' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$g' ) ) ) )
           => $false )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).

thf(1245,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ~ ( ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$g' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$g' ) ) ) )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(62,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$e' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$e' ) @ ( C @ 'inv_into$f' ) @ 'fun_app$f' ) )
        = ( D @ ( A @ 'fun_app$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom196) ).

thf(780,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$e' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$e' ) @ ( C @ 'inv_into$f' ) @ 'fun_app$f' ) )
        = ( D @ ( A @ 'fun_app$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(392,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$a' ) )
     => ( A @ ( B @ 'complements$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).

thf(2022,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$a' ) )
     => ( A @ ( B @ 'complements$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(420,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( 'assoc$b' @ ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) @ 'comp$aq' ) )
        = ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).

thf(2101,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$ac' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( ( 'assoc$b' @ ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) @ 'comp$aq' ) )
        = ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(315,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$a' ) @ ( C @ 'inv_into$m' ) @ 'fun_app$k' ) )
        = ( D @ ( A @ 'fun_app$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom197) ).

thf(1726,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$b' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$a' ) @ ( C @ 'inv_into$m' ) @ 'fun_app$k' ) )
        = ( D @ ( A @ 'fun_app$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(72,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$e' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$e' ) @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).

thf(851,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$e' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$e' ) @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(447,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ab' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$bb' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).

thf(2156,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ab' ) )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$bb' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(465,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ab' ) )
     => ( ( 'swap$d' @ ( B @ ( A @ 'register_pair$ar' ) @ 'comp$cr' ) )
        = ( A @ ( B @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).

thf(2207,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$ab' ) )
     => ( ( 'swap$d' @ ( B @ ( A @ 'register_pair$ar' ) @ 'comp$cr' ) )
        = ( A @ ( B @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(309,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$am' ) @ ( A @ 'fun_app$am' ) )
          = B )
     => ( 'top$g' @ ( 'top$g' @ ( A @ 'bij_betw$w' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).

thf(1694,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$am' ) @ ( A @ 'fun_app$am' ) )
          = B )
     => ( 'top$g' @ ( 'top$g' @ ( A @ 'bij_betw$w' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(41,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$c' @ 'inv_into$s' ) @ 'fun_app$m' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$m' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom247) ).

thf(685,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$m' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$s' ) @ 'fun_app$m' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$s' ) @ 'fun_app$m' ) ) )
         => ( ( B @ ( A @ 'fun_app$m' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(165,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$b' ) )
     => ( A @ ( B @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).

thf(1171,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$b' ) )
     => ( A @ ( B @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(467,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'compatible$ap' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom221) ).

thf(2212,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'compatible$ap' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(106,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dh' ) )
          = 'id$c' )
        & ( ( B @ ( A @ 'comp$dg' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).

thf(959,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dh' ) )
          = 'id$c' )
        & ( ( B @ ( A @ 'comp$dg' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$b' @ 'inv_into$' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(454,axiom,
    'top$a' @ ( 'top$d' @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ 'bij_betw$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).

thf(2171,plain,
    'top$a' @ ( 'top$d' @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ 'bij_betw$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(134,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$q' ) @ 'register$e' )
     => ( A @ 'register$ak' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).

thf(1066,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$q' ) @ 'register$e' )
     => ( A @ 'register$ak' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(263,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$u' ) @ 'fun_app$ao' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ae' ) )
        & ( A @ 'register$q' ) )
     => ( A @ 'regular_register$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).

thf(1528,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$u' ) @ 'fun_app$ao' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ae' ) )
        & ( A @ 'register$q' ) )
     => ( A @ 'regular_register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(439,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$a' ) @ 'register$g' )
     => ( B @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom511) ).

thf(2139,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$a' ) @ 'register$g' )
     => ( B @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(80,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$r' ) )
    <=> ( ( B @ ( A @ 'register_pair$q' ) @ 'iso_register$' )
        & ( B @ ( A @ 'compatible$u' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).

thf(883,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$q' ) @ 'iso_register$' )
          & ( B @ ( A @ 'compatible$u' ) ) )
       => ( B @ ( A @ 'complements$r' ) ) )
      & ( ( B @ ( A @ 'complements$r' ) )
       => ( ( B @ ( A @ 'register_pair$q' ) @ 'iso_register$' )
          & ( B @ ( A @ 'compatible$u' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(112,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dl' ) )
          = 'id$e' )
        & ( ( B @ ( A @ 'comp$dk' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$g' @ 'inv_into$o' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom583) ).

thf(986,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dl' ) )
          = 'id$e' )
        & ( ( B @ ( A @ 'comp$dk' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$g' @ 'inv_into$o' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(498,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$y' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$aw' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).

thf(2288,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$y' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$aw' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(478,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$p' ) )
        & ( C @ ( B @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( ( 'assoc$n' @ ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) @ 'comp$bc' ) )
        = ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).

thf(2239,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$p' ) )
        & ( C @ ( B @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$ab' ) ) )
     => ( ( 'assoc$n' @ ( C @ ( B @ 'register_pair$' ) @ ( A @ 'register_pair$d' ) @ 'comp$bc' ) )
        = ( C @ ( B @ ( A @ 'register_pair$ar' ) @ 'register_pair$aq' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(418,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( ( 'swap$i' @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$cw' ) )
        = ( A @ ( B @ 'register_pair$ar' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom527) ).

thf(2096,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( ( 'swap$i' @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$cw' ) )
        = ( A @ ( B @ 'register_pair$ar' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(423,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ak' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bj' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$bz' ) )
        = ( D @ ( B @ 'comp$y' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).

thf(2107,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$ak' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bj' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$bz' ) )
        = ( D @ ( B @ 'comp$y' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(241,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'compatible$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).

thf(1467,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'compatible$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(396,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'compatible$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).

thf(2037,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ ( A @ 'compatible$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(432,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ac' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$i' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$bc' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).

thf(2124,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ac' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$i' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$bc' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(68,axiom,
    ( ( 'id$c' @ ( 'top$b' @ 'inv_into$ag' ) )
    = 'id$c' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).

thf(812,plain,
    ( ( 'id$c' @ ( 'top$b' @ 'inv_into$ag' ) )
    = 'id$c' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(517,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$z' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$s' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$v' ) @ ( A @ 'comp$t' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).

thf(2333,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$z' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$s' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$v' ) @ ( A @ 'comp$t' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(512,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$al' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bk' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$ca' ) )
        = ( D @ ( B @ 'comp$m' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).

thf(2318,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$al' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bk' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$ca' ) )
        = ( D @ ( B @ 'comp$m' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(39,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$c' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$c' ) @ ( C @ 'inv_into$d' ) @ 'fun_app$c' ) )
        = ( D @ ( A @ 'fun_app$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).

thf(680,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$c' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$c' ) @ ( C @ 'inv_into$d' ) @ 'fun_app$c' ) )
        = ( D @ ( A @ 'fun_app$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(29,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).

thf(617,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( E @ ( B @ ( A @ ( D @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(463,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ 'equivalent_registers$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).

thf(2202,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( C @ ( A @ 'compatible$c' ) )
        & ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ 'equivalent_registers$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(48,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$a' ) )
         => ( ( E @ ( B @ 'fun_app$g' ) )
            = ( E @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'bij_betw$d' ) ) )
      <=> ( D @ ( A @ ( C @ 'bij_betw$d' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).

thf(712,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ! [E: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( A @ ( E @ 'member$a' ) )
         => ( ( E @ ( B @ 'fun_app$g' ) )
            = ( E @ ( C @ 'fun_app$g' ) ) ) )
     => ( ( ( D @ ( A @ ( C @ 'bij_betw$d' ) ) )
         => ( D @ ( A @ ( B @ 'bij_betw$d' ) ) ) )
        & ( ( D @ ( A @ ( B @ 'bij_betw$d' ) ) )
         => ( D @ ( A @ ( C @ 'bij_betw$d' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(74,axiom,
    ? [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$c' @ ( A @ 'member$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).

thf(855,plain,
    ? [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$c' @ ( A @ 'member$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(260,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ! [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$k' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$k' ) ) ) )
           => $false )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).

thf(1516,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$'] :
      ~ ( ! [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ~ ( ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                  ( ( B
                    = ( D @ ( A @ 'fun_app$k' ) ) )
                 => ( D = C ) )
              & ( B
                = ( C @ ( A @ 'fun_app$k' ) ) ) )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(378,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
    <=> ! [B: 'B_ell2_b_ell2_cblinfun$'] :
        ? [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$k' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$k' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).

thf(1961,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$k' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$k' ) )
              = B ) )
       => ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
      & ( ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) )
       => ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$k' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$k' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(78,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$a' @ 'inv_into$e' ) @ 'fun_app$g' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$f' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).

thf(872,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$f' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$a' @ 'inv_into$e' ) @ 'fun_app$g' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$a' @ 'inv_into$e' ) @ 'fun_app$g' ) ) )
         => ( ( B @ ( A @ 'fun_app$f' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(286,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = ( C @ ( 'id$e' @ 'comp$bj' ) ) )
     => ( ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( D @ ( C @ 'fun_app$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).

thf(1611,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',D: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( B @ ( A @ 'comp$a' ) )
        = ( C @ ( 'id$e' @ 'comp$bj' ) ) )
     => ( ( D @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) )
        = ( D @ ( C @ 'fun_app$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(321,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'comp$' ) )
          = C )
        & ( B @ 'iso_register$' )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).

thf(1753,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'comp$' ) )
          = C )
        & ( B @ 'iso_register$' )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(449,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$f' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) @ 'comp$au' ) )
        = ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).

thf(2160,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$f' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$am' ) @ 'comp$au' ) )
        = ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'register_pair$al' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(115,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$c' @ ( 'top$a' @ ( B @ 'bij_betw$c' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ ( B @ 'comp$ad' ) @ 'bij_betw$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).

thf(993,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$c' @ ( 'top$a' @ ( B @ 'bij_betw$c' ) ) )
        & ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) ) )
     => ( 'top$c' @ ( 'top$a' @ ( A @ ( B @ 'comp$ad' ) @ 'bij_betw$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(267,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'register$k' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom157) ).

thf(1547,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'register$k' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(60,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ah' ) )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'comp$' ) @ ( B @ ( A @ 'comp$ai' ) @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).

thf(776,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ah' ) )
        & ( A @ 'register$d' ) )
     => ( C @ ( A @ 'comp$' ) @ ( B @ ( A @ 'comp$ai' ) @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(404,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$k' @ ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) @ 'comp$az' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).

thf(2060,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$k' @ ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) @ 'comp$az' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(46,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dd' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).

thf(707,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dd' ) )
          = 'id$d' )
        & ( ( B @ ( A @ 'comp$ac' ) )
          = 'id$f' ) )
     => ( ( A @ ( 'top$d' @ 'inv_into$f' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(272,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$w' )
        & ( A @ 'register$t' ) )
     => ( ( D @ ( C @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_tensor$w' ) @ 'fun_app$n' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'tensor_op$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).

thf(1566,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( B @ 'register$w' )
        & ( A @ 'register$t' ) )
     => ( ( D @ ( C @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_tensor$w' ) @ 'fun_app$n' ) )
        = ( D @ ( B @ 'fun_app$ae' ) @ ( C @ ( A @ 'fun_app$ad' ) @ 'tensor_op$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(441,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$b' ) )
        & ( C @ ( B @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$o' @ ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) @ 'comp$bd' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).

thf(2143,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$b' ) )
        & ( C @ ( B @ 'compatible$p' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$o' @ ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) @ 'comp$bd' ) )
        = ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(371,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$x' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$cm' ) @ 'bij_betw$b' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).

thf(1941,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$x' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$cm' ) @ 'bij_betw$b' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$cm' ) @ 'bij_betw$b' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(104,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dj' ) )
          = 'id$e' )
        & ( ( B @ ( A @ 'comp$di' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$g' @ 'inv_into$ar' ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).

thf(954,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$'] :
      ( ( ( ( A @ ( B @ 'comp$dj' ) )
          = 'id$e' )
        & ( ( B @ ( A @ 'comp$di' ) )
          = 'id$' ) )
     => ( ( A @ ( 'top$g' @ 'inv_into$ar' ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(129,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$m' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$' ) @ 'bij_betw$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).

thf(1053,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$m' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$' ) @ 'bij_betw$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(451,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$g' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$az' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).

thf(2165,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$g' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( A @ 'register_pair$g' ) @ ( B @ ( A @ 'register_pair$' ) @ 'equivalent_registers$az' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(169,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'comp$dd' ) )
        = 'id$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom610) ).

thf(1186,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$b' )
     => ( ( A @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'comp$dd' ) )
        = 'id$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(18,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$c' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$c' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).

thf(585,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$c' ) ) )
     => ( B @ ( C @ ( A @ ( B @ 'inv_into$c' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(350,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'iso_register$j' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).

thf(1869,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$g' )
     => ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'iso_register$j' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(71,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$m' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$m' ) )
              = ( C @ ( A @ 'fun_app$m' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom635) ).

thf(840,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$m' ) ) )
        & ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$m' ) )
                = ( C @ ( A @ 'fun_app$m' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$m' ) )
                = ( C @ ( A @ 'fun_app$m' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(341,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) )
            = C )
        & ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$g' ) @ ( A @ 'fun_app$f' ) )
            = C ) )
     => ( ( B @ ( 'top$d' @ 'inv_into$f' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom178) ).

thf(1830,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$f' ) @ ( B @ 'fun_app$g' ) )
            = C )
        & ! [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$g' ) @ ( A @ 'fun_app$f' ) )
            = C ) )
     => ( ( B @ ( 'top$d' @ 'inv_into$f' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(302,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$n' )
     => ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).

thf(1658,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$n' )
     => ( 'top$c' @ ( 'top$d' @ ( A @ 'bij_betw$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(399,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ai' ) )
        & ( A @ 'register$' ) )
     => ( C @ ( A @ 'comp$aj' ) @ ( B @ ( A @ 'comp$m' ) @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).

thf(2044,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$ai' ) )
        & ( A @ 'register$' ) )
     => ( C @ ( A @ 'comp$aj' ) @ ( B @ ( A @ 'comp$m' ) @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(88,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( 'top$a' @ 'inv_into$b' ) @ 'bij_betw$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).

thf(907,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( 'top$a' @ 'inv_into$b' ) @ 'bij_betw$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(194,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( A @ 'compatible$t' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).

thf(1300,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$d' ) )
     => ( B @ ( A @ 'register_pair$i' ) @ 'complement$d' @ ( A @ 'compatible$t' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(234,axiom,
    'top$d' @ ( 'top$g' @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ 'bij_betw$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).

thf(1452,plain,
    'top$d' @ ( 'top$g' @ ( 'i$' @ ( 'id$' @ 'register_tensor$i' ) @ 'bij_betw$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(495,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$t' ) )
    <=> ( ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).

thf(2276,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
          & ( B @ ( A @ 'compatible$' ) ) )
       => ( B @ ( A @ 'complements$t' ) ) )
      & ( ( B @ ( A @ 'complements$t' ) )
       => ( ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
          & ( B @ ( A @ 'compatible$' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(469,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ 'equivalent_registers$z' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).

thf(2219,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ 'equivalent_registers$z' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(381,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'compatible$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).

thf(1980,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ 'complement$f' @ ( A @ 'compatible$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(481,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( A @ 'register_pair$k' ) @ ( B @ 'complements$i' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).

thf(2247,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( A @ 'register_pair$k' ) @ ( B @ 'complements$i' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(326,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ ( A @ 'complement$e' @ 'compatible$j' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).

thf(1766,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ ( A @ 'complement$e' @ 'compatible$j' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(187,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( ( A @ ( 'top$g' @ 'inv_into$o' ) @ ( A @ 'comp$dk' ) )
        = 'id$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom606) ).

thf(1257,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( ( A @ ( 'top$g' @ 'inv_into$o' ) @ ( A @ 'comp$dk' ) )
        = 'id$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(426,axiom,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$f' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$' @ 'equivalent_registers$g' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).

thf(2113,plain,
    ! [A: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$f' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$' @ 'equivalent_registers$g' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(248,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( ( 'swap$g' @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cu' ) )
        = ( A @ ( B @ 'register_pair$be' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).

thf(1485,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$c' ) )
     => ( ( 'swap$g' @ ( B @ ( A @ 'register_pair$g' ) @ 'comp$cu' ) )
        = ( A @ ( B @ 'register_pair$be' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(320,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ? [B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
          ( ( B @ ( A @ 'register_pair$x' ) @ 'iso_register$g' )
          & ( B @ ( A @ 'compatible$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).

thf(1749,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ? [B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
          ( ( B @ ( A @ 'register_pair$x' ) @ 'iso_register$g' )
          & ( B @ ( A @ 'compatible$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(256,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'fun_app$b' ) )
      = ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).

thf(1504,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'fun_app$b' ) )
      = ( C @ ( B @ 'fun_app$f' ) @ ( A @ 'fun_app$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(306,axiom,
    ! [A: 'C$',B: 'C$'] :
      ( ( ( A @ 'ket$b' )
        = ( B @ 'ket$b' ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).

thf(1670,plain,
    ! [A: 'C$',B: 'C$'] :
      ( ( ( A = B )
       => ( ( A @ 'ket$b' )
          = ( B @ 'ket$b' ) ) )
      & ( ( ( A @ 'ket$b' )
          = ( B @ 'ket$b' ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(119,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$e' ) ) )
     => ? [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).

thf(1008,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$e' ) ) )
     => ? [D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(22,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$c' ) ) )
     => ? [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).

thf(595,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_set$',C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$c' ) ) )
     => ? [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(76,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$s' )
    <=> ( ? [B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
            ( ( ( A @ ( B @ 'comp$dp' ) )
              = 'id$g' )
            & ( ( B @ ( A @ 'comp$do' ) )
              = 'id$i' )
            & ( B @ 'register$e' ) )
        & ( A @ 'register$as' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom587) ).

thf(859,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$dp' ) )
                = 'id$g' )
              & ( ( B @ ( A @ 'comp$do' ) )
                = 'id$i' )
              & ( B @ 'register$e' ) )
          & ( A @ 'register$as' ) )
       => ( A @ 'iso_register$s' ) )
      & ( ( A @ 'iso_register$s' )
       => ( ? [B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
              ( ( ( A @ ( B @ 'comp$dp' ) )
                = 'id$g' )
              & ( ( B @ ( A @ 'comp$do' ) )
                = 'id$i' )
              & ( B @ 'register$e' ) )
          & ( A @ 'register$as' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(24,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$e' )
        & ( C @ 'register$e' )
        & ( B @ 'register$d' )
        & ( A @ 'register$d' ) )
     => ( ( D @ ( C @ 'register_tensor$as' ) @ ( B @ ( A @ 'register_tensor$ab' ) @ 'comp$bp' ) )
        = ( D @ ( B @ 'comp$' ) @ ( C @ ( A @ 'comp$' ) @ 'register_tensor$bb' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).

thf(600,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',D: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$e' )
        & ( C @ 'register$e' )
        & ( B @ 'register$d' )
        & ( A @ 'register$d' ) )
     => ( ( D @ ( C @ 'register_tensor$as' ) @ ( B @ ( A @ 'register_tensor$ab' ) @ 'comp$bp' ) )
        = ( D @ ( B @ 'comp$' ) @ ( C @ ( A @ 'comp$' ) @ 'register_tensor$bb' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(375,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$s' ) @ 'register$aa' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).

thf(1955,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ ( A @ 'register_tensor$s' ) @ 'register$aa' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(276,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$aj' ) )
        & ( A @ 'register$a' ) )
     => ( C @ ( A @ 'comp$ak' ) @ ( B @ ( A @ 'comp$o' ) @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).

thf(1585,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$aj' ) )
        & ( A @ 'register$a' ) )
     => ( C @ ( A @ 'comp$ak' ) @ ( B @ ( A @ 'comp$o' ) @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(142,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).

thf(1094,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ? [D: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] : ( B @ ( C @ ( D @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(156,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
          ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
          & ( B @ ( A @ 'compatible$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom113) ).

thf(1140,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ? [B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
          ( ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
          & ( B @ ( A @ 'compatible$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(355,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$g' ) ) )
        & ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$g' ) )
              = ( C @ ( A @ 'fun_app$g' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom631) ).

thf(1881,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$g' ) ) )
        & ! [B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$g' ) )
                = ( C @ ( A @ 'fun_app$g' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$g' ) )
                = ( C @ ( A @ 'fun_app$g' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(192,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
    <=> ! [B: 'B_ell2_b_ell2_cblinfun$'] :
        ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$d' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$d' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).

thf(1272,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$d' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$d' ) )
              = B ) )
       => ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
      & ( ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) )
       => ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$d' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$d' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(27,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( B @ 'comp$ab' ) @ 'bij_betw$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).

thf(612,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$c' @ ( B @ 'bij_betw$b' ) ) )
        & ( 'top$c' @ ( 'top$a' @ ( A @ 'bij_betw$c' ) ) ) )
     => ( 'top$a' @ ( 'top$a' @ ( A @ ( B @ 'comp$ab' ) @ 'bij_betw$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(182,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$e' @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_tensor$u' ) @ 'complements$u' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).

thf(1240,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$e' @ 'register_tensor$ab' ) @ ( B @ ( A @ 'register_tensor$u' ) @ 'complements$u' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(114,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$f' )
     => ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom128) ).

thf(991,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$f' )
     => ( 'top$d' @ ( 'top$a' @ ( A @ 'bij_betw$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(288,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'compatible$aj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).

thf(1617,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$ag' ) )
        & ( C @ ( B @ 'compatible$a' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'register_pair$d' ) @ ( A @ 'compatible$aj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(414,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( ( 'assoc$m' @ ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) @ 'comp$bb' ) )
        = ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).

thf(2088,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( ( 'assoc$m' @ ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) @ 'comp$bb' ) )
        = ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(237,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( B @ ( A @ 'equivalent_registers$m' ) ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).

thf(1459,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$' ) )
        & ( B @ ( A @ 'equivalent_registers$m' ) ) )
     => ( C @ ( A @ 'equivalent_registers$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(97,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$b' ) )
         => ( C @ ( D @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).

thf(931,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$' ) ) )
     => ! [D: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( D @ 'member$b' ) )
         => ( C @ ( D @ ( A @ 'fun_app$k' ) @ 'member$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(373,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_op$l' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'fun_app$y' ) )
        = ( D @ ( B @ 'fun_app$v' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'tensor_op$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).

thf(1949,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_op$l' ) @ ( B @ ( A @ 'register_tensor$t' ) @ 'fun_app$y' ) )
        = ( D @ ( B @ 'fun_app$v' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'tensor_op$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(336,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) @ ( B @ ( A @ 'register_pair$bc' ) @ 'fun_app$as' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ai' ) )
        & ( A @ 'register$q' ) )
     => ( A @ 'regular_register$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).

thf(1817,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$j' ) @ ( B @ ( A @ 'register_pair$bc' ) @ 'fun_app$as' ) )
          = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( B @ ( A @ 'complements$ai' ) )
        & ( A @ 'register$q' ) )
     => ( A @ 'regular_register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(330,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$k' ) ) )
        & ! [B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$k' ) )
              = ( C @ ( A @ 'fun_app$k' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom634) ).

thf(1781,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$k' ) ) )
        & ! [B: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$',C: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$k' ) )
                = ( C @ ( A @ 'fun_app$k' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$k' ) )
                = ( C @ ( A @ 'fun_app$k' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(170,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$f' @ 'register_tensor$ad' ) @ ( B @ ( A @ 'register_tensor$s' ) @ 'complements$w' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).

thf(1189,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$f' @ 'register_tensor$ad' ) @ ( B @ ( A @ 'register_tensor$s' ) @ 'complements$w' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(408,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( A @ 'complements$t' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).

thf(2071,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( B @ ( A @ 'complements$t' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(162,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'comp$bh' ) )
      = ( C @ ( B @ 'comp$af' ) @ ( A @ 'comp$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).

thf(1157,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$a' ) @ 'comp$bh' ) )
      = ( C @ ( B @ 'comp$af' ) @ ( A @ 'comp$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(410,axiom,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) )
    = ( 'aF$' @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).

thf(2078,plain,
    ( ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ ( 'f$' @ 'complement$e' @ ( 'f$' @ 'register_pair$g' ) @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) )
    = ( 'aF$' @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(362,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'fun_app$g' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$p' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).

thf(1913,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$g' ) @ 'fun_app$g' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$p' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(509,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$p' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$f' @ 'equivalent_registers$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).

thf(2310,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_ell2_a_c_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$p' ) )
     => ( B @ 'complement$' @ ( A @ 'complement$f' @ 'equivalent_registers$q' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(87,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_op$m' ) @ ( B @ ( A @ 'register_tensor$r' ) @ 'fun_app$u' ) )
        = ( D @ ( B @ 'fun_app$v' ) @ ( C @ ( A @ 'fun_app$v' ) @ 'tensor_op$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).

thf(903,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$',D: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( B @ 'register$' )
        & ( A @ 'register$' ) )
     => ( ( D @ ( C @ 'tensor_op$m' ) @ ( B @ ( A @ 'register_tensor$r' ) @ 'fun_app$u' ) )
        = ( D @ ( B @ 'fun_app$v' ) @ ( C @ ( A @ 'fun_app$v' ) @ 'tensor_op$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(3,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ ( 'id$g' @ 'equivalent_registers$ah' ) )
    <=> ( A @ 'iso_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).

thf(524,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( A @ 'iso_register$' )
       => ( A @ ( 'id$g' @ 'equivalent_registers$ah' ) ) )
      & ( ( A @ ( 'id$g' @ 'equivalent_registers$ah' ) )
       => ( A @ 'iso_register$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(17,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'A_ell2_a_ell2_cblinfun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_op$p' ) @ ( B @ ( A @ 'register_tensor$u' ) @ 'fun_app$z' ) )
        = ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'tensor_op$n' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).

thf(581,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun$',D: 'A_ell2_a_ell2_cblinfun$'] :
      ( ( ( B @ 'register$a' )
        & ( A @ 'register$a' ) )
     => ( ( D @ ( C @ 'tensor_op$p' ) @ ( B @ ( A @ 'register_tensor$u' ) @ 'fun_app$z' ) )
        = ( D @ ( B @ 'fun_app$x' ) @ ( C @ ( A @ 'fun_app$x' ) @ 'tensor_op$n' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(300,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$w' ) )
        & ( B @ ( A @ 'complements$a' ) ) )
     => ( C @ ( A @ 'complements$a' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).

thf(1654,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$w' ) )
        & ( B @ ( A @ 'complements$a' ) ) )
     => ( C @ ( A @ 'complements$a' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(225,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
    <=> ( ? [C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
            ( ( ( C @ ( A @ 'comp$' ) )
              = B )
            & ( C @ 'iso_register$' ) )
        & ( A @ 'register$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).

thf(1412,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ? [C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
              ( ( ( C @ ( A @ 'comp$' ) )
                = B )
              & ( C @ 'iso_register$' ) )
          & ( A @ 'register$d' ) )
       => ( B @ ( A @ 'equivalent_registers$' ) ) )
      & ( ( B @ ( A @ 'equivalent_registers$' ) )
       => ( ? [C: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
              ( ( ( C @ ( A @ 'comp$' ) )
                = B )
              & ( C @ 'iso_register$' ) )
          & ( A @ 'register$d' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(514,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$e' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) @ 'comp$at' ) )
        = ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).

thf(2325,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( 'assoc$e' @ ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) @ 'comp$at' ) )
        = ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(54,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun$'] : ( 'top$a' @ ( A @ 'member$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).

thf(759,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun$'] : ( 'top$a' @ ( A @ 'member$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(424,axiom,
    'top$a' @ ( 'top$c' @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ 'bij_betw$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).

thf(2110,plain,
    'top$a' @ ( 'top$c' @ ( 'g$' @ 'complement$f' @ ( 'g$' @ 'register_pair$x' ) @ 'bij_betw$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(120,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
    <=> ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
        ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
              ( ( ( D @ ( A @ 'fun_app$m' ) )
                = B )
             => ( D = C ) )
          & ( ( C @ ( A @ 'fun_app$m' ) )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).

thf(1010,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$m' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$m' ) )
              = B ) )
       => ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) )
      & ( ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) )
       => ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ? [C: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
            ( ! [D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
                ( ( ( D @ ( A @ 'fun_app$m' ) )
                  = B )
               => ( D = C ) )
            & ( ( C @ ( A @ 'fun_app$m' ) )
              = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(215,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( B @ 'register$o' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).

thf(1390,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( B @ 'register$o' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(472,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$v' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$e' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$r' ) @ ( A @ 'comp$f' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).

thf(2226,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$v' ) )
        & ( A @ 'register$' ) )
     => ( ( C @ ( A @ 'comp$e' ) @ ( B @ ( A @ 'comp$d' ) @ 'register_pair$a' ) )
        = ( C @ ( B @ 'register_pair$r' ) @ ( A @ 'comp$f' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(235,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$p' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'comp$e' ) @ ( A @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).

thf(1453,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$p' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'comp$e' ) @ ( A @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(200,axiom,
    ( ( 'id$' @ ( 'id$' @ 'register_tensor$bq' ) )
    = 'id$a' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).

thf(1326,plain,
    ( ( 'id$' @ ( 'id$' @ 'register_tensor$bq' ) )
    = 'id$a' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(185,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( 'top$b' @ ( 'top$a' @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'bij_betw$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).

thf(1253,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) )
     => ( 'top$b' @ ( 'top$a' @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'bij_betw$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(452,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$af' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) @ ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) @ 'equivalent_registers$aq' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).

thf(2167,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$af' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$ak' ) @ ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'register_pair$ai' ) @ 'equivalent_registers$aq' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(496,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$w' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$x' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).

thf(2283,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$b' ) )
        & ( A @ 'register$j' ) )
     => ( ( C @ ( A @ 'comp$w' ) @ ( B @ ( A @ 'comp$j' ) @ 'register_pair$' ) )
        = ( C @ ( B @ 'register_pair$' ) @ ( A @ 'comp$x' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(132,axiom,
    ( ( 'id$' @ ( 'top$l' @ 'inv_into$z' ) )
    = 'id$' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).

thf(1062,plain,
    ( ( 'id$' @ ( 'top$l' @ 'inv_into$z' ) )
    = 'id$' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(343,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$' @ ( 'top$a' @ ( B @ 'bij_betw$j' ) ) )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( B @ ( A @ 'comp$ah' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$' @ 'inv_into$a' ) @ ( B @ ( 'top$a' @ 'inv_into$m' ) @ 'comp$ah' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).

thf(1854,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$' @ ( 'top$a' @ ( B @ 'bij_betw$j' ) ) )
        & ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) )
     => ( ( B @ ( A @ 'comp$ah' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$' @ 'inv_into$a' ) @ ( B @ ( 'top$a' @ 'inv_into$m' ) @ 'comp$ah' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(116,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ 'register$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).

thf(995,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ 'register$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(204,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( A @ 'register_pair$j' ) @ ( B @ 'complements$h' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).

thf(1341,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( A @ 'register_pair$j' ) @ ( B @ 'complements$h' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(84,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$s' )
     => ( A @ ( 'top$e' @ 'inv_into$i' ) @ 'iso_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).

thf(896,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$s' )
     => ( A @ ( 'top$e' @ 'inv_into$i' ) @ 'iso_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(499,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) @ ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) @ 'equivalent_registers$as' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).

thf(2290,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'register_pair$ao' ) @ ( C @ ( B @ 'register_pair$a' ) @ ( A @ 'register_pair$an' ) @ 'equivalent_registers$as' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(483,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$p' ) )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) @ ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$au' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).

thf(2251,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$p' ) )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$a' ) @ 'register_pair$n' ) @ ( C @ ( B @ 'register_pair$b' ) @ ( A @ 'register_pair$i' ) @ 'equivalent_registers$au' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(346,axiom,
    ( ( 'assoc$g' @ ( 'top$g' @ 'inv_into$af' ) )
    = 'assoc$o' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).

thf(1861,plain,
    ( ( 'assoc$g' @ ( 'top$g' @ 'inv_into$af' ) )
    = 'assoc$o' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(250,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$u' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).

thf(1491,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$u' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(15,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$e' ) ) )
        & ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$',C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( ( B @ ( A @ 'fun_app$e' ) )
              = ( C @ ( A @ 'fun_app$e' ) ) )
          <=> ( B = C ) ) )
     => ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).

thf(568,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [B: 'B_ell2_b_ell2_cblinfun$'] :
          ? [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( B
            = ( C @ ( A @ 'fun_app$e' ) ) )
        & ! [B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$',C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( ( B = C )
             => ( ( B @ ( A @ 'fun_app$e' ) )
                = ( C @ ( A @ 'fun_app$e' ) ) ) )
            & ( ( ( B @ ( A @ 'fun_app$e' ) )
                = ( C @ ( A @ 'fun_app$e' ) ) )
             => ( B = C ) ) ) )
     => ( 'top$a' @ ( 'top$b' @ ( A @ 'bij_betw$m' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(406,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$t' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).

thf(2066,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'equivalent_registers$t' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( A @ 'register_pair$a' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'equivalent_registers$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(172,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( A @ ( 'top$f' @ 'inv_into$k' ) @ 'comp$do' ) )
        = 'id$i' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom613) ).

thf(1193,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( A @ ( 'top$f' @ 'inv_into$k' ) @ 'comp$do' ) )
        = 'id$i' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(138,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$f' ) @ ( C @ 'inv_into$e' ) @ 'fun_app$g' ) )
        = ( D @ ( A @ 'fun_app$g' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).

thf(1077,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$a' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$f' ) @ ( C @ 'inv_into$e' ) @ 'fun_app$g' ) )
        = ( D @ ( A @ 'fun_app$g' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(430,axiom,
    'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'complements$a' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).

thf(2120,plain,
    'g$' @ ( 'f$' @ 'register_pair$a' ) @ 'complement$' @ ( 'g$' @ 'register_pair$b' ) @ ( 'f$' @ 'complements$a' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(417,axiom,
    'f$' @ 'regular_register$',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).

thf(2095,plain,
    'f$' @ 'regular_register$',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(391,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( ( A @ ( A @ ( 'top$g' @ 'inv_into$o' ) @ 'comp$dl' ) )
        = 'id$e' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom612) ).

thf(2019,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$e' )
     => ( ( A @ ( A @ ( 'top$g' @ 'inv_into$o' ) @ 'comp$dl' ) )
        = 'id$e' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(501,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$ac' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) @ ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) @ 'equivalent_registers$an' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).

thf(2294,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( B @ 'compatible$ac' ) )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$b' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$' ) @ 'register_pair$ab' ) @ ( C @ ( B @ 'register_pair$aa' ) @ ( A @ 'register_pair$z' ) @ 'equivalent_registers$an' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(198,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$' ) @ ( B @ 'fun_app$e' ) )
            = C )
        & ! [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$e' ) @ ( A @ 'fun_app$' ) )
            = C ) )
     => ( ( B @ ( 'top$b' @ 'inv_into$' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).

thf(1309,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ! [C: 'B_ell2_b_ell2_cblinfun$'] :
            ( ( C @ ( A @ 'fun_app$' ) @ ( B @ 'fun_app$e' ) )
            = C )
        & ! [C: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
            ( ( C @ ( B @ 'fun_app$e' ) @ ( A @ 'fun_app$' ) )
            = C ) )
     => ( ( B @ ( 'top$b' @ 'inv_into$' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(153,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( A @ ( B @ 'compatible$ab' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).

thf(1133,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( A @ ( B @ 'compatible$ab' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(118,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$c' @ 'inv_into$t' ) @ 'fun_app$n' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$o' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).

thf(999,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$',C: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$o' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$t' ) @ 'fun_app$n' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$c' @ 'inv_into$t' ) @ 'fun_app$n' ) ) )
         => ( ( B @ ( A @ 'fun_app$o' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(298,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$e' )
    <=> ( ? [B: 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$d' ) @ ( A @ 'complement$o' @ ( A @ 'register_pair$av' ) ) )
            = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
        & ( A @ 'register$q' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).

thf(1642,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$d' ) @ ( A @ 'complement$o' @ ( A @ 'register_pair$av' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$q' ) )
       => ( A @ 'regular_register$e' ) )
      & ( ( A @ 'regular_register$e' )
       => ( ? [B: 'A_a_complement_domain_ell2_a_a_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$d' ) @ ( A @ 'complement$o' @ ( A @ 'register_pair$av' ) ) )
              = ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) ) )
          & ( A @ 'register$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(259,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$t' ) @ 'fun_app$ap' ) )
          = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( B @ ( A @ 'complements$af' ) )
        & ( A @ 'register$t' ) )
     => ( A @ 'regular_register$f' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).

thf(1512,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$c' ) @ ( B @ ( A @ 'register_pair$t' ) @ 'fun_app$ap' ) )
          = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( B @ ( A @ 'complements$af' ) )
        & ( A @ 'register$t' ) )
     => ( A @ 'regular_register$f' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(376,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'compatible$ai' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).

thf(1957,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$af' ) )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( C @ ( B @ 'register_pair$aj' ) @ ( A @ 'compatible$ai' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(485,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( A @ 'register_pair$' ) @ ( B @ 'complements$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).

thf(2255,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( A @ 'register_pair$' ) @ ( B @ 'complements$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(475,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( B @ 'register_pair$e' ) @ ( A @ 'complements$e' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).

thf(2233,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'complement$b' @ ( B @ 'register_pair$e' ) @ ( A @ 'complements$e' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(217,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$r' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$f' @ 'equivalent_registers$s' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).

thf(1395,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$r' ) )
     => ( B @ 'complement$e' @ ( A @ 'complement$f' @ 'equivalent_registers$s' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(158,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ 'register$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).

thf(1148,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$a' )
     => ( A @ 'complement$e' @ 'register$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(322,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( 'top$f' @ 'inv_into$k' ) @ ( A @ 'comp$dp' ) )
        = 'id$g' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).

thf(1757,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( ( A @ ( 'top$f' @ 'inv_into$k' ) @ ( A @ 'comp$dp' ) )
        = 'id$g' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(246,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'compatible$al' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom217) ).

thf(1480,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'compatible$' ) )
        & ( C @ ( B @ 'compatible$' ) )
        & ( B @ ( A @ 'compatible$ah' ) ) )
     => ( C @ ( B @ ( A @ 'register_pair$ap' ) @ 'compatible$al' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(25,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$d' @ ( 'top$a' @ ( B @ 'bij_betw$e' ) ) )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( B @ ( A @ 'comp$ac' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( B @ ( 'top$a' @ 'inv_into$e' ) @ 'comp$ac' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom116) ).

thf(603,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( 'top$d' @ ( 'top$a' @ ( B @ 'bij_betw$e' ) ) )
        & ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) ) )
     => ( ( B @ ( A @ 'comp$ac' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = ( A @ ( 'top$d' @ 'inv_into$f' ) @ ( B @ ( 'top$a' @ 'inv_into$e' ) @ 'comp$ac' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(13,axiom,
    ? [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$d' @ ( A @ 'member$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).

thf(564,plain,
    ? [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$'] : ( 'top$d' @ ( A @ 'member$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(345,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( B @ 'register_pair$c' ) @ ( A @ 'complements$d' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).

thf(1859,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_c_prod_b_complement_domain_prod_ell2_a_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$a' ) )
     => ( B @ ( A @ 'register_pair$d' ) @ 'complement$a' @ ( B @ 'register_pair$c' ) @ ( A @ 'complements$d' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(93,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$q' ) @ 'register$e' )
     => ( B @ 'register$aq' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).

thf(918,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$q' ) @ 'register$e' )
     => ( B @ 'register$aq' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(252,axiom,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ ( 'top$f' @ 'inv_into$k' ) @ 'iso_register$s' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).

thf(1495,plain,
    ! [A: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$' )
     => ( A @ ( 'top$f' @ 'inv_into$k' ) @ 'iso_register$s' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(415,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( B @ 'equivalent_registers$ab' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).

thf(2091,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$a' ) @ 'iso_register$c' )
        & ( C @ ( A @ 'compatible$' ) )
        & ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( B @ ( A @ 'compatible$d' ) ) )
     => ( C @ ( B @ 'equivalent_registers$ab' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(96,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$m' ) @ ( A @ 'fun_app$m' ) )
          = B )
     => ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).

thf(928,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_c_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ! [B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
          ( ( B @ ( A @ 'fun_app$m' ) @ ( A @ 'fun_app$m' ) )
          = B )
     => ( 'top$c' @ ( 'top$c' @ ( A @ 'bij_betw$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(224,axiom,
    ( 'top$d'
    = ( 'top$s' @ 'collect$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).

thf(1410,plain,
    ( 'top$d'
    = ( 'top$s' @ 'collect$b' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(58,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( A @ 'register$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).

thf(767,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'equivalent_registers$' ) )
     => ( A @ 'register$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(471,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$p' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bi' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$by' ) )
        = ( D @ ( B @ 'comp$e' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).

thf(2223,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$p' )
        & ( C @ 'register$q' )
        & ( B @ ( A @ 'compatible$' ) ) )
     => ( ( D @ ( C @ 'register_tensor$bi' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'comp$by' ) )
        = ( D @ ( B @ 'comp$e' ) @ ( C @ ( A @ 'comp$g' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(243,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$v' ) ) )
     => ( B @ ( C @ 'comp$e' ) @ ( A @ ( C @ 'comp$d' ) @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom265) ).

thf(1473,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$' )
        & ( B @ ( A @ 'compatible$v' ) ) )
     => ( B @ ( C @ 'comp$e' ) @ ( A @ ( C @ 'comp$d' ) @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(206,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'comp$dh' ) )
        = 'id$c' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom609) ).

thf(1346,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$d' )
     => ( ( A @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'comp$dh' ) )
        = 'id$c' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(405,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$az' ) ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_pair$az' ) @ 'comp$bx' ) )
        = ( D @ ( B @ 'comp$k' ) @ ( C @ ( A @ 'comp$j' ) @ 'register_pair$a' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).

thf(2063,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',D: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( D @ 'register$' )
        & ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$az' ) ) )
     => ( ( D @ ( C @ 'register_tensor$t' ) @ ( B @ ( A @ 'register_pair$az' ) @ 'comp$bx' ) )
        = ( D @ ( B @ 'comp$k' ) @ ( C @ ( A @ 'comp$j' ) @ 'register_pair$a' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(380,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$b' ) @ ( 'top$i' @ 'inv_into$w' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$c' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).

thf(1977,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$b' ) @ ( 'top$i' @ 'inv_into$w' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$c' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(340,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$d' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$j' ) @ ( 'top$m' @ 'inv_into$aa' ) )
        = ( B @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$k' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).

thf(1827,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$d' )
        & ( A @ 'iso_register$g' ) )
     => ( ( B @ ( A @ 'register_tensor$j' ) @ ( 'top$m' @ 'inv_into$aa' ) )
        = ( B @ ( 'top$b' @ 'inv_into$' ) @ ( A @ ( 'top$c' @ 'inv_into$d' ) @ 'register_tensor$k' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(160,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$d' ) )
     => ( ( B @ ( A @ 'register_tensor$p' ) @ ( 'top$p' @ 'inv_into$ad' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'register_tensor$q' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).

thf(1152,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$b' )
        & ( A @ 'iso_register$d' ) )
     => ( ( B @ ( A @ 'register_tensor$p' ) @ ( 'top$p' @ 'inv_into$ad' ) )
        = ( B @ ( 'top$d' @ 'inv_into$f' ) @ ( A @ ( 'top$b' @ 'inv_into$' ) @ 'register_tensor$q' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(264,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$m' )
     => ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).

thf(1532,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$m' )
     => ( 'top$d' @ ( 'top$c' @ ( A @ 'bij_betw$l' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(213,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( ( B
          = ( C @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) ) )
      <=> ( ( B @ ( A @ 'fun_app$g' ) )
          = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom243) ).

thf(1378,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun$',C: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( 'top$a' @ ( 'top$d' @ ( A @ 'bij_betw$d' ) ) )
     => ( ( ( ( B @ ( A @ 'fun_app$g' ) )
            = C )
         => ( B
            = ( C @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) ) ) )
        & ( ( B
            = ( C @ ( A @ ( 'top$d' @ 'inv_into$f' ) @ 'fun_app$f' ) ) )
         => ( ( B @ ( A @ 'fun_app$g' ) )
            = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(490,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( B @ 'compatible$p' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).

thf(2265,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$' ) )
     => ( B @ ( A @ 'register_pair$a' ) @ 'complement$' @ ( B @ 'compatible$p' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(280,axiom,
    ( 'top$a'
    = ( 'top$u' @ 'collect$d' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).

thf(1597,plain,
    ( 'top$a'
    = ( 'top$u' @ 'collect$d' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(77,axiom,
    'top$a' @ ( 'top$a' @ ( 'id$f' @ 'bij_betw$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).

thf(871,plain,
    'top$a' @ ( 'top$a' @ ( 'id$f' @ 'bij_betw$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(254,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$av' ) ) )
     => ( B @ ( C @ ( A @ 'comp$j' ) @ 'compatible$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).

thf(1500,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ 'register$a' )
        & ( B @ ( A @ 'compatible$av' ) ) )
     => ( B @ ( C @ ( A @ 'comp$j' ) @ 'compatible$' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(365,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$x' ) @ 'fun_app$d' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$q' ) )
        & ( A @ 'register$' ) )
     => ( A @ 'regular_register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).

thf(1923,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_b_complement_domain_ell2_c_b_complement_domain_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) @ 'tensor_op$f' ) @ ( B @ ( A @ 'register_pair$x' ) @ 'fun_app$d' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$q' ) )
        & ( A @ 'register$' ) )
     => ( A @ 'regular_register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(49,axiom,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
      <=> ( E @ ( B @ ( A @ ( D @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).

thf(723,plain,
    ! [A: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',E: 'B_ell2_b_ell2_cblinfun_set$'] :
      ( ( C @ ( B @ ( A @ 'bij_betw$d' ) ) )
     => ( ( ( E @ ( B @ ( A @ ( D @ 'comp$r' ) @ 'bij_betw$d' ) ) )
         => ( E @ ( C @ ( D @ 'bij_betw$a' ) ) ) )
        & ( ( E @ ( C @ ( D @ 'bij_betw$a' ) ) )
         => ( E @ ( B @ ( A @ ( D @ 'comp$r' ) @ 'bij_betw$d' ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(219,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$t' )
     => ( A @ 'register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom222) ).

thf(1399,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$t' )
     => ( A @ 'register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(492,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'register$l' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).

thf(2270,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'compatible$b' ) )
     => ( B @ ( A @ 'register_pair$' ) @ 'register$l' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(290,axiom,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ ( A @ 'complement$f' @ 'compatible$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).

thf(1621,plain,
    ! [A: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'register$' )
     => ( A @ ( A @ 'complement$f' @ 'compatible$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(284,axiom,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( 'top$e' @ ( 'top$a' @ ( B @ 'bij_betw$g' ) ) )
        & ( 'top$f' @ ( 'top$e' @ ( A @ 'bij_betw$f' ) ) ) )
     => ( ( B @ ( A @ 'comp$ag' ) @ ( 'top$a' @ 'inv_into$g' ) )
        = ( A @ ( 'top$e' @ 'inv_into$i' ) @ ( B @ ( 'top$a' @ 'inv_into$h' ) @ 'comp$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).

thf(1606,plain,
    ! [A: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_a_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_fun$'] :
      ( ( ( 'top$e' @ ( 'top$a' @ ( B @ 'bij_betw$g' ) ) )
        & ( 'top$f' @ ( 'top$e' @ ( A @ 'bij_betw$f' ) ) ) )
     => ( ( B @ ( A @ 'comp$ag' ) @ ( 'top$a' @ 'inv_into$g' ) )
        = ( A @ ( 'top$e' @ 'inv_into$i' ) @ ( B @ ( 'top$a' @ 'inv_into$h' ) @ 'comp$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(317,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'complements$a' ) )
    <=> ( ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
        & ( B @ ( A @ 'compatible$d' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).

thf(1737,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
          & ( B @ ( A @ 'compatible$d' ) ) )
       => ( B @ ( A @ 'complements$a' ) ) )
      & ( ( B @ ( A @ 'complements$a' ) )
       => ( ( B @ ( A @ 'register_pair$i' ) @ 'iso_register$e' )
          & ( B @ ( A @ 'compatible$d' ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(168,axiom,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$k' )
     => ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).

thf(1184,plain,
    ! [A: 'A_c_prod_a_c_prod_b_complement_domain_prod_ell2_a_c_prod_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( A @ 'iso_register$k' )
     => ( 'top$a' @ ( 'top$' @ ( A @ 'bij_betw$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(239,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( B @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).

thf(1463,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( 'top$a' @ ( 'top$a' @ ( B @ 'bij_betw$a' ) ) )
        & ( 'top$a' @ ( 'top$c' @ ( A @ 'bij_betw$b' ) ) ) )
     => ( 'top$a' @ ( 'top$c' @ ( A @ ( B @ 'comp$ae' ) @ 'bij_betw$b' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(503,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$k' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).

thf(2297,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'A_c_prod_b_complement_domain_ell2_a_c_prod_b_complement_domain_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( ( C @ ( A @ 'register_pair$' ) @ 'iso_register$a' )
        & ( C @ ( A @ 'compatible$b' ) )
        & ( B @ ( A @ 'register_pair$g' ) @ 'iso_register$b' )
        & ( B @ ( A @ 'compatible$c' ) ) )
     => ( C @ ( B @ 'equivalent_registers$k' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(32,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( A @ ( 'top$u' @ 'fun_app$be' ) )
    <=> ( 'top$a' @ ( A @ 'member$' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).

thf(639,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun$'] :
      ( ( ( 'top$a' @ ( A @ 'member$' ) )
       => ( A @ ( 'top$u' @ 'fun_app$be' ) ) )
      & ( ( A @ ( 'top$u' @ 'fun_app$be' ) )
       => ( 'top$a' @ ( A @ 'member$' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(135,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).

thf(1069,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( 'top$a' @ ( 'top$a' @ ( A @ 'bij_betw$a' ) ) )
     => ( ( A @ ( 'top$a' @ 'inv_into$b' ) @ ( 'top$a' @ 'inv_into$b' ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(513,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$l' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$an' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$t' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).

thf(2321,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_ell2_c_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',C: 'C_ell2_c_ell2_cblinfun$'] :
      ( ( ( ( C @ ( 'default$a' @ 'ket$a' @ ( 'default$a' @ 'ket$a' @ 'butterfly$a' ) @ 'tensor_op$l' ) @ ( B @ ( A @ 'register_pair$a' ) @ 'fun_app$an' ) )
          = ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) ) )
        & ( B @ ( A @ 'complements$t' ) )
        & ( A @ 'register$a' ) )
     => ( A @ 'regular_register$' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(211,axiom,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( A @ 'regular_register$d' )
    <=> ( ? [B: 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$'] :
            ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$b' ) @ ( A @ 'complement$n' @ ( A @ 'register_pair$au' ) ) )
            = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
        & ( A @ 'register$s' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).

thf(1367,plain,
    ! [A: 'B_ell2_b_ell2_cblinfun_c_ell2_c_ell2_cblinfun_fun$'] :
      ( ( ( ? [B: 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$b' ) @ ( A @ 'complement$n' @ ( A @ 'register_pair$au' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$s' ) )
       => ( A @ 'regular_register$d' ) )
      & ( ( A @ 'regular_register$d' )
       => ( ? [B: 'B_c_complement_domain_ell2_b_c_complement_domain_ell2_cblinfun$'] :
              ( ( B @ ( 'default$' @ 'ket$' @ ( 'default$' @ 'ket$' @ 'butterfly$' ) @ 'tensor_op$b' ) @ ( A @ 'complement$n' @ ( A @ 'register_pair$au' ) ) )
              = ( 'default$b' @ 'ket$b' @ ( 'default$b' @ 'ket$b' @ 'butterfly$b' ) ) )
          & ( A @ 'register$s' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(100,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$s' )
        & ( A @ 'iso_register$z' ) )
     => ( ( B @ ( A @ 'register_tensor$h' ) @ ( 'top$d' @ 'inv_into$r' ) )
        = ( B @ ( 'top$e' @ 'inv_into$i' ) @ ( A @ ( 'top$l' @ 'inv_into$z' ) @ 'register_tensor$i' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).

thf(940,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_a_ell2_a_ell2_cblinfun_fun$',B: 'A_b_complement_domain_ell2_a_b_complement_domain_ell2_cblinfun_c_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( ( B @ 'iso_register$s' )
        & ( A @ 'iso_register$z' ) )
     => ( ( B @ ( A @ 'register_tensor$h' ) @ ( 'top$d' @ 'inv_into$r' ) )
        = ( B @ ( 'top$e' @ 'inv_into$i' ) @ ( A @ ( 'top$l' @ 'inv_into$z' ) @ 'register_tensor$i' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(363,axiom,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$i' ) @ 'register$n' )
     => ( A @ 'register$a' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).

thf(1917,plain,
    ! [A: 'A_ell2_a_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_c_prod_b_complement_domain_prod_ell2_c_a_c_prod_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$'] :
      ( ( B @ ( A @ 'register_pair$i' ) @ 'register$n' )
     => ( A @ 'register$a' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(37,axiom,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$d' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$' ) @ ( C @ 'inv_into$p' ) @ 'fun_app$e' ) )
        = ( D @ ( A @ 'fun_app$e' ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).

thf(676,plain,
    ! [A: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_a_a_c_prod_b_complement_domain_prod_prod_ell2_c_a_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$d' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$m' ) ) ) )
     => ( ( D @ ( A @ ( B @ 'inv_into$' ) @ ( C @ 'inv_into$p' ) @ 'fun_app$e' ) )
        = ( D @ ( A @ 'fun_app$e' ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(233,axiom,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$bi' ) @ 'comp$a' ) )
      = ( C @ ( B @ 'comp$a' ) @ ( A @ 'comp$bj' ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).

thf(1449,plain,
    ! [A: 'A_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',B: 'A_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_a_c_a_c_prod_b_complement_domain_prod_prod_ell2_cblinfun_fun$',C: 'B_ell2_b_ell2_cblinfun_a_a_b_complement_domain_prod_ell2_a_a_b_complement_domain_prod_ell2_cblinfun_fun$'] :
      ( ( C @ ( B @ ( A @ 'comp$bi' ) @ 'comp$a' ) )
      = ( C @ ( B @ 'comp$a' ) @ ( A @ 'comp$bj' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(334,axiom,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$d' ) @ ( A @ ( B @ 'inv_into$d' ) @ 'fun_app$c' ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).

thf(1812,plain,
    ! [A: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_b_ell2_b_ell2_cblinfun_fun$',B: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun_set$',C: 'B_ell2_b_ell2_cblinfun_set$',D: 'C_c_b_complement_domain_prod_ell2_c_c_b_complement_domain_prod_ell2_cblinfun$'] :
      ( ( ( B @ ( D @ 'member$c' ) )
        & ( C @ ( B @ ( A @ 'bij_betw$b' ) ) ) )
     => ( ( D @ ( A @ 'fun_app$d' ) @ ( A @ ( B @ 'inv_into$d' ) @ 'fun_app$c' ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(2378,plain,
    $false,
    inference(e,[status(thm)],[2199,809,1823,1633,1729,1237,2331,666,1549,1554,2163,645,892,1879,1718,1024,1469,2306,2341,2336,2131,1995,2263,909,628,962,1982,1200,523,2210,683,2231,1443,1401,1205,2099,1269,614,1437,1173,2117,2104,1422,1939,1305,597,1497,1426,533,1867,1999,2141,814,1260,913,1640,945,2042,1507,538,1354,2146,1196,898,2046,1576,1046,1935,1475,1803,2136,1904,1228,1623,1482,1055,2328,1792,2039,1871,1907,1330,1455,1191,2126,542,1760,1660,587,619,2274,702,1545,559,853,1892,2169,1704,1609,606,770,881,1115,2158,2024,2301,1815,2237,1465,1302,2105,1911,1109,2259,937,2034,806,966,2073,1051,2017,766,2058,2190,1072,1119,1351,2002,1405,1975,1526,2137,2242,2286,1104,1697,1242,1863,1651,1604,920,2204,1306,761,2118,810,2093,2296,2083,1768,1636,1163,746,1343,1255,1570,1502,1666,1619,2032,729,2015,1387,1723,957,894,2249,778,1217,2147,916,566,1920,2068,2181,1656,1027,757,1407,710,1573,1032,1602,1634,1392,2245,1592,1089,2115,1762,948,1328,1121,1064,1096,1138,593,783,989,1534,1953,980,1587,857,1397,1493,1160,933,1182,1461,1075,2080,2196,1937,2172,1214,1446,679,1424,2312,590,2085,1155,547,1744,1825,2304,1131,1552,1050,911,2006,1947,1984,1874,1599,1720,2272,1776,1263,997,1150,1478,1266,2153,1857,1202,1779,1286,674,1663,2221,530,2338,926,1135,1510,1764,2292,1680,1959,1747,1927,1631,2121,2235,2253,2149,562,1833,694,2048,732,1615,2188,1929,826,579,1403,2134,545,1488,2193,2308,1312,1865,804,704,1638,1356,672,1058,1107,2055,1092,764,900,2214,1894,1117,1524,1349,2257,2299,1144,2197,2151,2229,1043,1801,1376,1439,890,1877,1080,1339,1557,2111,1993,2267,1909,700,1029,964,943,2314,2129,535,2343,2261,1821,1112,1688,983,1198,2350,1594,1245,780,2022,2101,1726,851,2156,2207,1694,685,1171,2212,959,2171,1066,1528,2139,883,986,2288,2239,2096,2107,1467,2037,2124,812,2333,2318,680,617,2202,712,855,1516,1961,872,1611,1753,2160,993,1547,776,2060,707,1566,2143,1941,954,1053,2165,1186,585,1869,840,1830,1658,2044,907,1300,1452,2276,2219,1980,2247,1766,1257,2113,1485,1749,1504,1670,1008,595,859,600,1955,1585,1094,1140,1881,1272,612,1240,991,1617,2088,1459,931,1949,1817,1781,1189,2071,1157,2078,1913,2310,903,524,581,1654,1412,2325,759,2110,1010,1390,2226,1453,1326,1253,2167,2283,1062,1854,995,1341,896,2290,2251,1861,1491,568,2066,1193,1077,2120,2095,2019,2294,1309,1133,999,1642,1512,1957,2255,2233,1395,1148,1757,1480,603,564,1859,918,1495,2091,928,1410,767,2223,1473,1346,2063,1977,1827,1152,1532,1378,2265,1597,871,1500,1923,723,1399,2270,1621,1606,1737,1184,1463,2297,639,1069,2321,1367,940,1917,676,1449,1812]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ITP399_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08  % 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
% 0.14/0.40  % Computer : n001.cluster.edu
% 0.14/0.40  % Model    : x86_64 x86_64
% 0.14/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40  % Memory   : 8046.5625MB
% 0.14/0.40  % OS       : Linux 6.8.0-71-generic
% 0.14/0.40  % CPULimit : 300
% 0.14/0.40  % WCLimit  : 300
% 0.14/0.40  % DateTime : Fri Sep 25 19:16:25 UTC 2026
% 0.14/0.41  % CPUTime  : 
% 0.14/0.41  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
% 0.88/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 4.30/1.80  % [INFO] 	 Parsing done (814ms). 
% 4.30/1.82  % [INFO] 	 Running in sequential loop mode. 
% 4.96/2.21  % [INFO] 	 eprover registered as external prover. 
% 4.96/2.22  % [INFO] 	 Scanning for conjecture ... 
% 5.68/2.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 639 axioms. Running axiom selection ... 
% 7.85/3.05  % [INFO] 	 Axiom selection finished. Selected 520 axioms (removed 119 axioms). 
% 9.11/3.46  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 9.11/3.50  % [INFO] 	 Type checking passed. 
% 9.52/3.50  % [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 ... 
% 23.40/7.46  % External prover 'e' found a proof!
% 23.40/7.46  % [INFO] 	 Killing All external provers ... 
% 23.40/7.46  % Time passed: 6919ms (effective reasoning time: 5636ms)
% 23.40/7.46  % 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)>
% 23.40/7.47  % Axioms used in derivation (520): axiom326, axiom32, axiom635, axiom260, axiom280, axiom127, axiom626, axiom315, axiom546, axiom116, axiom527, axiom611, axiom452, axiom491, axiom28, axiom76, axiom273, axiom61, axiom100, axiom6, axiom503, axiom553, axiom54, axiom549, axiom25, axiom369, axiom14, axiom474, axiom333, axiom221, axiom295, axiom485, axiom214, axiom516, axiom307, axiom496, axiom311, axiom423, axiom622, axiom65, axiom36, axiom203, axiom531, axiom291, axiom441, axiom507, axiom430, axiom600, axiom50, axiom158, axiom131, axiom10, axiom386, axiom580, axiom119, axiom344, axiom138, axiom508, axiom392, axiom597, axiom337, axiom407, axiom460, axiom17, axiom397, axiom619, axiom587, axiom477, axiom467, axiom257, axiom579, axiom22, axiom147, axiom524, axiom434, axiom341, axiom504, axiom173, axiom638, axiom348, axiom184, axiom376, axiom172, axiom535, axiom266, axiom445, axiom42, axiom513, axiom239, axiom300, axiom350, axiom372, axiom195, axiom162, axiom583, axiom358, axiom161, axiom632, axiom123, axiom246, axiom383, axiom605, axiom2, axiom134, axiom33, axiom150, axiom104, axiom456, axiom87, axiom572, axiom11, axiom235, axiom98, axiom484, axiom304, axiom225, axiom473, axiom365, axiom499, axiom330, axiom251, axiom64, axiom591, axiom578, axiom530, axiom636, axiom294, axiom126, axiom314, axiom427, axiom59, axiom247, axiom48, axiom217, axiom343, axiom27, axiom352, axiom179, axiom363, axiom437, axiom601, axiom236, axiom151, axiom115, axiom623, axiom94, axiom83, axiom336, axiom308, axiom78, axiom24, axiom278, axiom272, axiom228, axiom405, axiom5, axiom101, axiom455, axiom475, axiom121, axiom132, axiom574, axiom56, axiom466, axiom137, axiom563, axiom240, axiom206, axiom318, axiom60, axiom631, axiom13, axiom53, axiom433, axiom143, axiom359, axiom416, axiom489, axiom108, axiom395, axiom387, axiom16, axiom459, axiom400, axiom517, axiom258, axiom75, axiom448, axiom552, axiom385, axiom157, axiom90, axiom168, axiom332, axiom9, axiom303, axiom612, axiom366, axiom207, axiom494, axiom133, axiom80, axiom252, axiom567, axiom355, axiom422, axiom185, axiom472, axiom146, axiom97, axiom360, axiom391, axiom604, axiom263, axiom382, axiom254, axiom444, axiom82, axiom45, axiom483, axiom174, axiom556, axiom347, axiom180, axiom67, axiom213, axiom534, axiom450, axiom196, axiom523, axiom232, axiom243, axiom426, axiom72, axiom461, axiom463, axiom310, axiom449, axiom438, axiom267, axiom163, axiom89, axiom512, axiom224, axiom122, axiom38, axiom419, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom111, axiom120, axiom297, axiom52, axiom156, axiom511, axiom279, axiom223, axiom12, axiom390, axiom37, axiom331, axiom212, axiom602, axiom432, axiom501, axiom342, axiom381, axiom193, axiom34, axiom630, axiom152, axiom425, axiom167, axiom607, axiom454, axiom205, axiom364, axiom628, axiom79, axiom190, axiom573, axiom443, axiom41, axiom96, axiom149, axiom189, axiom375, axiom23, axiom560, axiom93, axiom227, axiom182, axiom476, axiom216, axiom320, axiom409, axiom286, axiom313, axiom118, axiom275, axiom63, axiom19, axiom458, axiom613, axiom102, axiom8, axiom178, axiom370, axiom428, axiom479, axiom259, axiom74, axiom276, axiom451, axiom570, axiom85, axiom145, axiom509, axiom233, axiom220, axiom302, axiom367, axiom57, axiom599, axiom506, axiom186, axiom497, axiom164, axiom153, axiom440, axiom581, axiom282, axiom244, axiom271, axiom594, axiom287, axiom4, axiom255, axiom136, axiom106, axiom71, axiom462, axiom15, axiom129, axiom181, axiom403, axiom522, axiom436, axiom482, axiom486, axiom346, axiom262, axiom68, axiom335, axiom268, axiom293, axiom175, axiom237, axiom26, axiom493, axiom356, axiom298, axiom46, axiom439, axiom634, axiom110, axiom125, axiom603, axiom49, axiom219, axiom197, axiom248, axiom421, axiom590, axiom547, axiom226, axiom18, axiom338, axiom242, axiom88, axiom510, axiom166, axiom526, axiom559, axiom442, axiom327, axiom92, axiom399, axiom66, axiom345, axiom464, axiom215, axiom204, axiom141, axiom357, axiom274, axiom117, axiom393, axiom44, axiom222, axiom446, axiom84, axiom554, axiom269, axiom453, axiom81, axiom502, axiom103, axiom7, axiom515, axiom231, axiom306, axiom155, axiom495, axiom253, axiom249, axiom368, axiom565, axiom99, axiom148, axiom128, axiom316, axiom285, axiom20, axiom183, axiom301, axiom361, axiom429, axiom532, axiom177, axiom380, axiom188, axiom431, axiom208, axiom159, axiom487, axiom609, axiom519, axiom402, axiom384, axiom551, axiom73, axiom339, axiom154, axiom40, axiom265, axiom165, axiom518, axiom270, axiom113, axiom176, axiom171, axiom3, axiom305, axiom187, axiom245, axiom288, axiom69, axiom317, axiom135, axiom277, axiom198, axiom529, axiom144, axiom55, axiom584, axiom281, axiom424, axiom633, axiom536, axiom373, axiom435, axiom312, axiom95, axiom70, axiom238, axiom465, axiom299, axiom351, axiom505, axiom261, axiom413, axiom256, axiom334, axiom388, axiom160, axiom582, axiom514, axiom481, axiom606, axiom77, axiom637, axiom420, axiom62, axiom498, axiom209, axiom21, axiom139, axiom200, axiom250, axiom292, axiom525, axiom234, axiom362, axiom51, axiom309, axiom610, axiom470, axiom468, axiom492, axiom328, axiom140, axiom58, axiom624, axiom340, axiom194
% 23.40/7.47  % No. of inferences in proof: 1044
% 23.40/7.47  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6919 ms resp. 5636 ms w/o parsing
% 25.59/7.93  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.59/7.94  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------