%------------------------------------------------------------------------------
% File     : ITP383_10 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Interactive Theorem Proving
% Problem  : SMT-LIB Registers Laws 00281_010592
% Version  : ITP383_1 with the conjecture removed
% English  :

% Refs     : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [TPTP]
% Names    : 

% Status   : Satisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    : 1626 ( 247 unt; 931 typ;   0 def)
%            Number of atoms       : 1511 ( 672 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  816 (   0   ~;   0   |; 332   &)
%                                         (  49 <=>; 435  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :  255 ( 254 usr)
%            Number of type conns  : 1197 ( 640   >; 557   *;   0   +;   0  <<)
%            Number of predicates  :  181 ( 178 usr;   2 prp; 0-4 aty)
%            Number of functors    :  499 ( 499 usr;  37 con; 0-3 aty)
%            Number of variables   : 2331 (2331   !;   0   ?;2331   :)
% SPC      : TF0_SAT_EQU_NAR

% Comments : Translated from SMT format using smttotptp 0.9.10. See
%            https://bitbucket.org/peba123/smttotptp/src/master/
%          : SMT-LIB AUFLIA logic
%------------------------------------------------------------------------------
%% Types:
tff('C_a_prod_update_a_b_prod_update_fun$',type,
    'C_a_prod_update_a_b_prod_update_fun$': $tType ).

tff('C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$': $tType ).

tff('D_c_d_prod_prod_update_b_b_prod_update_fun$',type,
    'D_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

tff('C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$',type,
    'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('C_c_prod_update_b_b_prod_update_fun$',type,
    'C_c_prod_update_b_b_prod_update_fun$': $tType ).

tff('A_update_set$',type,
    'A_update_set$': $tType ).

tff('C_d_prod_d_prod_update_b_b_prod_update_fun$',type,
    'C_d_prod_d_prod_update_b_b_prod_update_fun$': $tType ).

tff('D_b_prod_update$',type,
    'D_b_prod_update$': $tType ).

tff('C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$',type,
    'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_set$',type,
    'C_d_prod_update_a_update_fun_set$': $tType ).

tff('B_update_b_update_prod$',type,
    'B_update_b_update_prod$': $tType ).

tff('C_d_prod_update_b_b_prod_update_fun$',type,
    'C_d_prod_update_b_b_prod_update_fun$': $tType ).

tff('A_a_prod_update$',type,
    'A_a_prod_update$': $tType ).

tff('C_d_prod_update_c_d_prod_update_prod$',type,
    'C_d_prod_update_c_d_prod_update_prod$': $tType ).

tff('A_update_d_d_prod_update_fun$',type,
    'A_update_d_d_prod_update_fun$': $tType ).

tff('C_d_prod_update_b_update_fun$',type,
    'C_d_prod_update_b_update_fun$': $tType ).

tff('A_update_c_d_prod_update_bool_fun_fun$',type,
    'A_update_c_d_prod_update_bool_fun_fun$': $tType ).

tff('B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$',type,
    'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

tff('C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('C_update_d_a_prod_update_fun$',type,
    'C_update_d_a_prod_update_fun$': $tType ).

tff('B_itself$',type,
    'B_itself$': $tType ).

tff('D_c_prod_update_b_b_prod_update_fun$',type,
    'D_c_prod_update_b_b_prod_update_fun$': $tType ).

tff('B_update_c_update_fun_c_update_b_update_fun_fun$',type,
    'B_update_c_update_fun_c_update_b_update_fun_fun$': $tType ).

tff('C_a_prod_update$',type,
    'C_a_prod_update$': $tType ).

tff('D_update_a_update_fun_bool_fun$',type,
    'D_update_a_update_fun_bool_fun$': $tType ).

tff('A_update$',type,
    'A_update$': $tType ).

tff('C_update_d_update_bool_fun_fun$',type,
    'C_update_d_update_bool_fun_fun$': $tType ).

tff('C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$',type,
    'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

tff('D_update_d_update_prod$',type,
    'D_update_d_update_prod$': $tType ).

tff('B_b_prod_update$',type,
    'B_b_prod_update$': $tType ).

tff('C_d_prod_update_a_b_prod_update_fun$',type,
    'C_d_prod_update_a_b_prod_update_fun$': $tType ).

tff('B_update_a_update_fun$',type,
    'B_update_a_update_fun$': $tType ).

tff('C_update_c_update_prod_b_update_b_update_prod_fun$',type,
    'C_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_a_prod_update_a_a_prod_update_fun$',type,
    'A_a_prod_update_a_a_prod_update_fun$': $tType ).

tff('A_update_d_update_bool_fun_fun$',type,
    'A_update_d_update_bool_fun_fun$': $tType ).

tff('C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$',type,
    'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('D_d_prod_update_b_update_fun$',type,
    'D_d_prod_update_b_update_fun$': $tType ).

tff('D_update_c_update_prod_a_update_a_update_prod_fun$',type,
    'D_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('A_update_b_a_prod_update_fun$',type,
    'A_update_b_a_prod_update_fun$': $tType ).

tff('A_a_prod_update_b_update_fun$',type,
    'A_a_prod_update_b_update_fun$': $tType ).

tff('B_update_b_d_prod_update_fun$',type,
    'B_update_b_d_prod_update_fun$': $tType ).

tff('C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$',type,
    'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_c_prod_update_a_update_fun$',type,
    'C_c_prod_update_a_update_fun$': $tType ).

tff('C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$',type,
    'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

tff('C_a_prod_update_b_b_prod_update_fun$',type,
    'C_a_prod_update_b_b_prod_update_fun$': $tType ).

tff('A_d_prod_update_a_update_fun$',type,
    'A_d_prod_update_a_update_fun$': $tType ).

tff('C_update_a_update_fun_set$',type,
    'C_update_a_update_fun_set$': $tType ).

tff('C_update_a_update_fun_c_update_b_update_fun_fun$',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun$': $tType ).

tff('A_c_prod_update$',type,
    'A_c_prod_update$': $tType ).

tff('C_d_prod_update_c_d_prod_update_fun$',type,
    'C_d_prod_update_c_d_prod_update_fun$': $tType ).

tff('C_update_d_update_prod_b_update_b_update_prod_fun$',type,
    'C_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('B_update_c_update_bool_fun_fun$',type,
    'B_update_c_update_bool_fun_fun$': $tType ).

tff('A_c_prod_update_b_b_prod_update_fun$',type,
    'A_c_prod_update_b_b_prod_update_fun$': $tType ).

tff('C_update_b_update_b_update_prod_fun$',type,
    'C_update_b_update_b_update_prod_fun$': $tType ).

tff('C_update_b_a_prod_update_fun$',type,
    'C_update_b_a_prod_update_fun$': $tType ).

tff('A_update_a_update_fun_c_update_b_update_fun_fun$',type,
    'A_update_a_update_fun_c_update_b_update_fun_fun$': $tType ).

tff('D_update_a_b_prod_update_fun$',type,
    'D_update_a_b_prod_update_fun$': $tType ).

tff('D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$',type,
    'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('A_update_a_update_bool_fun_fun$',type,
    'A_update_a_update_bool_fun_fun$': $tType ).

tff('C_a_prod_update_b_update_fun$',type,
    'C_a_prod_update_b_update_fun$': $tType ).

tff('D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$',type,
    'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_d_prod_update_b_a_prod_update_fun$',type,
    'A_d_prod_update_b_a_prod_update_fun$': $tType ).

tff('D_update_set$',type,
    'D_update_set$': $tType ).

tff('D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('D_c_prod_update_a_b_prod_update_fun$',type,
    'D_c_prod_update_a_b_prod_update_fun$': $tType ).

tff('A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$',type,
    'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$': $tType ).

tff('D_d_prod_update_a_b_prod_update_fun$',type,
    'D_d_prod_update_a_b_prod_update_fun$': $tType ).

tff('C_b_prod_update$',type,
    'C_b_prod_update$': $tType ).

tff('C_d_prod_update_c_update_prod$',type,
    'C_d_prod_update_c_update_prod$': $tType ).

tff('D_update_bool_fun$',type,
    'D_update_bool_fun$': $tType ).

tff('D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

tff('A_update_a_c_prod_update_fun$',type,
    'A_update_a_c_prod_update_fun$': $tType ).

tff('B_update_d_update_fun$',type,
    'B_update_d_update_fun$': $tType ).

tff('D_update_d_update_fun$',type,
    'D_update_d_update_fun$': $tType ).

tff('C_c_prod_update_a_b_prod_update_fun$',type,
    'C_c_prod_update_a_b_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('A_itself$',type,
    'A_itself$': $tType ).

tff('D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('A_update_a_update_fun$',type,
    'A_update_a_update_fun$': $tType ).

tff('B_d_prod_update$',type,
    'B_d_prod_update$': $tType ).

tff('A_update_b_update_fun$',type,
    'A_update_b_update_fun$': $tType ).

tff('C_d_prod_c_prod_update_b_b_prod_update_fun$',type,
    'C_d_prod_c_prod_update_b_b_prod_update_fun$': $tType ).

tff('D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$',type,
    'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

tff('D_update_c_update_fun$',type,
    'D_update_c_update_fun$': $tType ).

tff('C_update_d_update_prod$',type,
    'C_update_d_update_prod$': $tType ).

tff('C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$',type,
    'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_update_b_d_prod_update_fun$',type,
    'A_update_b_d_prod_update_fun$': $tType ).

tff('C_c_prod_update$',type,
    'C_c_prod_update$': $tType ).

tff('C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$',type,
    'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

tff('A_a_prod_update_c_c_prod_update_fun$',type,
    'A_a_prod_update_c_c_prod_update_fun$': $tType ).

tff('C_d_prod_update_c_update_bool_fun_fun$',type,
    'C_d_prod_update_c_update_bool_fun_fun$': $tType ).

tff('D_update_c_d_prod_update_prod$',type,
    'D_update_c_d_prod_update_prod$': $tType ).

tff('D_update_a_update_fun$',type,
    'D_update_a_update_fun$': $tType ).

tff('B_update_a_b_prod_update_fun$',type,
    'B_update_a_b_prod_update_fun$': $tType ).

tff('C_d_prod_d_prod_update_a_a_prod_update_fun$',type,
    'C_d_prod_d_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_c_d_prod_update_bool_fun_fun$',type,
    'C_d_prod_update_c_d_prod_update_bool_fun_fun$': $tType ).

tff('B_update_d_update_fun_c_update_b_update_fun_fun$',type,
    'B_update_d_update_fun_c_update_b_update_fun_fun$': $tType ).

tff('A_update_b_update_b_update_prod_fun$',type,
    'A_update_b_update_b_update_prod_fun$': $tType ).

tff('D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$',type,
    'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

tff('C_update_c_d_prod_update_fun$',type,
    'C_update_c_d_prod_update_fun$': $tType ).

tff('B_update_c_update_fun$',type,
    'B_update_c_update_fun$': $tType ).

tff('D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

tff('D_c_prod_update_b_update_fun$',type,
    'D_c_prod_update_b_update_fun$': $tType ).

tff('C_d_prod_update_b_update_bool_fun_fun$',type,
    'C_d_prod_update_b_update_bool_fun_fun$': $tType ).

tff('B_a_prod_update_b_update_fun$',type,
    'B_a_prod_update_b_update_fun$': $tType ).

tff('C_update_b_update_fun$',type,
    'C_update_b_update_fun$': $tType ).

tff('C_update_bool_fun$',type,
    'C_update_bool_fun$': $tType ).

tff('C_update$',type,
    'C_update$': $tType ).

tff('A_b_prod_update_b_update_fun$',type,
    'A_b_prod_update_b_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

tff('C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

tff('A_d_prod_update_b_update_fun$',type,
    'A_d_prod_update_b_update_fun$': $tType ).

tff('D_d_prod_update_b_b_prod_update_fun$',type,
    'D_d_prod_update_b_b_prod_update_fun$': $tType ).

tff('D_update_a_update_bool_fun_fun$',type,
    'D_update_a_update_bool_fun_fun$': $tType ).

tff('B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$',type,
    'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

tff('A_d_prod_update$',type,
    'A_d_prod_update$': $tType ).

tff('C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

tff('C_update_c_update_prod_a_update_a_update_prod_fun$',type,
    'C_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('C_update_d_update_prod_a_update_a_update_prod_fun$',type,
    'C_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('D_update_c_update_prod$',type,
    'D_update_c_update_prod$': $tType ).

tff('B_update_d_update_fun_d_update_b_update_fun_fun$',type,
    'B_update_d_update_fun_d_update_b_update_fun_fun$': $tType ).

tff('A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$',type,
    'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$': $tType ).

tff('D_update_c_d_prod_update_bool_fun_fun$',type,
    'D_update_c_d_prod_update_bool_fun_fun$': $tType ).

tff('C_c_prod_update_b_update_fun$',type,
    'C_c_prod_update_b_update_fun$': $tType ).

tff('D_c_prod_update_a_a_prod_update_fun$',type,
    'D_c_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

tff('D_c_d_prod_prod_update_a_a_prod_update_fun$',type,
    'D_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_b_update_b_update_prod_fun$',type,
    'C_d_prod_update_b_update_b_update_prod_fun$': $tType ).

tff('A_update_a_d_prod_update_fun$',type,
    'A_update_a_d_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_bool_fun_fun$',type,
    'C_d_prod_update_a_update_bool_fun_fun$': $tType ).

tff('D_update_b_update_fun$',type,
    'D_update_b_update_fun$': $tType ).

tff('A_update_a_update_prod_b_update_b_update_prod_fun$',type,
    'A_update_a_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_update_c_update_fun$',type,
    'A_update_c_update_fun$': $tType ).

tff('D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$': $tType ).

tff('B_update_c_d_prod_update_fun$',type,
    'B_update_c_d_prod_update_fun$': $tType ).

tff('A_update_c_d_prod_update_fun$',type,
    'A_update_c_d_prod_update_fun$': $tType ).

tff('C_d_prod_c_prod_update_a_a_prod_update_fun$',type,
    'C_d_prod_c_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$',type,
    'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('C_d_prod_update_d_update_bool_fun_fun$',type,
    'C_d_prod_update_d_update_bool_fun_fun$': $tType ).

tff('D_update_d_b_prod_update_fun$',type,
    'D_update_d_b_prod_update_fun$': $tType ).

tff('A_c_prod_update_b_a_prod_update_fun$',type,
    'A_c_prod_update_b_a_prod_update_fun$': $tType ).

tff('A_a_prod_update_b_b_prod_update_fun$',type,
    'A_a_prod_update_b_b_prod_update_fun$': $tType ).

tff('A_update_a_b_prod_update_fun$',type,
    'A_update_a_b_prod_update_fun$': $tType ).

tff('A_b_prod_update$',type,
    'A_b_prod_update$': $tType ).

tff('B_update_set_b_update_fun$',type,
    'B_update_set_b_update_fun$': $tType ).

tff('B_update_b_a_prod_update_fun$',type,
    'B_update_b_a_prod_update_fun$': $tType ).

tff('D_update_a_update_a_update_prod_fun$',type,
    'D_update_a_update_a_update_prod_fun$': $tType ).

tff('C_update_d_b_prod_update_fun$',type,
    'C_update_d_b_prod_update_fun$': $tType ).

tff('B_update_d_a_prod_update_fun$',type,
    'B_update_d_a_prod_update_fun$': $tType ).

tff('A_update_d_a_prod_update_fun$',type,
    'A_update_d_a_prod_update_fun$': $tType ).

tff('D_update$',type,
    'D_update$': $tType ).

tff('A_c_prod_update_b_update_fun$',type,
    'A_c_prod_update_b_update_fun$': $tType ).

tff('C_update_c_update_prod$',type,
    'C_update_c_update_prod$': $tType ).

tff('B_update_b_update_fun$',type,
    'B_update_b_update_fun$': $tType ).

tff('C_update_a_a_prod_update_fun$',type,
    'C_update_a_a_prod_update_fun$': $tType ).

tff('C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

tff('C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$',type,
    'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('B_update_c_update_fun_a_update_a_update_fun_fun$',type,
    'B_update_c_update_fun_a_update_a_update_fun_fun$': $tType ).

tff('C_update_c_d_prod_update_prod$',type,
    'C_update_c_d_prod_update_prod$': $tType ).

tff('A_update_d_b_prod_update_fun$',type,
    'A_update_d_b_prod_update_fun$': $tType ).

tff('C_update_a_b_prod_update_fun$',type,
    'C_update_a_b_prod_update_fun$': $tType ).

tff('B_update_c_d_prod_update_bool_fun_fun$',type,
    'B_update_c_d_prod_update_bool_fun_fun$': $tType ).

tff('D_update_d_update_prod_b_update_b_update_prod_fun$',type,
    'D_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('C_d_prod_update_a_update_fun$',type,
    'C_d_prod_update_a_update_fun$': $tType ).

tff('C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$',type,
    'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$',type,
    'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

tff('A_b_prod_update_a_update_fun$',type,
    'A_b_prod_update_a_update_fun$': $tType ).

tff('D_a_prod_update_a_b_prod_update_fun$',type,
    'D_a_prod_update_a_b_prod_update_fun$': $tType ).

tff('C_c_prod_update_a_a_prod_update_fun$',type,
    'C_c_prod_update_a_a_prod_update_fun$': $tType ).

tff('B_update_set$',type,
    'B_update_set$': $tType ).

tff('C_update_b_b_prod_update_fun$',type,
    'C_update_b_b_prod_update_fun$': $tType ).

tff('B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$',type,
    'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$': $tType ).

tff('D_a_prod_update$',type,
    'D_a_prod_update$': $tType ).

tff('C_update_b_update_bool_fun_fun$',type,
    'C_update_b_update_bool_fun_fun$': $tType ).

tff('C_c_d_prod_prod_update_a_a_prod_update_fun$',type,
    'C_c_d_prod_prod_update_a_a_prod_update_fun$': $tType ).

tff('B_update_d_b_prod_update_fun$',type,
    'B_update_d_b_prod_update_fun$': $tType ).

tff('C_update_a_update_fun$',type,
    'C_update_a_update_fun$': $tType ).

tff('B_update_b_b_prod_update_fun$',type,
    'B_update_b_b_prod_update_fun$': $tType ).

tff('A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$',type,
    'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$': $tType ).

tff('D_update_b_update_bool_fun_fun$',type,
    'D_update_b_update_bool_fun_fun$': $tType ).

tff('B_update$',type,
    'B_update$': $tType ).

tff('C_d_prod_update_c_update_fun$',type,
    'C_d_prod_update_c_update_fun$': $tType ).

tff('C_d_prod_update_a_a_prod_update_fun$',type,
    'C_d_prod_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

tff('C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$',type,
    'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('D_update_a_update_fun_set$',type,
    'D_update_a_update_fun_set$': $tType ).

tff('C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$',type,
    'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$': $tType ).

tff('B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',type,
    'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$': $tType ).

tff('C_update_a_update_bool_fun_fun$',type,
    'C_update_a_update_bool_fun_fun$': $tType ).

tff('C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

tff('C_update_b_d_prod_update_fun$',type,
    'C_update_b_d_prod_update_fun$': $tType ).

tff('D_c_prod_update$',type,
    'D_c_prod_update$': $tType ).

tff('C_c_prod_update_b_a_prod_update_fun$',type,
    'C_c_prod_update_b_a_prod_update_fun$': $tType ).

tff('D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$',type,
    'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$': $tType ).

tff('A_update_d_c_prod_update_fun$',type,
    'A_update_d_c_prod_update_fun$': $tType ).

tff('D_update_d_update_bool_fun_fun$',type,
    'D_update_d_update_bool_fun_fun$': $tType ).

tff('A_d_prod_update_b_b_prod_update_fun$',type,
    'A_d_prod_update_b_b_prod_update_fun$': $tType ).

tff('C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$': $tType ).

tff('D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('D_update_c_update_bool_fun_fun$',type,
    'D_update_c_update_bool_fun_fun$': $tType ).

tff('B_update_d_update_fun_a_update_a_update_fun_fun$',type,
    'B_update_d_update_fun_a_update_a_update_fun_fun$': $tType ).

tff('B_update_c_update_fun_d_update_b_update_fun_fun$',type,
    'B_update_c_update_fun_d_update_b_update_fun_fun$': $tType ).

tff('C_update_c_update_fun$',type,
    'C_update_c_update_fun$': $tType ).

tff('A_update_b_update_bool_fun_fun$',type,
    'A_update_b_update_bool_fun_fun$': $tType ).

tff('D_a_prod_update_b_update_fun$',type,
    'D_a_prod_update_b_update_fun$': $tType ).

tff('C_update_a_c_prod_update_fun$',type,
    'C_update_a_c_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_bool_fun$',type,
    'C_d_prod_update_a_update_fun_bool_fun$': $tType ).

tff('C_update_c_d_prod_update_bool_fun_fun$',type,
    'C_update_c_d_prod_update_bool_fun_fun$': $tType ).

tff('C_d_prod_update$',type,
    'C_d_prod_update$': $tType ).

tff('D_update_b_b_prod_update_fun$',type,
    'D_update_b_b_prod_update_fun$': $tType ).

tff('C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$',type,
    'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$': $tType ).

tff('D_update_a_d_prod_update_fun$',type,
    'D_update_a_d_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_a_update_prod_fun$',type,
    'C_d_prod_update_a_update_a_update_prod_fun$': $tType ).

tff('D_update_b_update_b_update_prod_fun$',type,
    'D_update_b_update_b_update_prod_fun$': $tType ).

tff('D_update_a_update_fun_d_update_b_update_fun_fun$',type,
    'D_update_a_update_fun_d_update_b_update_fun_fun$': $tType ).

tff('A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$',type,
    'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$': $tType ).

tff('B_update_a_update_bool_fun_fun$',type,
    'B_update_a_update_bool_fun_fun$': $tType ).

tff('C_c_d_prod_prod_update_b_b_prod_update_fun$',type,
    'C_c_d_prod_prod_update_b_b_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('B_update_bool_fun$',type,
    'B_update_bool_fun$': $tType ).

tff('B_update_d_update_bool_fun_fun$',type,
    'B_update_d_update_bool_fun_fun$': $tType ).

tff('B_update_b_update_bool_fun_fun$',type,
    'B_update_b_update_bool_fun_fun$': $tType ).

tff('A_update_a_update_prod$',type,
    'A_update_a_update_prod$': $tType ).

tff('D_d_prod_update_a_a_prod_update_fun$',type,
    'D_d_prod_update_a_a_prod_update_fun$': $tType ).

tff('A_update_b_update_fun_bool_fun$',type,
    'A_update_b_update_fun_bool_fun$': $tType ).

tff('C_update_a_update_fun_bool_fun$',type,
    'C_update_a_update_fun_bool_fun$': $tType ).

tff('D_update_d_update_prod_a_update_a_update_prod_fun$',type,
    'D_update_d_update_prod_a_update_a_update_prod_fun$': $tType ).

tff('A_update_c_update_bool_fun_fun$',type,
    'A_update_c_update_bool_fun_fun$': $tType ).

tff('A_update_a_update_fun_d_update_b_update_fun_fun$',type,
    'A_update_a_update_fun_d_update_b_update_fun_fun$': $tType ).

tff('C_update_d_update_fun$',type,
    'C_update_d_update_fun$': $tType ).

tff('C_d_prod_update_d_update_prod$',type,
    'C_d_prod_update_d_update_prod$': $tType ).

tff('C_update_c_update_bool_fun_fun$',type,
    'C_update_c_update_bool_fun_fun$': $tType ).

tff('B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$',type,
    'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$': $tType ).

tff('A_update_bool_fun$',type,
    'A_update_bool_fun$': $tType ).

tff('D_update_b_d_prod_update_fun$',type,
    'D_update_b_d_prod_update_fun$': $tType ).

tff('B_c_prod_update$',type,
    'B_c_prod_update$': $tType ).

tff('C_update_a_update_a_update_prod_fun$',type,
    'C_update_a_update_a_update_prod_fun$': $tType ).

tff('A_update_d_update_fun$',type,
    'A_update_d_update_fun$': $tType ).

tff('D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$',type,
    'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$': $tType ).

tff('D_d_prod_update$',type,
    'D_d_prod_update$': $tType ).

tff('C_d_prod_update_bool_fun$',type,
    'C_d_prod_update_bool_fun$': $tType ).

tff('B_a_prod_update$',type,
    'B_a_prod_update$': $tType ).

tff('A_update_b_b_prod_update_fun$',type,
    'A_update_b_b_prod_update_fun$': $tType ).

tff('D_update_b_a_prod_update_fun$',type,
    'D_update_b_a_prod_update_fun$': $tType ).

tff('C_update_set$',type,
    'C_update_set$': $tType ).

tff('C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$': $tType ).

tff('D_update_c_update_prod_b_update_b_update_prod_fun$',type,
    'D_update_c_update_prod_b_update_b_update_prod_fun$': $tType ).

tff('A_update_a_a_prod_update_fun$',type,
    'A_update_a_a_prod_update_fun$': $tType ).

tff('C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$',type,
    'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$': $tType ).

tff('B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$',type,
    'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$': $tType ).

tff('C_d_prod_update_set$',type,
    'C_d_prod_update_set$': $tType ).

%% Declarations:
tff('comp$s',type,
    'comp$s': ( 'A_b_prod_update_b_update_fun$' * 'C_a_prod_update_a_b_prod_update_fun$' ) > 'C_a_prod_update_b_update_fun$' ).

tff('uu$',type,
    'uu$': 'C_d_prod_update_set$' > 'C_d_prod_update_bool_fun$' ).

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

tff('fun_app$dk',type,
    'fun_app$dk': ( 'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_c_d_prod_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('fun_app$cx',type,
    'fun_app$cx': ( 'C_update_d_update_fun$' * 'C_update$' ) > 'D_update$' ).

tff('type_definition$j',type,
    'type_definition$j': ( 'B_update_d_update_fun$' * 'D_update_b_update_fun$' * 'D_update_set$' ) > $o ).

tff('quotient$a',type,
    'quotient$a': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_c_update_fun$' * 'C_update_a_update_fun$' * 'A_update_c_update_bool_fun_fun$' ) > $o ).

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

tff('rel_fun$f',type,
    'rel_fun$f': ( 'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' * 'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' ).

tff('register$',type,
    'register$': 'C_update_a_update_fun_bool_fun$' ).

tff('uun$',type,
    'uun$': 'A_update_b_update_fun$' > 'A_update_b_b_prod_update_fun$' ).

tff('comp$as',type,
    'comp$as': ( 'C_update_a_update_fun$' * 'D_update_c_update_fun$' ) > 'D_update_a_update_fun$' ).

tff('comp_update$i',type,
    'comp_update$i': ( 'D_d_prod_update$' * 'D_d_prod_update$' ) > 'D_d_prod_update$' ).

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

tff('rel_fun$ae',type,
    'rel_fun$ae': ( 'D_update_c_d_prod_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' ).

tff('fun_app$g',type,
    'fun_app$g': ( 'B_update_a_b_prod_update_fun$' * 'B_update$' ) > 'A_b_prod_update$' ).

tff('register_tensor$p',type,
    'register_tensor$p': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_a_prod_update_b_b_prod_update_fun$' ).

tff('pred_fun$',type,
    'pred_fun$': ( 'C_update_bool_fun$' * 'B_update_bool_fun$' * 'C_update_b_update_fun$' ) > $o ).

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

tff('fun_app$dt',type,
    'fun_app$dt': ( 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' * 'A_update_a_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('member$d',type,
    'member$d': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update_a_update_fun_set$' ) > $o ).

tff('relcompp$f',type,
    'relcompp$f': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_c_update_bool_fun_fun$' ) > 'A_update_c_update_bool_fun_fun$' ).

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

tff('comp$cc',type,
    'comp$cc': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'D_update_d_update_prod_a_update_a_update_prod_fun$' ) > 'D_update_d_update_prod_b_update_b_update_prod_fun$' ).

tff('comp$cf',type,
    'comp$cf': ( 'A_update_d_update_fun$' * 'B_update_a_update_fun$' ) > 'B_update_d_update_fun$' ).

tff('rel_fun$v',type,
    'rel_fun$v': ( 'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' * 'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' ).

tff('register_tensor$s',type,
    'register_tensor$s': ( 'C_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'C_d_prod_update_a_a_prod_update_fun$' ).

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

tff('rel_fun$i',type,
    'rel_fun$i': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' ) > $o ).

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

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

tff('separating$c',type,
    'separating$c': ( 'B_itself$' * 'B_update_set$' ) > $o ).

tff('fun_app$cw',type,
    'fun_app$cw': ( 'B_update_c_update_fun_c_update_b_update_fun_fun$' * 'B_update_c_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('comp$be',type,
    'comp$be': ( 'C_update_b_update_b_update_prod_fun$' * 'C_update_c_update_fun$' ) > 'C_update_b_update_b_update_prod_fun$' ).

tff('uvt$',type,
    'uvt$': 'C_update_bool_fun$' ).

tff('relcompp$h',type,
    'relcompp$h': ( 'C_d_prod_update_a_update_bool_fun_fun$' * 'A_update_c_d_prod_update_bool_fun_fun$' ) > 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' ).

tff('compatible$j',type,
    'compatible$j': ( 'B_update_b_update_fun$' * 'A_update_b_update_fun$' ) > $o ).

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

tff('id$',type,
    'id$': 'B_update_b_update_fun$' ).

tff('comp$h',type,
    'comp$h': ( 'D_update_b_update_fun$' * 'A_update_d_update_fun$' ) > 'A_update_b_update_fun$' ).

tff('register_pair$q',type,
    'register_pair$q': ( 'A_update_d_update_fun$' * 'D_update_d_update_fun$' * 'A_d_prod_update$' ) > 'D_update$' ).

tff('fun_app$an',type,
    'fun_app$an': ( 'B_update_bool_fun$' * 'B_update$' ) > $o ).

tff('register_pair$w',type,
    'register_pair$w': ( 'A_update_b_a_prod_update_fun$' * 'C_update_b_a_prod_update_fun$' ) > 'A_c_prod_update_b_a_prod_update_fun$' ).

tff('comp$av',type,
    'comp$av': ( 'A_update_a_update_fun_d_update_b_update_fun_fun$' * 'B_update_c_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_update_fun_d_update_b_update_fun_fun$' ).

tff('tensor_update$n',type,
    'tensor_update$n': ( 'B_update$' * 'C_update$' ) > 'B_c_prod_update$' ).

tff('fun_app$dd',type,
    'fun_app$dd': ( 'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' * 'C_update_c_d_prod_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('register_pair$e',type,
    'register_pair$e': ( 'A_update_b_update_fun$' * 'B_update_b_update_fun$' ) > 'A_b_prod_update_b_update_fun$' ).

tff('map_prod$k',type,
    'map_prod$k': ( 'C_d_prod_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' ).

tff('id_update$c',type,
    'id_update$c': 'B_update$' ).

tff('rel_fun$k',type,
    'rel_fun$k': ( 'C_update_d_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' ).

tff('uuw$',type,
    'uuw$': 'A_update_d_update_fun$' > 'A_update_d_d_prod_update_fun$' ).

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

tff('tensor_update$o',type,
    'tensor_update$o': ( 'C_update$' * 'B_update$' ) > 'C_b_prod_update$' ).

tff('comp$aq',type,
    'comp$aq': ( 'A_update_a_update_fun$' * 'B_update_a_update_fun$' ) > 'B_update_a_update_fun$' ).

tff('tensor_update$h',type,
    'tensor_update$h': ( 'C_update$' * 'D_update$' ) > 'C_d_prod_update$' ).

tff('comp$bi',type,
    'comp$bi': ( 'A_update_b_update_b_update_prod_fun$' * 'A_update_a_update_fun$' ) > 'A_update_b_update_b_update_prod_fun$' ).

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

tff('comp$w',type,
    'comp$w': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_c_d_prod_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('fun_app$ai',type,
    'fun_app$ai': ( 'C_update_bool_fun$' * 'C_update$' ) > $o ).

tff('convol$',type,
    'convol$': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_update_b_update_b_update_prod_fun$' ).

tff('tensor_update$k',type,
    'tensor_update$k': ( 'D_update$' * 'C_update$' ) > 'D_c_prod_update$' ).

tff('fun_app$bn',type,
    'fun_app$bn': ( 'C_a_prod_update_a_b_prod_update_fun$' * 'C_a_prod_update$' ) > 'A_b_prod_update$' ).

tff('type_definition$b',type,
    'type_definition$b': ( 'C_update_c_update_fun$' * 'C_update_c_update_fun$' * 'C_update_set$' ) > $o ).

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

tff('map_fun$d',type,
    'map_fun$d': ( 'C_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ).

tff('fun_app$e',type,
    'fun_app$e': ( 'C_update_a_c_prod_update_fun$' * 'C_update$' ) > 'A_c_prod_update$' ).

tff('register$as',type,
    'register$as': 'C_update_b_b_prod_update_fun$' > $o ).

tff('uvj$',type,
    'uvj$': 'A_update_b_update_fun$' > 'A_update_b_b_prod_update_fun$' ).

tff('fun_app$du',type,
    'fun_app$du': ( 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_c_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

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

tff('register_tensor$y',type,
    'register_tensor$y': ( 'C_d_prod_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_d_prod_c_prod_update_b_b_prod_update_fun$' ).

tff('compatible$n',type,
    'compatible$n': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > $o ).

tff('fun_app$a',type,
    'fun_app$a': ( 'A_update_b_a_prod_update_fun$' * 'A_update$' ) > 'B_a_prod_update$' ).

tff('fun_app$ab',type,
    'fun_app$ab': ( 'A_update_c_d_prod_update_fun$' * 'A_update$' ) > 'C_d_prod_update$' ).

tff('conversep$',type,
    'conversep$': 'B_update_a_update_bool_fun_fun$' > 'A_update_b_update_bool_fun_fun$' ).

tff('fun_app$bp',type,
    'fun_app$bp': ( 'C_c_prod_update_b_a_prod_update_fun$' * 'C_c_prod_update$' ) > 'B_a_prod_update$' ).

tff('fun_app$di',type,
    'fun_app$di': ( 'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_c_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('pred_fun$a',type,
    'pred_fun$a': ( 'C_update_bool_fun$' * 'A_update_bool_fun$' ) > 'C_update_a_update_fun_bool_fun$' ).

tff('collect$c',type,
    'collect$c': 'A_update_bool_fun$' > 'A_update_set$' ).

tff('rel_fun$c',type,
    'rel_fun$c': ( 'C_update_c_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' ).

tff('preregister$j',type,
    'preregister$j': 'C_d_prod_update_a_update_fun_bool_fun$' ).

tff('comp$j',type,
    'comp$j': 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' ).

tff('fun_app$br',type,
    'fun_app$br': ( 'C_a_prod_update_b_b_prod_update_fun$' * 'C_a_prod_update$' ) > 'B_b_prod_update$' ).

tff('uum$',type,
    'uum$': 'C_update_b_update_fun$' > 'C_update_b_b_prod_update_fun$' ).

tff('comp$by',type,
    'comp$by': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ) > 'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

tff('tensor_update$e',type,
    'tensor_update$e': ( 'B_update$' * 'D_update$' ) > 'B_d_prod_update$' ).

tff('fun_app$ad',type,
    'fun_app$ad': ( 'A_update_b_d_prod_update_fun$' * 'A_update$' ) > 'B_d_prod_update$' ).

tff('register_tensor$af',type,
    'register_tensor$af': ( 'A_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'A_d_prod_update_b_b_prod_update_fun$' ).

tff('comp$an',type,
    'comp$an': ( 'D_update_b_update_fun$' * 'C_update_d_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('tensor_update$g',type,
    'tensor_update$g': ( 'D_update$' * 'D_update$' ) > 'D_d_prod_update$' ).

tff('fun_app$db',type,
    'fun_app$db': ( 'C_update_c_update_prod_a_update_a_update_prod_fun$' * 'C_update_c_update_prod$' ) > 'A_update_a_update_prod$' ).

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

tff('comp$ao',type,
    'comp$ao': ( 'D_update_b_update_fun$' * 'D_update_d_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('image$b',type,
    'image$b': ( 'C_update_a_update_fun$' * 'C_update_set$' ) > 'A_update_set$' ).

tff('comp$a',type,
    'comp$a': 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' ).

tff('compatible$x',type,
    'compatible$x': ( 'A_update_d_update_fun$' * 'D_update_d_update_fun$' ) > $o ).

tff('fun_app$cm',type,
    'fun_app$cm': ( 'D_d_prod_update_b_update_fun$' * 'D_d_prod_update$' ) > 'B_update$' ).

tff('fun_app$bm',type,
    'fun_app$bm': ( 'C_c_prod_update_a_b_prod_update_fun$' * 'C_c_prod_update$' ) > 'A_b_prod_update$' ).

tff('rel_fun$g',type,
    'rel_fun$g': ( 'C_update_c_d_prod_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' ).

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

tff('register_tensor$a',type,
    'register_tensor$a': ( 'C_update_a_update_fun$' * 'C_update_b_update_fun$' ) > 'C_c_prod_update_a_b_prod_update_fun$' ).

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

tff('comp$k',type,
    'comp$k': ( 'A_a_prod_update_b_update_fun$' * 'D_d_prod_update_a_a_prod_update_fun$' ) > 'D_d_prod_update_b_update_fun$' ).

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

tff('rel_fun$l',type,
    'rel_fun$l': ( 'C_update_d_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ).

tff('register$ae',type,
    'register$ae': 'C_d_prod_update_a_update_fun_bool_fun$' ).

tff('comp$bv',type,
    'comp$bv': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ) > 'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

tff('compatible$k',type,
    'compatible$k': ( 'D_update_a_update_fun$' * 'A_update_a_update_fun$' ) > $o ).

tff('register_pair$t',type,
    'register_pair$t': ( 'A_update_b_b_prod_update_fun$' * 'D_update_b_b_prod_update_fun$' ) > 'A_d_prod_update_b_b_prod_update_fun$' ).

tff('uub$',type,
    'uub$': 'C_update_set$' > 'C_update_bool_fun$' ).

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

tff('fun_app$aj',type,
    'fun_app$aj': ( 'A_update_bool_fun$' * 'A_update$' ) > $o ).

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

tff('fun_app$cy',type,
    'fun_app$cy': ( 'C_d_prod_update_c_update_fun$' * 'C_d_prod_update$' ) > 'C_update$' ).

tff('preregister$e',type,
    'preregister$e': 'B_update_a_update_fun$' > $o ).

tff('fun_app$u',type,
    'fun_app$u': ( 'C_update_a_update_fun$' * 'C_update$' ) > 'A_update$' ).

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

tff('register_tensor$q',type,
    'register_tensor$q': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'D_d_prod_update_b_b_prod_update_fun$' ).

tff('compatible$z',type,
    'compatible$z': ( 'C_update_a_update_fun$' * 'B_update_a_update_fun$' ) > $o ).

tff('register$ap',type,
    'register$ap': 'B_update_b_d_prod_update_fun$' > $o ).

tff('map_fun$i',type,
    'map_fun$i': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' ).

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

tff('separating$d',type,
    'separating$d': ( 'B_itself$' * 'A_update_set$' ) > $o ).

tff('map_prod$i',type,
    'map_prod$i': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_d_prod_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

tff('comp$m',type,
    'comp$m': ( 'A_b_prod_update_b_update_fun$' * 'D_c_prod_update_a_b_prod_update_fun$' ) > 'D_c_prod_update_b_update_fun$' ).

tff('rel_fun$aj',type,
    'rel_fun$aj': ( 'D_update_d_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ).

tff('map_fun$n',type,
    'map_fun$n': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'B_update_d_update_fun_d_update_b_update_fun_fun$' ).

tff('fun_app$bu',type,
    'fun_app$bu': ( 'A_c_prod_update_b_b_prod_update_fun$' * 'A_c_prod_update$' ) > 'B_b_prod_update$' ).

tff('fun_app$bv',type,
    'fun_app$bv': ( 'D_update_a_update_fun_d_update_b_update_fun_fun$' * 'D_update_a_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('comp$i',type,
    'comp$i': ( 'C_update_b_update_fun$' * 'A_update_c_update_fun$' ) > 'A_update_b_update_fun$' ).

tff('fun_app$dq',type,
    'fun_app$dq': ( 'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' * 'D_update_c_d_prod_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('compatible$aa',type,
    'compatible$aa': ( 'C_update_b_update_fun$' * 'B_update_b_update_fun$' ) > $o ).

tff('fun_app$v',type,
    'fun_app$v': ( 'C_update_a_a_prod_update_fun$' * 'C_update$' ) > 'A_a_prod_update$' ).

tff('grp$c',type,
    'grp$c': ( 'D_update_a_update_fun_set$' * 'D_update_a_update_fun_d_update_b_update_fun_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$' ).

tff('fun_app$bg',type,
    'fun_app$bg': ( 'D_update_d_update_fun$' * 'D_update$' ) > 'D_update$' ).

tff('comp$v',type,
    'comp$v': ( 'B_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

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

tff('tensor_update$f',type,
    'tensor_update$f': ( 'B_update$' * 'B_update$' ) > 'B_b_prod_update$' ).

tff('comp$x',type,
    'comp$x': ( 'D_update_a_update_fun$' * 'D_update_d_update_fun$' ) > 'D_update_a_update_fun$' ).

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

tff('comp$bp',type,
    'comp$bp': ( 'A_update_a_update_fun_d_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' ).

tff('register$d',type,
    'register$d': 'B_update_b_update_fun$' > $o ).

tff('map_fun$m',type,
    'map_fun$m': ( 'D_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' ).

tff('compatible$as',type,
    'compatible$as': ( 'A_update_b_a_prod_update_fun$' * 'C_update_b_a_prod_update_fun$' ) > $o ).

tff('register_tensor$h',type,
    'register_tensor$h': ( 'A_update_b_update_fun$' * 'C_update_a_update_fun$' ) > 'A_c_prod_update_b_a_prod_update_fun$' ).

tff('separating$',type,
    'separating$': ( 'A_itself$' * 'D_update_set$' ) > $o ).

tff('register_pair$',type,
    'register_pair$': ( 'C_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'C_d_prod_update_a_update_fun$' ).

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

tff('fun_app$ch',type,
    'fun_app$ch': ( 'C_a_prod_update_b_update_fun$' * 'C_a_prod_update$' ) > 'B_update$' ).

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

tff('fun_app$k',type,
    'fun_app$k': ( 'C_update_a_update_fun_bool_fun$' * 'C_update_a_update_fun$' ) > $o ).

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

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

tff('register_tensor$k',type,
    'register_tensor$k': ( 'D_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'D_c_prod_update_a_a_prod_update_fun$' ).

tff('fun_app$bo',type,
    'fun_app$bo': ( 'C_d_prod_update_a_b_prod_update_fun$' * 'C_d_prod_update$' ) > 'A_b_prod_update$' ).

tff('fun_app$bf',type,
    'fun_app$bf': ( 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_fun$' ).

tff('fun_app$cp',type,
    'fun_app$cp': ( 'B_update_d_update_fun_a_update_a_update_fun_fun$' * 'B_update_d_update_fun$' ) > 'A_update_a_update_fun$' ).

tff('fun_app$bq',type,
    'fun_app$bq': ( 'C_c_prod_update_b_b_prod_update_fun$' * 'C_c_prod_update$' ) > 'B_b_prod_update$' ).

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

tff('quotient$',type,
    'quotient$': ( 'B_update_b_update_bool_fun_fun$' * 'B_update_a_update_fun$' * 'A_update_b_update_fun$' * 'B_update_a_update_bool_fun_fun$' ) > $o ).

tff('relcompp$l',type,
    'relcompp$l': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_d_update_bool_fun_fun$' ) > 'A_update_d_update_bool_fun_fun$' ).

tff('rel_fun$am',type,
    'rel_fun$am': ( 'D_update_d_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_bool_fun_fun$' ).

tff('fun_app$dw',type,
    'fun_app$dw': ( 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_d_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('comp_update$k',type,
    'comp_update$k': ( 'C_b_prod_update$' * 'C_b_prod_update$' ) > 'C_b_prod_update$' ).

tff('g$',type,
    'g$': 'C_update_a_update_fun$' ).

tff('comp$bg',type,
    'comp$bg': ( 'C_update_a_update_a_update_prod_fun$' * 'D_update_c_update_fun$' ) > 'D_update_a_update_a_update_prod_fun$' ).

tff('fun_app$ba',type,
    'fun_app$ba': ( 'A_update_d_c_prod_update_fun$' * 'A_update$' ) > 'D_c_prod_update$' ).

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

tff('comp_update$e',type,
    'comp_update$e': ( 'B_d_prod_update$' * 'B_d_prod_update$' ) > 'B_d_prod_update$' ).

tff('fun_app$aa',type,
    'fun_app$aa': ( 'A_update_d_update_fun$' * 'A_update$' ) > 'D_update$' ).

tff('preregister$i',type,
    'preregister$i': 'D_update_a_update_fun_bool_fun$' ).

tff('fun_app$cg',type,
    'fun_app$cg': ( 'C_c_prod_update_b_update_fun$' * 'C_c_prod_update$' ) > 'B_update$' ).

tff('fun_app$ck',type,
    'fun_app$ck': ( 'D_c_prod_update_b_update_fun$' * 'D_c_prod_update$' ) > 'B_update$' ).

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

tff('fun_app$l',type,
    'fun_app$l': ( 'D_update_b_d_prod_update_fun$' * 'D_update$' ) > 'B_d_prod_update$' ).

tff('convol$f',type,
    'convol$f': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_update_a_update_a_update_prod_fun$' ).

tff('register_tensor$ad',type,
    'register_tensor$ad': ( 'A_update_c_update_fun$' * 'A_update_c_update_fun$' ) > 'A_a_prod_update_c_c_prod_update_fun$' ).

tff('fun_app$ca',type,
    'fun_app$ca': ( 'B_a_prod_update_b_update_fun$' * 'B_a_prod_update$' ) > 'B_update$' ).

tff('map_prod$r',type,
    'map_prod$r': ( 'D_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'D_update_d_update_prod_a_update_a_update_prod_fun$' ).

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

tff('convol$b',type,
    'convol$b': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_update_a_update_a_update_prod_fun$' ).

tff('comp_update$d',type,
    'comp_update$d': ( 'B_b_prod_update$' * 'B_b_prod_update$' ) > 'B_b_prod_update$' ).

tff('register_tensor$v',type,
    'register_tensor$v': ( 'D_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'D_c_d_prod_prod_update_a_a_prod_update_fun$' ).

tff('register_pair$f',type,
    'register_pair$f': ( 'D_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'D_a_prod_update_b_update_fun$' ).

tff('rel_fun$s',type,
    'rel_fun$s': ( 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' ).

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

tff('map_fun$l',type,
    'map_fun$l': ( 'D_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'B_update_c_update_fun_d_update_b_update_fun_fun$' ).

tff('comp$bz',type,
    'comp$bz': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$' ) > 'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' ).

tff('fun_app$s',type,
    'fun_app$s': ( 'C_update_b_a_prod_update_fun$' * 'C_update$' ) > 'B_a_prod_update$' ).

tff('fcomp$c',type,
    'fcomp$c': ( 'B_update_d_update_fun_a_update_a_update_fun_fun$' * 'A_update_a_update_fun_c_update_b_update_fun_fun$' ) > 'B_update_d_update_fun_c_update_b_update_fun_fun$' ).

tff('uuk$',type,
    'uuk$': 'A_update_d_update_fun$' > 'A_update_d_d_prod_update_fun$' ).

tff('register_pair$a',type,
    'register_pair$a': ( 'C_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

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

tff('fun_app$bh',type,
    'fun_app$bh': ( 'D_update_c_update_fun$' * 'D_update$' ) > 'C_update$' ).

tff('type_definition$f',type,
    'type_definition$f': ( 'A_update_c_update_fun$' * 'C_update_a_update_fun$' * 'C_update_set$' ) > $o ).

tff('map_prod$h',type,
    'map_prod$h': ( 'C_d_prod_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$' ).

tff('quotient$b',type,
    'quotient$b': ( 'B_update_b_update_bool_fun_fun$' * 'B_update_c_update_fun$' * 'C_update_b_update_fun$' * 'B_update_c_update_bool_fun_fun$' ) > $o ).

tff('rel_fun$z',type,
    'rel_fun$z': ( 'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' * 'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' ).

tff('fun_app$cj',type,
    'fun_app$cj': ( 'A_a_prod_update_b_update_fun$' * 'A_a_prod_update$' ) > 'B_update$' ).

tff('fun_app$cn',type,
    'fun_app$cn': ( 'B_update_d_update_fun_d_update_b_update_fun_fun$' * 'B_update_d_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('register_tensor$d',type,
    'register_tensor$d': ( 'C_update_b_update_fun$' * 'C_update_a_update_fun$' ) > 'C_c_prod_update_b_a_prod_update_fun$' ).

tff('map_fun$g',type,
    'map_fun$g': ( 'C_d_prod_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('fun_app$dv',type,
    'fun_app$dv': ( 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('uvc$',type,
    'uvc$': 'A_update_a_c_prod_update_fun$' ).

tff('register_tensor$t',type,
    'register_tensor$t': ( 'C_d_prod_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'C_d_prod_d_prod_update_a_a_prod_update_fun$' ).

tff('fcomp$e',type,
    'fcomp$e': ( 'C_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('comp$bb',type,
    'comp$bb': ( 'C_update_b_update_fun$' * 'C_d_prod_update_c_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('register_tensor$b',type,
    'register_tensor$b': ( 'C_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'C_a_prod_update_a_b_prod_update_fun$' ).

tff('rel_fun$x',type,
    'rel_fun$x': ( 'C_d_prod_update_d_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_d_prod_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ).

tff('register_pair$h',type,
    'register_pair$h': ( 'C_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'C_a_prod_update_b_update_fun$' ).

tff('compatible$o',type,
    'compatible$o': ( 'A_update_b_update_fun$' * 'D_update_b_update_fun$' ) > $o ).

tff('map_fun$k',type,
    'map_fun$k': ( 'D_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_a_update_fun_d_update_b_update_fun_fun$' ).

tff('comp_update$j',type,
    'comp_update$j': ( 'D_c_prod_update$' * 'D_c_prod_update$' ) > 'D_c_prod_update$' ).

tff('comp$cg',type,
    'comp$cg': ( 'D_update_b_update_fun$' * 'B_update_d_update_fun$' ) > 'B_update_b_update_fun$' ).

tff('fun_app$al',type,
    'fun_app$al': ( 'D_update_d_update_bool_fun_fun$' * 'D_update$' ) > 'D_update_bool_fun$' ).

tff('comp$bt',type,
    'comp$bt': ( 'B_update_bool_fun$' * 'A_update_b_update_fun$' ) > 'A_update_bool_fun$' ).

tff('compatible$af',type,
    'compatible$af': ( 'C_update_d_update_fun$' * 'D_update_d_update_fun$' ) > $o ).

tff('comp$r',type,
    'comp$r': ( 'A_b_prod_update_b_update_fun$' * 'C_c_prod_update_a_b_prod_update_fun$' ) > 'C_c_prod_update_b_update_fun$' ).

tff('register_tensor$l',type,
    'register_tensor$l': ( 'D_update_a_update_fun$' * 'C_update_b_update_fun$' ) > 'D_c_prod_update_a_b_prod_update_fun$' ).

tff('f$',type,
    'f$': 'A_update_b_update_fun$' ).

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

tff('fun_app$cc',type,
    'fun_app$cc': ( 'A_d_prod_update_a_update_fun$' * 'A_d_prod_update$' ) > 'A_update$' ).

tff('member$f',type,
    'member$f': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun_set$' ) > $o ).

tff('fun_app$cd',type,
    'fun_app$cd': ( 'A_d_prod_update_b_update_fun$' * 'A_d_prod_update$' ) > 'B_update$' ).

tff('fun_app$dl',type,
    'fun_app$dl': ( 'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$' * 'C_d_prod_update_d_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('fun_app$w',type,
    'fun_app$w': ( 'B_update_b_d_prod_update_fun$' * 'B_update$' ) > 'B_d_prod_update$' ).

tff('fun_app$f',type,
    'fun_app$f': ( 'A_update_a_b_prod_update_fun$' * 'A_update$' ) > 'A_b_prod_update$' ).

tff('convol$c',type,
    'convol$c': ( 'D_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'D_update_a_update_a_update_prod_fun$' ).

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

tff('fun_app$bb',type,
    'fun_app$bb': ( 'A_update_d_b_prod_update_fun$' * 'A_update$' ) > 'D_b_prod_update$' ).

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

tff('comp_update$l',type,
    'comp_update$l': ( 'C_a_prod_update$' * 'C_a_prod_update$' ) > 'C_a_prod_update$' ).

tff('fun_app$m',type,
    'fun_app$m': ( 'D_update_b_update_fun$' * 'D_update$' ) > 'B_update$' ).

tff('member$c',type,
    'member$c': ( 'A_update$' * 'A_update_set$' ) > $o ).

tff('register_pair$n',type,
    'register_pair$n': ( 'B_update_a_update_fun$' * 'A_update_a_update_fun$' * 'B_a_prod_update$' ) > 'A_update$' ).

tff('fun_app$cz',type,
    'fun_app$cz': ( 'C_update_c_d_prod_update_fun$' * 'C_update$' ) > 'C_d_prod_update$' ).

tff('register$bl',type,
    'register$bl': 'A_update_a_c_prod_update_fun$' > $o ).

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

tff('comp$bq',type,
    'comp$bq': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_update_a_update_a_update_prod_fun$' ) > 'C_update_b_update_b_update_prod_fun$' ).

tff('register_pair$v',type,
    'register_pair$v': ( 'A_update_b_b_prod_update_fun$' * 'C_update_b_b_prod_update_fun$' ) > 'A_c_prod_update_b_b_prod_update_fun$' ).

tff('type$',type,
    'type$': 'B_itself$' ).

tff('member$g',type,
    'member$g': ( 'B_update$' * 'B_update_set$' ) > $o ).

tff('rel_fun$aa',type,
    'rel_fun$aa': ( 'D_update_c_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'D_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' ).

tff('compatible$c',type,
    'compatible$c': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > $o ).

tff('rel_fun$ai',type,
    'rel_fun$ai': ( 'D_update_d_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' ).

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

tff('top$a',type,
    'top$a': 'D_update_set$' ).

tff('fun_app$cb',type,
    'fun_app$cb': ( 'B_update_c_update_fun$' * 'B_update$' ) > 'C_update$' ).

tff('rel_fun$af',type,
    'rel_fun$af': ( 'D_update_c_d_prod_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ).

tff('top$',type,
    'top$': 'C_d_prod_update_set$' ).

tff('map_prod$',type,
    'map_prod$': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_a_update_prod_b_update_b_update_prod_fun$' ).

tff('uwd$',type,
    'uwd$': 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' ).

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

tff('fcomp$',type,
    'fcomp$': ( 'B_update_d_update_fun_a_update_a_update_fun_fun$' * 'A_update_a_update_fun_d_update_b_update_fun_fun$' ) > 'B_update_d_update_fun_d_update_b_update_fun_fun$' ).

tff('comp$ca',type,
    'comp$ca': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'D_update_c_update_prod_a_update_a_update_prod_fun$' ) > 'D_update_c_update_prod_b_update_b_update_prod_fun$' ).

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

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

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

tff('comp$aa',type,
    'comp$aa': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'D_d_prod_update_a_a_prod_update_fun$' ) > 'D_d_prod_update_b_b_prod_update_fun$' ).

tff('rel_fun$b',type,
    'rel_fun$b': ( 'C_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' * 'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' ).

tff('id_update$a',type,
    'id_update$a': 'D_update$' ).

tff('quotient$e',type,
    'quotient$e': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_d_update_fun$' * 'D_update_a_update_fun$' * 'A_update_d_update_bool_fun_fun$' ) > $o ).

tff('comp$e',type,
    'comp$e': ( 'C_update_a_update_fun$' * 'C_update_c_update_fun$' ) > 'C_update_a_update_fun$' ).

tff('fun_app$au',type,
    'fun_app$au': ( 'D_update_a_update_fun$' * 'D_update$' ) > 'A_update$' ).

tff('fun_app$bz',type,
    'fun_app$bz': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update$' ) > 'B_update$' ).

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

tff('register_tensor$o',type,
    'register_tensor$o': ( 'A_update_b_update_fun$' * 'D_update_a_update_fun$' ) > 'A_d_prod_update_b_a_prod_update_fun$' ).

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

tff('comp$bx',type,
    'comp$bx': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$' ) > 'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' ).

tff('comp$ak',type,
    'comp$ak': ( 'C_update_a_update_fun$' * 'A_update_c_update_fun$' ) > 'A_update_a_update_fun$' ).

tff('comp$at',type,
    'comp$at': ( 'A_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'D_update_a_update_fun$' ).

tff('preregister$f',type,
    'preregister$f': 'A_update_d_update_fun$' > $o ).

tff('register$be',type,
    'register$be': 'A_update_b_a_prod_update_fun$' > $o ).

tff('comp$ai',type,
    'comp$ai': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$' ) > 'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$' ).

tff('comp$d',type,
    'comp$d': ( 'B_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('rel_fun$ak',type,
    'rel_fun$ak': ( 'C_update_c_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$' ).

tff('uwb$',type,
    'uwb$': 'A_update_set$' > 'C_d_prod_update_a_update_fun_bool_fun$' ).

tff('member$b',type,
    'member$b': ( 'C_update$' * 'C_update_set$' ) > $o ).

tff('comp$u',type,
    'comp$u': ( 'B_a_prod_update_b_update_fun$' * 'A_d_prod_update_b_a_prod_update_fun$' ) > 'A_d_prod_update_b_update_fun$' ).

tff('fun_app$as',type,
    'fun_app$as': ( 'D_update_d_b_prod_update_fun$' * 'D_update$' ) > 'D_b_prod_update$' ).

tff('compatible$t',type,
    'compatible$t': ( 'B_update_b_update_fun$' * 'C_update_b_update_fun$' ) > $o ).

tff('register_pair$d',type,
    'register_pair$d': ( 'D_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'D_c_prod_update_b_update_fun$' ).

tff('rel_fun$ag',type,
    'rel_fun$ag': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' ) > $o ).

tff('comp$aj',type,
    'comp$aj': ( 'C_c_prod_update_a_a_prod_update_fun$' * 'A_a_prod_update_c_c_prod_update_fun$' ) > 'A_a_prod_update_a_a_prod_update_fun$' ).

tff('comp$aw',type,
    'comp$aw': ( 'A_update_a_update_fun_c_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ).

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

tff('fun_app$az',type,
    'fun_app$az': ( 'B_update_a_update_fun$' * 'B_update$' ) > 'A_update$' ).

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

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

tff('type_definition$a',type,
    'type_definition$a': ( 'B_update_b_update_fun$' * 'B_update_b_update_fun$' * 'B_update_set$' ) > $o ).

tff('register_tensor$m',type,
    'register_tensor$m': ( 'D_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'D_a_prod_update_a_b_prod_update_fun$' ).

tff('comp$bl',type,
    'comp$bl': ( 'A_update_b_update_b_update_prod_fun$' * 'D_update_a_update_fun$' ) > 'D_update_b_update_b_update_prod_fun$' ).

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

tff('comp$ay',type,
    'comp$ay': ( 'A_update_a_update_fun_c_update_b_update_fun_fun$' * 'B_update_c_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_update_fun_c_update_b_update_fun_fun$' ).

tff('uvw$',type,
    'uvw$': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_bool_fun$' ).

tff('map_fun$h',type,
    'map_fun$h': ( 'C_d_prod_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('map_prod$a',type,
    'map_prod$a': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_update_c_update_prod_b_update_b_update_prod_fun$' ).

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

tff('fun_app$c',type,
    'fun_app$c': ( 'D_update_a_d_prod_update_fun$' * 'D_update$' ) > 'A_d_prod_update$' ).

tff('fun_app$ar',type,
    'fun_app$ar': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'A_update_b_update_fun$' ) > 'A_update_b_update_fun_bool_fun$' ).

tff('fun_app$de',type,
    'fun_app$de': ( 'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' * 'C_update_c_d_prod_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('fun_app$ce',type,
    'fun_app$ce': ( 'C_d_prod_update_c_d_prod_update_fun$' * 'C_d_prod_update$' ) > 'C_d_prod_update$' ).

tff('compatible$s',type,
    'compatible$s': ( 'B_update_b_update_fun$' * 'D_update_b_update_fun$' ) > $o ).

tff('relcompp$d',type,
    'relcompp$d': ( 'B_update_a_update_bool_fun_fun$' * 'A_update_d_update_bool_fun_fun$' ) > 'B_update_d_update_bool_fun_fun$' ).

tff('fun_app$cr',type,
    'fun_app$cr': ( 'B_update_c_update_fun_a_update_a_update_fun_fun$' * 'B_update_c_update_fun$' ) > 'A_update_a_update_fun$' ).

tff('register_tensor$f',type,
    'register_tensor$f': ( 'C_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'C_a_prod_update_b_b_prod_update_fun$' ).

tff('fun_app$dy',type,
    'fun_app$dy': ( 'B_update_set_b_update_fun$' * 'B_update_set$' ) > 'B_update$' ).

tff('comp$bk',type,
    'comp$bk': ( 'A_update_b_update_b_update_prod_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

tff('fun_app$aw',type,
    'fun_app$aw': ( 'C_update_d_a_prod_update_fun$' * 'C_update$' ) > 'D_a_prod_update$' ).

tff('uve$',type,
    'uve$': 'A_update_a_a_prod_update_fun$' ).

tff('separating$a',type,
    'separating$a': ( 'B_itself$' * 'C_update_set$' ) > $o ).

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

tff('top$c',type,
    'top$c': 'A_update_set$' ).

tff('comp$ac',type,
    'comp$ac': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_d_prod_update_a_a_prod_update_fun$' ) > 'C_d_prod_update_b_b_prod_update_fun$' ).

tff('register_pair$b',type,
    'register_pair$b': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_a_prod_update_b_update_fun$' ).

tff('uvf$',type,
    'uvf$': 'D_update_b_update_fun$' > 'D_update_b_b_prod_update_fun$' ).

tff('fun_app$cl',type,
    'fun_app$cl': ( 'D_a_prod_update_b_update_fun$' * 'D_a_prod_update$' ) > 'B_update$' ).

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

tff('comp$t',type,
    'comp$t': ( 'B_a_prod_update_b_update_fun$' * 'C_c_prod_update_b_a_prod_update_fun$' ) > 'C_c_prod_update_b_update_fun$' ).

tff('rel_fun$y',type,
    'rel_fun$y': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'D_update_a_update_fun_d_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ) > $o ).

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

tff('quotient$d',type,
    'quotient$d': ( 'B_update_b_update_bool_fun_fun$' * 'B_update_c_d_prod_update_fun$' * 'C_d_prod_update_b_update_fun$' * 'B_update_c_d_prod_update_bool_fun_fun$' ) > $o ).

tff('register$bm',type,
    'register$bm': 'A_update_a_b_prod_update_fun$' > $o ).

tff('compatible$am',type,
    'compatible$am': ( 'C_update_b_b_prod_update_fun$' * 'A_update_b_b_prod_update_fun$' ) > $o ).

tff('rel_fun$h',type,
    'rel_fun$h': ( 'C_update_c_d_prod_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ).

tff('collect$',type,
    'collect$': 'C_d_prod_update_bool_fun$' > 'C_d_prod_update_set$' ).

tff('fun_app$bl',type,
    'fun_app$bl': ( 'C_c_prod_update_a_a_prod_update_fun$' * 'C_c_prod_update$' ) > 'A_a_prod_update$' ).

tff('rel_fun$al',type,
    'rel_fun$al': ( 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ).

tff('fun_app$t',type,
    'fun_app$t': ( 'C_update_a_b_prod_update_fun$' * 'C_update$' ) > 'A_b_prod_update$' ).

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

tff('fun_app$b',type,
    'fun_app$b': ( 'A_update_a_d_prod_update_fun$' * 'A_update$' ) > 'A_d_prod_update$' ).

tff('compatible$l',type,
    'compatible$l': ( 'B_update_a_update_fun$' * 'A_update_a_update_fun$' ) > $o ).

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

tff('comp$ap',type,
    'comp$ap': ( 'B_update_a_update_fun$' * 'D_update_b_update_fun$' ) > 'D_update_a_update_fun$' ).

tff('register_pair$j',type,
    'register_pair$j': ( 'A_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'A_d_prod_update_b_update_fun$' ).

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

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

tff('comp$z',type,
    'comp$z': ( 'C_update_b_update_fun$' * 'B_update_c_update_fun$' ) > 'B_update_b_update_fun$' ).

tff('convol$d',type,
    'convol$d': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

tff('rel_fun$',type,
    'rel_fun$': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_update_a_update_fun_c_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ) > $o ).

tff('compatible$aj',type,
    'compatible$aj': ( 'C_update_b_a_prod_update_fun$' * 'D_update_b_a_prod_update_fun$' ) > $o ).

tff('comp$bh',type,
    'comp$bh': ( 'C_update_a_update_a_update_prod_fun$' * 'C_update_c_update_fun$' ) > 'C_update_a_update_a_update_prod_fun$' ).

tff('fun_app$bw',type,
    'fun_app$bw': ( 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_fun$' ).

tff('compatible$v',type,
    'compatible$v': ( 'B_update_d_update_fun$' * 'A_update_d_update_fun$' ) > $o ).

tff('register$bj',type,
    'register$bj': 'B_update_b_a_prod_update_fun$' > $o ).

tff('comp$bu',type,
    'comp$bu': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_update_c_update_prod_a_update_a_update_prod_fun$' ) > 'C_update_c_update_prod_b_update_b_update_prod_fun$' ).

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

tff('quotient$f',type,
    'quotient$f': ( 'B_update_b_update_bool_fun_fun$' * 'B_update_d_update_fun$' * 'D_update_b_update_fun$' * 'B_update_d_update_bool_fun_fun$' ) > $o ).

tff('tensor_update$m',type,
    'tensor_update$m': ( 'C_update$' * 'A_update$' ) > 'C_a_prod_update$' ).

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

tff('relcompp$c',type,
    'relcompp$c': ( 'B_update_a_update_bool_fun_fun$' * 'A_update_c_d_prod_update_bool_fun_fun$' ) > 'B_update_c_d_prod_update_bool_fun_fun$' ).

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

tff('fun_app$x',type,
    'fun_app$x': ( 'B_update_b_update_fun$' * 'B_update$' ) > 'B_update$' ).

tff('comp$br',type,
    'comp$br': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_a_update_a_update_prod_fun$' ) > 'C_d_prod_update_b_update_b_update_prod_fun$' ).

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

tff('id_update$',type,
    'id_update$': 'A_update$' ).

tff('convol$a',type,
    'convol$a': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_b_update_b_update_prod_fun$' ).

tff('compatible$ag',type,
    'compatible$ag': ( 'C_update_a_a_prod_update_fun$' * 'C_update_a_a_prod_update_fun$' ) > $o ).

tff('pred_fun$d',type,
    'pred_fun$d': ( 'D_update_bool_fun$' * 'B_update_bool_fun$' * 'D_update_b_update_fun$' ) > $o ).

tff('pred_fun$e',type,
    'pred_fun$e': ( 'D_update_bool_fun$' * 'A_update_bool_fun$' ) > 'D_update_a_update_fun_bool_fun$' ).

tff('rel_fun$w',type,
    'rel_fun$w': ( 'C_d_prod_update_d_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' ).

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

tff('comp_update$f',type,
    'comp_update$f': ( 'B_c_prod_update$' * 'B_c_prod_update$' ) > 'B_c_prod_update$' ).

tff('relcompp$e',type,
    'relcompp$e': ( 'C_update_a_update_bool_fun_fun$' * 'A_update_c_update_bool_fun_fun$' ) > 'C_update_c_update_bool_fun_fun$' ).

tff('preregister$p',type,
    'preregister$p': 'B_update_c_update_fun$' > $o ).

tff('map_prod$l',type,
    'map_prod$l': ( 'C_d_prod_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'C_d_prod_update_d_update_prod_a_update_a_update_prod_fun$' ).

tff('collect$b',type,
    'collect$b': 'C_update_bool_fun$' > 'C_update_set$' ).

tff('register_pair$g',type,
    'register_pair$g': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_c_prod_update_b_update_fun$' ).

tff('fun_app$',type,
    'fun_app$': ( 'B_update_b_a_prod_update_fun$' * 'B_update$' ) > 'B_a_prod_update$' ).

tff('comp$bf',type,
    'comp$bf': ( 'C_update_b_update_b_update_prod_fun$' * 'A_update_c_update_fun$' ) > 'A_update_b_update_b_update_prod_fun$' ).

tff('map_fun$a',type,
    'map_fun$a': ( 'A_update_b_update_fun$' * 'C_update_a_update_fun$' ) > 'B_update_c_update_fun_a_update_a_update_fun_fun$' ).

tff('uvx$',type,
    'uvx$': 'C_update_c_update_bool_fun_fun$' ).

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

tff('rel_fun$ah',type,
    'rel_fun$ah': ( 'D_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' * 'D_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' ).

tff('register$r',type,
    'register$r': 'D_update_d_update_fun$' > $o ).

tff('comp$ae',type,
    'comp$ae': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_d_prod_d_prod_update_a_a_prod_update_fun$' ) > 'C_d_prod_d_prod_update_b_b_prod_update_fun$' ).

tff('fun_app$dn',type,
    'fun_app$dn': ( 'D_update_c_update_prod_a_update_a_update_prod_fun$' * 'D_update_c_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('fun_app$bc',type,
    'fun_app$bc': ( 'A_update_d_a_prod_update_fun$' * 'A_update$' ) > 'D_a_prod_update$' ).

tff('relcompp$g',type,
    'relcompp$g': ( 'C_update_a_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'C_update_b_update_bool_fun_fun$' ).

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

tff('map_fun$e',type,
    'map_fun$e': ( 'A_update_b_update_fun$' * 'D_update_a_update_fun$' ) > 'B_update_d_update_fun_a_update_a_update_fun_fun$' ).

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

tff('register_tensor$r',type,
    'register_tensor$r': ( 'D_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'D_c_prod_update_b_b_prod_update_fun$' ).

tff('quotient$c',type,
    'quotient$c': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_c_d_prod_update_fun$' * 'C_d_prod_update_a_update_fun$' * 'A_update_c_d_prod_update_bool_fun_fun$' ) > $o ).

tff('compatible$y',type,
    'compatible$y': ( 'A_update_c_update_fun$' * 'D_update_c_update_fun$' ) > $o ).

tff('image$f',type,
    'image$f': ( 'A_update_b_update_fun$' * 'A_update_set$' ) > 'B_update_set$' ).

tff('uud$',type,
    'uud$': 'D_update_a_update_fun_set$' > 'D_update_a_update_fun_bool_fun$' ).

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

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

tff('uvd$',type,
    'uvd$': 'A_update_a_b_prod_update_fun$' ).

tff('fun_app$n',type,
    'fun_app$n': ( 'D_update_b_b_prod_update_fun$' * 'D_update$' ) > 'B_b_prod_update$' ).

tff('fun_app$cq',type,
    'fun_app$cq': ( 'B_update_c_update_fun_d_update_b_update_fun_fun$' * 'B_update_c_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('uuc$',type,
    'uuc$': 'A_update_set$' > 'A_update_bool_fun$' ).

tff('h$',type,
    'h$': 'D_update_a_update_fun$' ).

tff('compatible$aq',type,
    'compatible$aq': ( 'C_update_a_b_prod_update_fun$' * 'A_update_a_b_prod_update_fun$' ) > $o ).

tff('register_tensor$ac',type,
    'register_tensor$ac': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_d_prod_c_d_prod_prod_update_b_b_prod_update_fun$' ).

tff('fun_app$da',type,
    'fun_app$da': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'A_update_a_update_prod$' ) > 'B_update_b_update_prod$' ).

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

tff('comp$az',type,
    'comp$az': ( 'C_d_prod_update_a_update_fun$' * 'C_update_c_d_prod_update_fun$' ) > 'C_update_a_update_fun$' ).

tff('compatible$f',type,
    'compatible$f': ( 'C_update_b_update_fun$' * 'D_update_b_update_fun$' ) > $o ).

tff('comp$y',type,
    'comp$y': ( 'D_update_a_update_fun$' * 'C_update_d_update_fun$' ) > 'C_update_a_update_fun$' ).

tff('compatible$a',type,
    'compatible$a': ( 'A_update_b_update_fun$' * 'C_update_b_update_fun$' ) > $o ).

tff('fun_app$dr',type,
    'fun_app$dr': ( 'D_update_d_update_prod_a_update_a_update_prod_fun$' * 'D_update_d_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('uvb$',type,
    'uvb$': 'A_update_a_d_prod_update_fun$' ).

tff('register_tensor$c',type,
    'register_tensor$c': ( 'C_update_a_update_fun$' * 'D_update_b_update_fun$' ) > 'C_d_prod_update_a_b_prod_update_fun$' ).

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

tff('uva$',type,
    'uva$': 'B_update_b_a_prod_update_fun$' ).

tff('comp$bs',type,
    'comp$bs': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'D_update_a_update_a_update_prod_fun$' ) > 'D_update_b_update_b_update_prod_fun$' ).

tff('fun_app$ao',type,
    'fun_app$ao': ( 'B_update_b_update_bool_fun_fun$' * 'B_update$' ) > 'B_update_bool_fun$' ).

tff('register_pair$r',type,
    'register_pair$r': ( 'A_update_c_update_fun$' * 'D_update_c_update_fun$' * 'A_d_prod_update$' ) > 'C_update$' ).

tff('uwf$',type,
    'uwf$': 'B_update_b_update_bool_fun_fun$' ).

tff('fun_app$bs',type,
    'fun_app$bs': ( 'C_d_prod_update_b_b_prod_update_fun$' * 'C_d_prod_update$' ) > 'B_b_prod_update$' ).

tff('compatible$h',type,
    'compatible$h': ( 'D_update_b_update_fun$' * 'C_update_b_update_fun$' ) > $o ).

tff('comp$bo',type,
    'comp$bo': ( 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_d_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('map_prod$p',type,
    'map_prod$p': ( 'D_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ).

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

tff('comp_update$g',type,
    'comp_update$g': ( 'D_b_prod_update$' * 'D_b_prod_update$' ) > 'D_b_prod_update$' ).

tff('compatible$an',type,
    'compatible$an': ( 'C_update_b_b_prod_update_fun$' * 'D_update_b_b_prod_update_fun$' ) > $o ).

tff('fun_app$dg',type,
    'fun_app$dg': ( 'C_update_d_update_prod_b_update_b_update_prod_fun$' * 'C_update_d_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('fun_app$ds',type,
    'fun_app$ds': ( 'D_update_d_update_prod_b_update_b_update_prod_fun$' * 'D_update_d_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('image$e',type,
    'image$e': ( 'D_update_b_update_fun$' * 'D_update_set$' ) > 'B_update_set$' ).

tff('top$b',type,
    'top$b': 'C_update_set$' ).

tff('register_tensor$',type,
    'register_tensor$': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_c_prod_update_a_a_prod_update_fun$' ).

tff('uvu$',type,
    'uvu$': 'C_d_prod_update_bool_fun$' ).

tff('comp$bc',type,
    'comp$bc': ( 'C_update_a_update_fun$' * 'C_d_prod_update_c_update_fun$' ) > 'C_d_prod_update_a_update_fun$' ).

tff('fun_app$ae',type,
    'fun_app$ae': ( 'A_update_b_update_fun$' * 'A_update$' ) > 'B_update$' ).

tff('image$d',type,
    'image$d': ( 'C_d_prod_update_b_update_fun$' * 'C_d_prod_update_set$' ) > 'B_update_set$' ).

tff('comp$bj',type,
    'comp$bj': ( 'A_update_b_update_b_update_prod_fun$' * 'C_update_a_update_fun$' ) > 'C_update_b_update_b_update_prod_fun$' ).

tff('register_tensor$aa',type,
    'register_tensor$aa': ( 'C_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_c_d_prod_prod_update_b_b_prod_update_fun$' ).

tff('uua$',type,
    'uua$': 'D_update_set$' > 'D_update_bool_fun$' ).

tff('uuv$',type,
    'uuv$': 'B_update_a_update_fun$' > 'B_update_d_a_prod_update_fun$' ).

tff('map_prod$j',type,
    'map_prod$j': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ).

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

tff('type_definition$h',type,
    'type_definition$h': ( 'A_update_d_update_fun$' * 'D_update_a_update_fun$' * 'D_update_set$' ) > $o ).

tff('fun_app$ac',type,
    'fun_app$ac': ( 'A_update_c_update_fun$' * 'A_update$' ) > 'C_update$' ).

tff('fun_app$cs',type,
    'fun_app$cs': ( 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun$' ) > 'C_update_b_update_fun$' ).

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

tff('uvy$',type,
    'uvy$': 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' ).

tff('compatible$ae',type,
    'compatible$ae': ( 'C_update_c_update_fun$' * 'D_update_c_update_fun$' ) > $o ).

tff('comp$bd',type,
    'comp$bd': ( 'A_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_update_a_update_fun$' ).

tff('register_pair$l',type,
    'register_pair$l': ( 'A_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'A_c_prod_update_b_update_fun$' ).

tff('map_fun$c',type,
    'map_fun$c': ( 'A_update_b_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' ).

tff('register_pair$p',type,
    'register_pair$p': ( 'B_update_c_update_fun$' * 'A_update_c_update_fun$' * 'B_a_prod_update$' ) > 'C_update$' ).

tff('fun_app$ag',type,
    'fun_app$ag': ( 'C_d_prod_update_bool_fun$' * 'C_d_prod_update$' ) > $o ).

tff('tensor_update$l',type,
    'tensor_update$l': ( 'C_update$' * 'C_update$' ) > 'C_c_prod_update$' ).

tff('rel_fun$q',type,
    'rel_fun$q': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' ) > $o ).

tff('grp$',type,
    'grp$': ( 'A_update_set$' * 'A_update_b_update_fun$' ) > 'A_update_b_update_bool_fun_fun$' ).

tff('comp$cd',type,
    'comp$cd': ( 'A_update_c_update_fun$' * 'B_update_a_update_fun$' ) > 'B_update_c_update_fun$' ).

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

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

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

tff('fun_app$dj',type,
    'fun_app$dj': ( 'C_d_prod_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' * 'C_d_prod_update_c_d_prod_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('register$t',type,
    'register$t': 'B_update_d_update_fun$' > $o ).

tff('fun_app$r',type,
    'fun_app$r': ( 'C_update_b_b_prod_update_fun$' * 'C_update$' ) > 'B_b_prod_update$' ).

tff('comp$ad',type,
    'comp$ad': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_c_prod_update_a_a_prod_update_fun$' ) > 'C_c_prod_update_b_b_prod_update_fun$' ).

tff('map_fun$',type,
    'map_fun$': ( 'C_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_a_update_fun_c_update_b_update_fun_fun$' ).

tff('register_pair$c',type,
    'register_pair$c': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'D_d_prod_update_b_update_fun$' ).

tff('image$c',type,
    'image$c': ( 'C_update_b_update_fun$' * 'C_update_set$' ) > 'B_update_set$' ).

tff('comp$l',type,
    'comp$l': ( 'A_a_prod_update_b_update_fun$' * 'D_c_prod_update_a_a_prod_update_fun$' ) > 'D_c_prod_update_b_update_fun$' ).

tff('compatible$w',type,
    'compatible$w': ( 'B_update_c_update_fun$' * 'A_update_c_update_fun$' ) > $o ).

tff('fun_app$q',type,
    'fun_app$q': ( 'C_update_b_update_fun$' * 'C_update$' ) > 'B_update$' ).

tff('register_tensor$i',type,
    'register_tensor$i': ( 'A_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'A_c_prod_update_b_b_prod_update_fun$' ).

tff('register_tensor$g',type,
    'register_tensor$g': ( 'C_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'C_d_prod_update_b_b_prod_update_fun$' ).

tff('map_prod$n',type,
    'map_prod$n': ( 'D_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'D_update_c_update_prod_a_update_a_update_prod_fun$' ).

tff('rel_fun$m',type,
    'rel_fun$m': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ) > $o ).

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

tff('uuu$',type,
    'uuu$': 'B_update_b_update_fun$' > 'B_update_d_b_prod_update_fun$' ).

tff('rel_fun$a',type,
    'rel_fun$a': ( 'A_update_a_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' ).

tff('register$bk',type,
    'register$bk': 'A_update_a_d_prod_update_fun$' > $o ).

tff('map_fun$j',type,
    'map_fun$j': ( 'C_d_prod_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'B_update_d_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('rel_fun$ac',type,
    'rel_fun$ac': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' ) > $o ).

tff('compatible$b',type,
    'compatible$b': ( 'A_update_b_update_fun$' * 'B_update_b_update_fun$' ) > $o ).

tff('register_pair$s',type,
    'register_pair$s': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_c_prod_update_a_update_fun$' ).

tff('rel_fun$u',type,
    'rel_fun$u': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_d_update_a_update_fun_d_update_b_update_fun_fun_fun$' ) > $o ).

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

tff('map_fun$f',type,
    'map_fun$f': ( 'C_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'B_update_d_update_fun_c_update_b_update_fun_fun$' ).

tff('register_tensor$ae',type,
    'register_tensor$ae': ( 'A_update_a_update_fun$' * 'A_update_a_update_fun$' ) > 'A_a_prod_update_a_a_prod_update_fun$' ).

tff('register$bb',type,
    'register$bb': 'B_update_d_a_prod_update_fun$' > $o ).

tff('fun_app$cu',type,
    'fun_app$cu': ( 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' * 'B_update_c_d_prod_update_fun$' ) > 'A_update_a_update_fun$' ).

tff('fun_app$h',type,
    'fun_app$h': ( 'A_update_a_a_prod_update_fun$' * 'A_update$' ) > 'A_a_prod_update$' ).

tff('comp$cb',type,
    'comp$cb': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ) > 'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

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

tff('fun_app$ah',type,
    'fun_app$ah': ( 'D_update_bool_fun$' * 'D_update$' ) > $o ).

tff('comp$bm',type,
    'comp$bm': ( 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_c_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('rel_fun$ad',type,
    'rel_fun$ad': ( 'D_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' * 'D_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ) > 'D_update_a_update_fun_d_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' ).

tff('fun_app$av',type,
    'fun_app$av': ( 'C_update_d_b_prod_update_fun$' * 'C_update$' ) > 'D_b_prod_update$' ).

tff('register_tensor$j',type,
    'register_tensor$j': ( 'D_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'D_d_prod_update_a_a_prod_update_fun$' ).

tff('fun_app$bd',type,
    'fun_app$bd': ( 'A_update_a_update_fun$' * 'A_update$' ) > 'A_update$' ).

tff('comp$bw',type,
    'comp$bw': ( 'A_update_a_update_prod_b_update_b_update_prod_fun$' * 'C_update_d_update_prod_a_update_a_update_prod_fun$' ) > 'C_update_d_update_prod_b_update_b_update_prod_fun$' ).

tff('compatible$ab',type,
    'compatible$ab': ( 'A_update_a_update_fun$' * 'A_update_a_update_fun$' ) > $o ).

tff('comp$',type,
    'comp$': 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ).

tff('comp$ag',type,
    'comp$ag': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_d_prod_c_prod_update_a_a_prod_update_fun$' ) > 'C_d_prod_c_prod_update_b_b_prod_update_fun$' ).

tff('fun_app$cv',type,
    'fun_app$cv': ( 'B_update_d_update_fun_c_update_b_update_fun_fun$' * 'B_update_d_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('fun_app$dh',type,
    'fun_app$dh': ( 'C_d_prod_update_c_update_prod_a_update_a_update_prod_fun$' * 'C_d_prod_update_c_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('relcompp$b',type,
    'relcompp$b': ( 'B_update_a_update_bool_fun_fun$' * 'A_update_c_update_bool_fun_fun$' ) > 'B_update_c_update_bool_fun_fun$' ).

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

tff('comp$au',type,
    'comp$au': ( 'A_update_a_update_fun_d_update_b_update_fun_fun$' * 'B_update_d_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_d_update_fun_d_update_b_update_fun_fun$' ).

tff('rel_fun$o',type,
    'rel_fun$o': ( 'C_d_prod_update_c_update_bool_fun_fun$' * 'A_update_a_update_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' ).

tff('map_prod$f',type,
    'map_prod$f': ( 'C_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'C_update_d_update_prod_a_update_a_update_prod_fun$' ).

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

tff('pred_fun$b',type,
    'pred_fun$b': ( 'C_d_prod_update_bool_fun$' * 'B_update_bool_fun$' * 'C_d_prod_update_b_update_fun$' ) > $o ).

tff('type_definition$c',type,
    'type_definition$c': ( 'C_update_d_update_fun$' * 'D_update_c_update_fun$' * 'D_update_set$' ) > $o ).

tff('type_definition$i',type,
    'type_definition$i': ( 'B_update_c_update_fun$' * 'C_update_b_update_fun$' * 'C_update_set$' ) > $o ).

tff('map_prod$b',type,
    'map_prod$b': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_update_c_update_prod_a_update_a_update_prod_fun$' ).

tff('comp$ax',type,
    'comp$ax': ( 'A_update_a_update_fun_c_update_b_update_fun_fun$' * 'B_update_d_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_d_update_fun_c_update_b_update_fun_fun$' ).

tff('map_prod$d',type,
    'map_prod$d': ( 'C_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' ).

tff('fcomp$a',type,
    'fcomp$a': ( 'B_update_c_update_fun_a_update_a_update_fun_fun$' * 'A_update_a_update_fun_d_update_b_update_fun_fun$' ) > 'B_update_c_update_fun_d_update_b_update_fun_fun$' ).

tff('comp$af',type,
    'comp$af': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'D_c_d_prod_prod_update_a_a_prod_update_fun$' ) > 'D_c_d_prod_prod_update_b_b_prod_update_fun$' ).

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

tff('compatible$p',type,
    'compatible$p': ( 'D_update_b_update_fun$' * 'A_update_b_update_fun$' ) > $o ).

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

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

tff('separating$b',type,
    'separating$b': ( 'A_itself$' * 'C_update_set$' ) > $o ).

tff('tensor_update$j',type,
    'tensor_update$j': ( 'D_update$' * 'A_update$' ) > 'D_a_prod_update$' ).

tff('compatible$i',type,
    'compatible$i': ( 'C_update_b_update_fun$' * 'A_update_b_update_fun$' ) > $o ).

tff('fun_app$bj',type,
    'fun_app$bj': ( 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('compatible$ak',type,
    'compatible$ak': ( 'C_update_a_b_prod_update_fun$' * 'C_update_a_b_prod_update_fun$' ) > $o ).

tff('compatible$ap',type,
    'compatible$ap': ( 'A_update_b_b_prod_update_fun$' * 'C_update_b_b_prod_update_fun$' ) > $o ).

tff('fun_app$by',type,
    'fun_app$by': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update$' ) > 'A_update$' ).

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

tff('register_pair$x',type,
    'register_pair$x': ( 'A_update_b_b_prod_update_fun$' * 'A_update_b_b_prod_update_fun$' ) > 'A_a_prod_update_b_b_prod_update_fun$' ).

tff('map_fun$b',type,
    'map_fun$b': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'B_update_c_update_fun_c_update_b_update_fun_fun$' ).

tff('register_pair$i',type,
    'register_pair$i': ( 'B_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'B_a_prod_update_b_update_fun$' ).

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

tff('register_tensor$z',type,
    'register_tensor$z': ( 'C_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_c_d_prod_prod_update_a_a_prod_update_fun$' ).

tff('fun_app$ay',type,
    'fun_app$ay': ( 'B_update_d_a_prod_update_fun$' * 'B_update$' ) > 'D_a_prod_update$' ).

tff('grp$a',type,
    'grp$a': ( 'C_update_a_update_fun_set$' * 'C_update_a_update_fun_c_update_b_update_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_bool_fun_fun$' ).

tff('fun_app$am',type,
    'fun_app$am': ( 'C_update_c_update_bool_fun_fun$' * 'C_update$' ) > 'C_update_bool_fun$' ).

tff('compatible$r',type,
    'compatible$r': 'B_update_a_update_fun$' > 'D_update_a_update_fun_bool_fun$' ).

tff('convol$e',type,
    'convol$e': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'D_update_b_update_b_update_prod_fun$' ).

tff('fun_app$bt',type,
    'fun_app$bt': ( 'A_c_prod_update_b_a_prod_update_fun$' * 'A_c_prod_update$' ) > 'B_a_prod_update$' ).

tff('compatible$ar',type,
    'compatible$ar': ( 'C_update_a_b_prod_update_fun$' * 'D_update_a_b_prod_update_fun$' ) > $o ).

tff('register$av',type,
    'register$av': 'B_update_b_b_prod_update_fun$' > $o ).

tff('comp$f',type,
    'comp$f': ( 'C_update_b_update_fun$' * 'C_update_c_update_fun$' ) > 'C_update_b_update_fun$' ).

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

tff('separating$e',type,
    'separating$e': ( 'B_itself$' * 'C_d_prod_update_set$' ) > $o ).

tff('register_pair$k',type,
    'register_pair$k': ( 'A_update_a_update_fun$' * 'D_update_a_update_fun$' ) > 'A_d_prod_update_a_update_fun$' ).

tff('relcompp$j',type,
    'relcompp$j': ( 'C_d_prod_update_a_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'C_d_prod_update_b_update_bool_fun_fun$' ).

tff('register_tensor$w',type,
    'register_tensor$w': ( 'D_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'D_c_d_prod_prod_update_b_b_prod_update_fun$' ).

tff('fun_app$ax',type,
    'fun_app$ax': ( 'B_update_d_b_prod_update_fun$' * 'B_update$' ) > 'D_b_prod_update$' ).

tff('compatible$q',type,
    'compatible$q': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > $o ).

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

tff('rel_fun$r',type,
    'rel_fun$r': ( 'C_d_prod_update_a_update_fun_c_d_prod_update_a_update_fun_bool_fun_fun$' * 'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' ).

tff('uup$',type,
    'uup$': 'B_update_b_update_fun$' > 'B_update_b_b_prod_update_fun$' ).

tff('rel_fun$ab',type,
    'rel_fun$ab': ( 'D_update_c_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'D_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ).

tff('compatible$al',type,
    'compatible$al': ( 'C_update_b_b_prod_update_fun$' * 'C_update_b_b_prod_update_fun$' ) > $o ).

tff('register$aq',type,
    'register$aq': 'A_update_d_d_prod_update_fun$' > $o ).

tff('uue$',type,
    'uue$': 'C_d_prod_update_a_update_fun_set$' > 'C_d_prod_update_a_update_fun_bool_fun$' ).

tff('compatible$ai',type,
    'compatible$ai': ( 'C_update_b_a_prod_update_fun$' * 'A_update_b_a_prod_update_fun$' ) > $o ).

tff('rel_fun$j',type,
    'rel_fun$j': ( 'C_update_a_update_fun_d_update_a_update_fun_bool_fun_fun$' * 'C_update_b_update_fun_d_update_b_update_fun_bool_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_fun_d_update_a_update_fun_d_update_b_update_fun_fun_bool_fun_fun$' ).

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

tff('fun_app$p',type,
    'fun_app$p': ( 'C_update_b_d_prod_update_fun$' * 'C_update$' ) > 'B_d_prod_update$' ).

tff('map_prod$o',type,
    'map_prod$o': ( 'D_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'D_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

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

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

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

tff('comp$ce',type,
    'comp$ce': ( 'A_update_c_d_prod_update_fun$' * 'B_update_a_update_fun$' ) > 'B_update_c_d_prod_update_fun$' ).

tff('member$a',type,
    'member$a': ( 'D_update$' * 'D_update_set$' ) > $o ).

tff('image$a',type,
    'image$a': ( 'D_update_a_update_fun$' * 'D_update_set$' ) > 'A_update_set$' ).

tff('register_pair$m',type,
    'register_pair$m': ( 'A_update_a_update_fun$' * 'B_update_a_update_fun$' ) > 'A_b_prod_update_a_update_fun$' ).

tff('fun_app$d',type,
    'fun_app$d': ( 'A_update_a_c_prod_update_fun$' * 'A_update$' ) > 'A_c_prod_update$' ).

tff('grp$b',type,
    'grp$b': ( 'C_d_prod_update_a_update_fun_set$' * 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ).

tff('rel_fun$p',type,
    'rel_fun$p': ( 'C_d_prod_update_c_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ).

tff('fun_app$dc',type,
    'fun_app$dc': ( 'C_update_c_update_prod_b_update_b_update_prod_fun$' * 'C_update_c_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('fcomp$f',type,
    'fcomp$f': ( 'C_d_prod_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'C_d_prod_update_b_update_fun$' ).

tff('uuj$',type,
    'uuj$': 'B_update_b_update_fun$' > 'B_update_b_d_prod_update_fun$' ).

tff('fun_app$aq',type,
    'fun_app$aq': ( 'A_update_b_update_fun_bool_fun$' * 'A_update_b_update_fun$' ) > $o ).

tff('comp$g',type,
    'comp$g': ( 'B_update_b_update_fun$' * 'A_update_b_update_fun$' ) > 'A_update_b_update_fun$' ).

tff('uvv$',type,
    'uvv$': 'D_update_bool_fun$' ).

tff('preregister$a',type,
    'preregister$a': 'C_update_a_update_fun_bool_fun$' ).

tff('relcompp$',type,
    'relcompp$': ( 'B_update_a_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'B_update_b_update_bool_fun_fun$' ).

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

tff('uuz$',type,
    'uuz$': 'C_update_b_update_fun$' > 'C_update_b_b_prod_update_fun$' ).

tff('preregister$k',type,
    'preregister$k': 'B_update_b_update_fun$' > $o ).

tff('comp$p',type,
    'comp$p': ( 'B_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'D_update_b_update_fun$' ).

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

tff('fun_app$bx',type,
    'fun_app$bx': ( 'C_update_c_update_fun$' * 'C_update$' ) > 'C_update$' ).

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

tff('compatible$ac',type,
    'compatible$ac': ( 'C_update_a_update_fun$' * 'A_update_a_update_fun$' ) > $o ).

tff('type_definition$d',type,
    'type_definition$d': ( 'D_update_c_update_fun$' * 'C_update_d_update_fun$' * 'C_update_set$' ) > $o ).

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

tff('register$ba',type,
    'register$ba': 'B_update_d_b_prod_update_fun$' > $o ).

tff('register_tensor$n',type,
    'register_tensor$n': ( 'D_update_a_update_fun$' * 'D_update_b_update_fun$' ) > 'D_d_prod_update_a_b_prod_update_fun$' ).

tff('map_prod$m',type,
    'map_prod$m': ( 'D_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'D_update_c_update_prod_b_update_b_update_prod_fun$' ).

tff('id_update$b',type,
    'id_update$b': 'C_update$' ).

tff('comp$ba',type,
    'comp$ba': ( 'C_d_prod_update_b_update_fun$' * 'C_update_c_d_prod_update_fun$' ) > 'C_update_b_update_fun$' ).

tff('register$at',type,
    'register$at': 'A_update_b_b_prod_update_fun$' > $o ).

tff('type_definition$e',type,
    'type_definition$e': ( 'D_update_d_update_fun$' * 'D_update_d_update_fun$' * 'D_update_set$' ) > $o ).

tff('comp$o',type,
    'comp$o': ( 'A_b_prod_update_b_update_fun$' * 'D_d_prod_update_a_b_prod_update_fun$' ) > 'D_d_prod_update_b_update_fun$' ).

tff('relcompp$m',type,
    'relcompp$m': ( 'D_update_a_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'D_update_b_update_bool_fun_fun$' ).

tff('uwe$',type,
    'uwe$': 'A_update_a_update_bool_fun_fun$' ).

tff('map_prod$q',type,
    'map_prod$q': ( 'D_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'D_update_d_update_prod_b_update_b_update_prod_fun$' ).

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

tff('comp$c',type,
    'comp$c': ( 'B_update_a_update_fun$' * 'C_update_b_update_fun$' ) > 'C_update_a_update_fun$' ).

tff('comp$al',type,
    'comp$al': ( 'C_update_b_update_fun$' * 'D_update_c_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('image$',type,
    'image$': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update_set$' ) > 'A_update_set$' ).

tff('comp$am',type,
    'comp$am': ( 'A_update_b_update_fun$' * 'A_update_a_update_fun$' ) > 'A_update_b_update_fun$' ).

tff('fun_app$bi',type,
    'fun_app$bi': ( 'B_update_d_update_fun$' * 'B_update$' ) > 'D_update$' ).

tff('register_pair$o',type,
    'register_pair$o': ( 'B_update_d_update_fun$' * 'A_update_d_update_fun$' * 'B_a_prod_update$' ) > 'D_update$' ).

tff('map_prod$c',type,
    'map_prod$c': ( 'C_update_b_update_fun$' * 'C_d_prod_update_b_update_fun$' ) > 'C_update_c_d_prod_update_prod_b_update_b_update_prod_fun$' ).

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

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

tff('type_definition$',type,
    'type_definition$': ( 'A_update_a_update_fun$' * 'A_update_a_update_fun$' * 'A_update_set$' ) > $o ).

tff('member$',type,
    'member$': ( 'C_d_prod_update$' * 'C_d_prod_update_set$' ) > $o ).

tff('fun_app$y',type,
    'fun_app$y': ( 'B_update_b_b_prod_update_fun$' * 'B_update$' ) > 'B_b_prod_update$' ).

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

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

tff('register_tensor$x',type,
    'register_tensor$x': ( 'C_d_prod_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_d_prod_c_prod_update_a_a_prod_update_fun$' ).

tff('fcomp$d',type,
    'fcomp$d': ( 'B_update_c_update_fun_a_update_a_update_fun_fun$' * 'A_update_a_update_fun_c_update_b_update_fun_fun$' ) > 'B_update_c_update_fun_c_update_b_update_fun_fun$' ).

tff('fun_app$dm',type,
    'fun_app$dm': ( 'C_d_prod_update_d_update_prod_b_update_b_update_prod_fun$' * 'C_d_prod_update_d_update_prod$' ) > 'B_update_b_update_prod$' ).

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

tff('register_pair$u',type,
    'register_pair$u': ( 'A_update_b_a_prod_update_fun$' * 'D_update_b_a_prod_update_fun$' ) > 'A_d_prod_update_b_a_prod_update_fun$' ).

tff('fun_app$do',type,
    'fun_app$do': ( 'D_update_c_update_prod_b_update_b_update_prod_fun$' * 'D_update_c_update_prod$' ) > 'B_update_b_update_prod$' ).

tff('pred_fun$c',type,
    'pred_fun$c': ( 'C_d_prod_update_bool_fun$' * 'A_update_bool_fun$' ) > 'C_d_prod_update_a_update_fun_bool_fun$' ).

tff('fun_app$dp',type,
    'fun_app$dp': ( 'D_update_c_d_prod_update_prod_a_update_a_update_prod_fun$' * 'D_update_c_d_prod_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('fun_app$af',type,
    'fun_app$af': ( 'A_update_b_b_prod_update_fun$' * 'A_update$' ) > 'B_b_prod_update$' ).

tff('fun_app$ap',type,
    'fun_app$ap': ( 'A_update_a_update_bool_fun_fun$' * 'A_update$' ) > 'A_update_bool_fun$' ).

tff('collect$a',type,
    'collect$a': 'D_update_bool_fun$' > 'D_update_set$' ).

tff('comp$bn',type,
    'comp$bn': ( 'A_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' ) > 'B_update_c_d_prod_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('tensor_update$i',type,
    'tensor_update$i': ( 'D_update$' * 'B_update$' ) > 'D_b_prod_update$' ).

tff('rel_fun$e',type,
    'rel_fun$e': ( 'A_update_b_update_fun_a_update_b_update_fun_bool_fun_fun$' * 'C_update_a_update_fun_c_update_b_update_fun_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_bool_fun_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' ) > $o ).

tff('comp$n',type,
    'comp$n': ( 'A_b_prod_update_b_update_fun$' * 'D_a_prod_update_a_b_prod_update_fun$' ) > 'D_a_prod_update_b_update_fun$' ).

tff('fun_app$i',type,
    'fun_app$i': ( 'C_d_prod_update_a_update_fun_bool_fun$' * 'C_d_prod_update_a_update_fun$' ) > $o ).

tff('fun_app$o',type,
    'fun_app$o': ( 'D_update_b_a_prod_update_fun$' * 'D_update$' ) > 'B_a_prod_update$' ).

tff('compatible$e',type,
    'compatible$e': ( 'A_update_a_update_fun$' * 'B_update_a_update_fun$' ) > $o ).

tff('relcompp$a',type,
    'relcompp$a': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_b_update_bool_fun_fun$' ) > 'A_update_b_update_bool_fun_fun$' ).

tff('comp$ab',type,
    'comp$ab': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'D_c_prod_update_a_a_prod_update_fun$' ) > 'D_c_prod_update_b_b_prod_update_fun$' ).

tff('rel_fun$d',type,
    'rel_fun$d': ( 'C_update_c_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ).

tff('relcompp$i',type,
    'relcompp$i': ( 'A_update_a_update_bool_fun_fun$' * 'A_update_c_d_prod_update_bool_fun_fun$' ) > 'A_update_c_d_prod_update_bool_fun_fun$' ).

tff('comp$ah',type,
    'comp$ah': ( 'A_a_prod_update_b_b_prod_update_fun$' * 'C_c_d_prod_prod_update_a_a_prod_update_fun$' ) > 'C_c_d_prod_prod_update_b_b_prod_update_fun$' ).

tff('register_tensor$e',type,
    'register_tensor$e': ( 'C_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_c_prod_update_b_b_prod_update_fun$' ).

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

tff('fun_app$co',type,
    'fun_app$co': ( 'A_update_a_update_fun_d_update_b_update_fun_fun$' * 'A_update_a_update_fun$' ) > 'D_update_b_update_fun$' ).

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

tff('register_tensor$u',type,
    'register_tensor$u': ( 'C_d_prod_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'C_d_prod_d_prod_update_b_b_prod_update_fun$' ).

tff('member$e',type,
    'member$e': ( 'D_update_a_update_fun$' * 'D_update_a_update_fun_set$' ) > $o ).

tff('rel_fun$n',type,
    'rel_fun$n': ( 'C_d_prod_update_a_update_fun_c_update_a_update_fun_bool_fun_fun$' * 'C_d_prod_update_b_update_fun_c_update_b_update_fun_bool_fun_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_c_update_a_update_fun_c_update_b_update_fun_fun_bool_fun_fun$' ).

tff('uvz$',type,
    'uvz$': 'D_update_d_update_bool_fun_fun$' ).

tff('register$e',type,
    'register$e': 'D_update_a_update_fun_bool_fun$' ).

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

tff('map_prod$g',type,
    'map_prod$g': ( 'C_d_prod_update_b_update_fun$' * 'C_update_b_update_fun$' ) > 'C_d_prod_update_c_update_prod_b_update_b_update_prod_fun$' ).

tff('fun_app$be',type,
    'fun_app$be': ( 'C_update_a_update_fun_c_update_b_update_fun_fun$' * 'C_update_a_update_fun$' ) > 'C_update_b_update_fun$' ).

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

tff('compatible$ah',type,
    'compatible$ah': ( 'C_update_b_a_prod_update_fun$' * 'C_update_b_a_prod_update_fun$' ) > $o ).

tff('collect$d',type,
    'collect$d': 'D_update_a_update_fun_bool_fun$' > 'D_update_a_update_fun_set$' ).

tff('register_tensor$ab',type,
    'register_tensor$ab': ( 'C_d_prod_update_a_update_fun$' * 'C_d_prod_update_a_update_fun$' ) > 'C_d_prod_c_d_prod_prod_update_a_a_prod_update_fun$' ).

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

tff('compatible$ao',type,
    'compatible$ao': ( 'A_update_a_b_prod_update_fun$' * 'C_update_a_b_prod_update_fun$' ) > $o ).

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

tff('fun_app$cf',type,
    'fun_app$cf': ( 'C_c_prod_update_a_update_fun$' * 'C_c_prod_update$' ) > 'A_update$' ).

tff('relcompp$k',type,
    'relcompp$k': ( 'D_update_a_update_bool_fun_fun$' * 'A_update_d_update_bool_fun_fun$' ) > 'D_update_d_update_bool_fun_fun$' ).

tff('fcomp$g',type,
    'fcomp$g': ( 'D_update_a_update_fun$' * 'A_update_b_update_fun$' ) > 'D_update_b_update_fun$' ).

tff('comp$q',type,
    'comp$q': ( 'A_a_prod_update_b_update_fun$' * 'C_c_prod_update_a_a_prod_update_fun$' ) > 'C_c_prod_update_b_update_fun$' ).

tff('compatible$u',type,
    'compatible$u': ( 'B_update_b_update_fun$' * 'B_update_b_update_fun$' ) > $o ).

tff('comp_update$h',type,
    'comp_update$h': ( 'D_a_prod_update$' * 'D_a_prod_update$' ) > 'D_a_prod_update$' ).

tff('register$ad',type,
    'register$ad': 'A_b_prod_update_a_update_fun$' > $o ).

tff('less_eq$',type,
    'less_eq$': ( 'A_update_set$' * 'A_update_set$' ) > $o ).

tff('fun_app$df',type,
    'fun_app$df': ( 'C_update_d_update_prod_a_update_a_update_prod_fun$' * 'C_update_d_update_prod$' ) > 'A_update_a_update_prod$' ).

tff('fun_app$ci',type,
    'fun_app$ci': ( 'A_c_prod_update_b_update_fun$' * 'A_c_prod_update$' ) > 'B_update$' ).

tff('fun_app$z',type,
    'fun_app$z': ( 'A_update_d_d_prod_update_fun$' * 'A_update$' ) > 'D_d_prod_update$' ).

tff('fun_app$dx',type,
    'fun_app$dx': ( 'B_update_c_d_prod_update_fun_d_update_b_update_fun_fun$' * 'B_update_c_d_prod_update_fun$' ) > 'D_update_b_update_fun$' ).

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

tff('comp$b',type,
    'comp$b': ( 'A_update_a_update_fun$' * 'C_update_a_update_fun$' ) > 'C_update_a_update_fun$' ).

tff('register$bf',type,
    'register$bf': 'D_update_a_d_prod_update_fun$' > $o ).

tff('fun_app$ak',type,
    'fun_app$ak': ( 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' * 'C_d_prod_update$' ) > 'C_d_prod_update_bool_fun$' ).

tff('type_definition$g',type,
    'type_definition$g': ( 'B_update_a_update_fun$' * 'A_update_b_update_fun$' * 'A_update_set$' ) > $o ).

tff('comp$ar',type,
    'comp$ar': ( 'D_update_a_update_fun$' * 'A_update_d_update_fun$' ) > 'A_update_a_update_fun$' ).

tff('fcomp$b',type,
    'fcomp$b': ( 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$' * 'A_update_a_update_fun_c_update_b_update_fun_fun$' ) > 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$' ).

tff('top$d',type,
    'top$d': 'B_update_set$' ).

tff('fun_app$j',type,
    'fun_app$j': ( 'D_update_a_update_fun_bool_fun$' * 'D_update_a_update_fun$' ) > $o ).

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

tff('map_prod$e',type,
    'map_prod$e': ( 'C_update_b_update_fun$' * 'D_update_b_update_fun$' ) > 'C_update_d_update_prod_b_update_b_update_prod_fun$' ).

tff('rel_fun$t',type,
    'rel_fun$t': ( 'C_d_prod_update_c_d_prod_update_bool_fun_fun$' * 'B_update_b_update_bool_fun_fun$' ) > 'C_d_prod_update_b_update_fun_c_d_prod_update_b_update_fun_bool_fun_fun$' ).

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

tff('fun_app$bk',type,
    'fun_app$bk': ( 'A_update_b_update_fun_c_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun_fun$' * 'A_update_b_update_fun$' ) > 'C_d_prod_update_a_update_fun_c_d_prod_update_b_update_fun_fun$' ).

tff('fun_app$at',type,
    'fun_app$at': ( 'D_update_a_b_prod_update_fun$' * 'D_update$' ) > 'A_b_prod_update$' ).

tff('fun_app$ct',type,
    'fun_app$ct': ( 'A_update_a_update_fun_c_update_b_update_fun_fun$' * 'A_update_a_update_fun$' ) > 'C_update_b_update_fun$' ).

%% Assertions:
%% ∀ ?v0:B_update$ (fun_app$(uva$, ?v0) = fun_app$a(tensor_update$(?v0), id_update$))
tff(axiom0,axiom,
    ! [A__questionmark_v0: 'B_update$'] : 'fun_app$'('uva$',A__questionmark_v0) = 'fun_app$a'('tensor_update$'(A__questionmark_v0),'id_update$') ).

%% ∀ ?v0:A_update$ (fun_app$b(uvb$, ?v0) = fun_app$c(tensor_update$a(?v0), id_update$a))
tff(axiom1,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$b'('uvb$',A__questionmark_v0) = 'fun_app$c'('tensor_update$a'(A__questionmark_v0),'id_update$a') ).

%% ∀ ?v0:A_update$ (fun_app$d(uvc$, ?v0) = fun_app$e(tensor_update$b(?v0), id_update$b))
tff(axiom2,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$d'('uvc$',A__questionmark_v0) = 'fun_app$e'('tensor_update$b'(A__questionmark_v0),'id_update$b') ).

%% ∀ ?v0:A_update$ (fun_app$f(uvd$, ?v0) = fun_app$g(tensor_update$c(?v0), id_update$c))
tff(axiom3,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$f'('uvd$',A__questionmark_v0) = 'fun_app$g'('tensor_update$c'(A__questionmark_v0),'id_update$c') ).

%% ∀ ?v0:A_update$ (fun_app$h(uve$, ?v0) = fun_app$h(tensor_update$d(?v0), id_update$))
tff(axiom4,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$h'('uve$',A__questionmark_v0) = 'fun_app$h'('tensor_update$d'(A__questionmark_v0),'id_update$') ).

%% ∀ ?v0:A_update_set$ ?v1:C_d_prod_update_a_update_fun$ (fun_app$i(uwb$(?v0), ?v1) = less_eq$(image$(?v1, top$), ?v0))
tff(axiom5,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$'] :
      ( 'fun_app$i'('uwb$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'less_eq$'('image$'(A__questionmark_v1,'top$'),A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_set$ ?v1:D_update_a_update_fun$ (fun_app$j(uwc$(?v0), ?v1) = less_eq$(image$a(?v1, top$a), ?v0))
tff(axiom6,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('uwc$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'less_eq$'('image$a'(A__questionmark_v1,'top$a'),A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_set$ ?v1:C_update_a_update_fun$ (fun_app$k(uwa$(?v0), ?v1) = less_eq$(image$b(?v1, top$b), ?v0))
tff(axiom7,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('uwa$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'less_eq$'('image$b'(A__questionmark_v1,'top$b'),A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$l(uui$(?v0), ?v1) = tensor_update$e(fun_app$m(?v0, ?v1), id_update$a))
tff(axiom8,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$l'('uui$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$e'('fun_app$m'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$n(uuo$(?v0), ?v1) = tensor_update$f(fun_app$m(?v0, ?v1), id_update$c))
tff(axiom9,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$n'('uuo$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('fun_app$m'(A__questionmark_v0,A__questionmark_v1),'id_update$c') ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$o(uvn$(?v0), ?v1) = fun_app$a(tensor_update$(fun_app$m(?v0, ?v1)), id_update$))
tff(axiom10,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$o'('uvn$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('tensor_update$'('fun_app$m'(A__questionmark_v0,A__questionmark_v1)),'id_update$') ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$p(uug$(?v0), ?v1) = tensor_update$e(fun_app$q(?v0, ?v1), id_update$a))
tff(axiom11,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$p'('uug$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$e'('fun_app$q'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$r(uum$(?v0), ?v1) = tensor_update$f(fun_app$q(?v0, ?v1), id_update$c))
tff(axiom12,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$r'('uum$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('fun_app$q'(A__questionmark_v0,A__questionmark_v1),'id_update$c') ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$s(uvm$(?v0), ?v1) = fun_app$a(tensor_update$(fun_app$q(?v0, ?v1)), id_update$))
tff(axiom13,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$s'('uvm$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('tensor_update$'('fun_app$q'(A__questionmark_v0,A__questionmark_v1)),'id_update$') ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ (fun_app$t(uvp$(?v0), ?v1) = fun_app$g(tensor_update$c(fun_app$u(?v0, ?v1)), id_update$c))
tff(axiom14,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$t'('uvp$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$g'('tensor_update$c'('fun_app$u'(A__questionmark_v0,A__questionmark_v1)),'id_update$c') ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ (fun_app$v(uvl$(?v0), ?v1) = fun_app$h(tensor_update$d(fun_app$u(?v0, ?v1)), id_update$))
tff(axiom15,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$v'('uvl$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$h'('tensor_update$d'('fun_app$u'(A__questionmark_v0,A__questionmark_v1)),'id_update$') ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:B_update$ (fun_app$w(uuj$(?v0), ?v1) = tensor_update$e(fun_app$x(?v0, ?v1), id_update$a))
tff(axiom16,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'B_update$'] : 'fun_app$w'('uuj$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$e'('fun_app$x'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:B_update$ (fun_app$y(uup$(?v0), ?v1) = tensor_update$f(fun_app$x(?v0, ?v1), id_update$c))
tff(axiom17,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'B_update$'] : 'fun_app$y'('uup$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('fun_app$x'(A__questionmark_v0,A__questionmark_v1),'id_update$c') ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:A_update$ (fun_app$z(uuk$(?v0), ?v1) = tensor_update$g(fun_app$aa(?v0, ?v1), id_update$a))
tff(axiom18,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$z'('uuk$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$g'('fun_app$aa'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:A_update$ (fun_app$ab(uul$(?v0), ?v1) = tensor_update$h(fun_app$ac(?v0, ?v1), id_update$a))
tff(axiom19,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$ab'('uul$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$h'('fun_app$ac'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$ad(uuh$(?v0), ?v1) = tensor_update$e(fun_app$ae(?v0, ?v1), id_update$a))
tff(axiom20,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$ad'('uuh$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$e'('fun_app$ae'(A__questionmark_v0,A__questionmark_v1),'id_update$a') ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$af(uun$(?v0), ?v1) = tensor_update$f(fun_app$ae(?v0, ?v1), id_update$c))
tff(axiom21,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$af'('uun$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('fun_app$ae'(A__questionmark_v0,A__questionmark_v1),'id_update$c') ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$a(uvg$(?v0), ?v1) = fun_app$a(tensor_update$(fun_app$ae(?v0, ?v1)), id_update$))
tff(axiom22,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$a'('uvg$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('tensor_update$'('fun_app$ae'(A__questionmark_v0,A__questionmark_v1)),'id_update$') ).

%% ∀ ?v0:C_d_prod_update_set$ ?v1:C_d_prod_update$ (fun_app$ag(uu$(?v0), ?v1) = member$(?v1, ?v0))
tff(axiom23,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_set$',A__questionmark_v1: 'C_d_prod_update$'] :
      ( 'fun_app$ag'('uu$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_set$ ?v1:D_update$ (fun_app$ah(uua$(?v0), ?v1) = member$a(?v1, ?v0))
tff(axiom24,axiom,
    ! [A__questionmark_v0: 'D_update_set$',A__questionmark_v1: 'D_update$'] :
      ( 'fun_app$ah'('uua$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$a'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_set$ ?v1:C_update$ (fun_app$ai(uub$(?v0), ?v1) = member$b(?v1, ?v0))
tff(axiom25,axiom,
    ! [A__questionmark_v0: 'C_update_set$',A__questionmark_v1: 'C_update$'] :
      ( 'fun_app$ai'('uub$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$b'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_set$ ?v1:A_update$ (fun_app$aj(uuc$(?v0), ?v1) = member$c(?v1, ?v0))
tff(axiom26,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'A_update$'] :
      ( 'fun_app$aj'('uuc$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$c'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun_set$ ?v1:C_d_prod_update_a_update_fun$ (fun_app$i(uue$(?v0), ?v1) = member$d(?v1, ?v0))
tff(axiom27,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun_set$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$'] :
      ( 'fun_app$i'('uue$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$d'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_a_update_fun_set$ ?v1:D_update_a_update_fun$ (fun_app$j(uud$(?v0), ?v1) = member$e(?v1, ?v0))
tff(axiom28,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun_set$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('uud$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$e'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_a_update_fun_set$ ?v1:C_update_a_update_fun$ (fun_app$k(uuf$(?v0), ?v1) = member$f(?v1, ?v0))
tff(axiom29,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun_set$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('uuf$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$f'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_d_prod_update$ ?v1:C_d_prod_update$ (fun_app$ag(fun_app$ak(uvy$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom30,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update$',A__questionmark_v1: 'C_d_prod_update$'] :
      ( 'fun_app$ag'('fun_app$ak'('uvy$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:D_update$ ?v1:D_update$ (fun_app$ah(fun_app$al(uvz$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom31,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'D_update$'] :
      ( 'fun_app$ah'('fun_app$al'('uvz$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:C_update$ ?v1:C_update$ (fun_app$ai(fun_app$am(uvx$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom32,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'C_update$'] :
      ( 'fun_app$ai'('fun_app$am'('uvx$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:B_update$ ?v1:B_update$ (fun_app$an(fun_app$ao(uwf$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom33,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'B_update$'] :
      ( 'fun_app$an'('fun_app$ao'('uwf$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A_update$ ?v1:A_update$ (fun_app$aj(fun_app$ap(uwe$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom34,axiom,
    ! [A__questionmark_v0: 'A_update$',A__questionmark_v1: 'A_update$'] :
      ( 'fun_app$aj'('fun_app$ap'('uwe$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (fun_app$aq(fun_app$ar(uwd$, ?v0), ?v1) = (?v0 = ?v1))
tff(axiom35,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'fun_app$aq'('fun_app$ar'('uwd$',A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$as(uut$(?v0), ?v1) = tensor_update$i(id_update$a, fun_app$m(?v0, ?v1)))
tff(axiom36,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$as'('uut$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$i'('id_update$a','fun_app$m'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$n(uvf$(?v0), ?v1) = tensor_update$f(id_update$c, fun_app$m(?v0, ?v1)))
tff(axiom37,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$n'('uvf$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('id_update$c','fun_app$m'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ (fun_app$at(uvr$(?v0), ?v1) = fun_app$g(tensor_update$c(id_update$), fun_app$m(?v0, ?v1)))
tff(axiom38,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$at'('uvr$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$g'('tensor_update$c'('id_update$'),'fun_app$m'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update$ (fun_app$o(uvh$(?v0), ?v1) = fun_app$a(tensor_update$(id_update$c), fun_app$au(?v0, ?v1)))
tff(axiom39,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update$'] : 'fun_app$o'('uvh$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('tensor_update$'('id_update$c'),'fun_app$au'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$av(uur$(?v0), ?v1) = tensor_update$i(id_update$a, fun_app$q(?v0, ?v1)))
tff(axiom40,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$av'('uur$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$i'('id_update$a','fun_app$q'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$r(uuz$(?v0), ?v1) = tensor_update$f(id_update$c, fun_app$q(?v0, ?v1)))
tff(axiom41,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$r'('uuz$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('id_update$c','fun_app$q'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ (fun_app$t(uvo$(?v0), ?v1) = fun_app$g(tensor_update$c(id_update$), fun_app$q(?v0, ?v1)))
tff(axiom42,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$t'('uvo$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$g'('tensor_update$c'('id_update$'),'fun_app$q'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ (fun_app$aw(uuq$(?v0), ?v1) = tensor_update$j(id_update$a, fun_app$u(?v0, ?v1)))
tff(axiom43,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$aw'('uuq$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$j'('id_update$a','fun_app$u'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ (fun_app$s(uvi$(?v0), ?v1) = fun_app$a(tensor_update$(id_update$c), fun_app$u(?v0, ?v1)))
tff(axiom44,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$s'('uvi$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('tensor_update$'('id_update$c'),'fun_app$u'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ (fun_app$v(uvk$(?v0), ?v1) = fun_app$h(tensor_update$d(id_update$), fun_app$u(?v0, ?v1)))
tff(axiom45,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$'] : 'fun_app$v'('uvk$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$h'('tensor_update$d'('id_update$'),'fun_app$u'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:B_update$ (fun_app$ax(uuu$(?v0), ?v1) = tensor_update$i(id_update$a, fun_app$x(?v0, ?v1)))
tff(axiom46,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'B_update$'] : 'fun_app$ax'('uuu$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$i'('id_update$a','fun_app$x'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:B_update$ (fun_app$ay(uuv$(?v0), ?v1) = tensor_update$j(id_update$a, fun_app$az(?v0, ?v1)))
tff(axiom47,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'B_update$'] : 'fun_app$ay'('uuv$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$j'('id_update$a','fun_app$az'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:A_update$ (fun_app$z(uuw$(?v0), ?v1) = tensor_update$g(id_update$a, fun_app$aa(?v0, ?v1)))
tff(axiom48,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$z'('uuw$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$g'('id_update$a','fun_app$aa'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:A_update$ (fun_app$ba(uux$(?v0), ?v1) = tensor_update$k(id_update$a, fun_app$ac(?v0, ?v1)))
tff(axiom49,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$ba'('uux$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$k'('id_update$a','fun_app$ac'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$bb(uus$(?v0), ?v1) = tensor_update$i(id_update$a, fun_app$ae(?v0, ?v1)))
tff(axiom50,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$bb'('uus$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$i'('id_update$a','fun_app$ae'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$af(uvj$(?v0), ?v1) = tensor_update$f(id_update$c, fun_app$ae(?v0, ?v1)))
tff(axiom51,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$af'('uvj$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$f'('id_update$c','fun_app$ae'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ (fun_app$f(uvq$(?v0), ?v1) = fun_app$g(tensor_update$c(id_update$), fun_app$ae(?v0, ?v1)))
tff(axiom52,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$f'('uvq$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$g'('tensor_update$c'('id_update$'),'fun_app$ae'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update$ (fun_app$bc(uuy$(?v0), ?v1) = tensor_update$j(id_update$a, fun_app$bd(?v0, ?v1)))
tff(axiom53,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update$'] : 'fun_app$bc'('uuy$'(A__questionmark_v0),A__questionmark_v1) = 'tensor_update$j'('id_update$a','fun_app$bd'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update$ (fun_app$aj(uvw$(?v0, ?v1), ?v2) = (fun_app$ae(?v0, ?v2) = fun_app$ae(?v1, ?v2)))
tff(axiom54,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update$'] :
      ( 'fun_app$aj'('uvw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( 'fun_app$ae'(A__questionmark_v0,A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:B_update$ ?v1:A_update$ (fun_app$ae(uvs$(?v0), ?v1) = ?v0)
tff(axiom55,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'A_update$'] : 'fun_app$ae'('uvs$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:C_d_prod_update$ (fun_app$ag(uvu$, ?v0) = true)
tff(axiom56,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update$'] :
      ( 'fun_app$ag'('uvu$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:D_update$ (fun_app$ah(uvv$, ?v0) = true)
tff(axiom57,axiom,
    ! [A__questionmark_v0: 'D_update$'] :
      ( 'fun_app$ah'('uvv$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:C_update$ (fun_app$ai(uvt$, ?v0) = true)
tff(axiom58,axiom,
    ! [A__questionmark_v0: 'C_update$'] :
      ( 'fun_app$ai'('uvt$',A__questionmark_v0)
    <=> $true ) ).

%% ¬fun_app$k(register$, g$)
% tff(conjecture59,conjecture,
%     'fun_app$k'('register$','g$') ).

%% fun_app$j(compatible$(g$), h$)
tff(axiom60,axiom,
    'fun_app$j'('compatible$'('g$'),'h$') ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$a(?v0, ?v1) ⇒ register$a(?v0))
tff(axiom61,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
     => 'register$a'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ (compatible$b(?v0, ?v1) ⇒ register$a(?v0))
tff(axiom62,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$'] :
      ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
     => 'register$a'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$c(?v0, ?v1) ⇒ register$a(?v0))
tff(axiom63,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
     => 'register$a'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ register$b(?v0))
tff(axiom64,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => 'register$b'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:B_update_a_update_fun$ (compatible$e(?v0, ?v1) ⇒ register$b(?v0))
tff(axiom65,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'B_update_a_update_fun$'] :
      ( 'compatible$e'(A__questionmark_v0,A__questionmark_v1)
     => 'register$b'(A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$(?v0), ?v1) ⇒ fun_app$k(register$, ?v0))
tff(axiom66,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$k'('register$',A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$f(?v0, ?v1) ⇒ register$c(?v0))
tff(axiom67,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => 'register$c'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$a(?v0, ?v1) ⇒ register$c(?v1))
tff(axiom68,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
     => 'register$c'(A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ (compatible$b(?v0, ?v1) ⇒ register$d(?v1))
tff(axiom69,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$'] :
      ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
     => 'register$d'(A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$c(?v0, ?v1) ⇒ register$a(?v1))
tff(axiom70,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
     => 'register$a'(A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ fun_app$j(register$e, ?v1))
tff(axiom71,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$j'('register$e',A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:B_update_a_update_fun$ (compatible$e(?v0, ?v1) ⇒ register$f(?v1))
tff(axiom72,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'B_update_a_update_fun$'] :
      ( 'compatible$e'(A__questionmark_v0,A__questionmark_v1)
     => 'register$f'(A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$(?v0), ?v1) ⇒ fun_app$j(register$e, ?v1))
tff(axiom73,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$j'('register$e',A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$f(?v0, ?v1) ⇒ register$g(?v1))
tff(axiom74,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => 'register$g'(A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ fun_app$k(register$, ?v1)) ⇒ register$h(register_tensor$(?v0, ?v1)))
tff(axiom75,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'register$h'('register_tensor$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$c(?v1)) ⇒ register$i(register_tensor$a(?v0, ?v1)))
tff(axiom76,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$i'('register_tensor$a'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$a(?v1)) ⇒ register$j(register_tensor$b(?v0, ?v1)))
tff(axiom77,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'register$j'('register_tensor$b'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$g(?v1)) ⇒ register$k(register_tensor$c(?v0, ?v1)))
tff(axiom78,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'register$k'('register_tensor$c'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$c(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ register$l(register_tensor$d(?v0, ?v1)))
tff(axiom79,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'register$l'('register_tensor$d'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$c(?v0) ∧ register$c(?v1)) ⇒ register$m(register_tensor$e(?v0, ?v1)))
tff(axiom80,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$m'('register_tensor$e'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$c(?v0) ∧ register$a(?v1)) ⇒ register$n(register_tensor$f(?v0, ?v1)))
tff(axiom81,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'register$n'('register_tensor$f'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$c(?v0) ∧ register$g(?v1)) ⇒ register$o(register_tensor$g(?v0, ?v1)))
tff(axiom82,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'register$o'('register_tensor$g'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$a(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ register$p(register_tensor$h(?v0, ?v1)))
tff(axiom83,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'register$p'('register_tensor$h'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$a(?v0) ∧ register$c(?v1)) ⇒ register$q(register_tensor$i(?v0, ?v1)))
tff(axiom84,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$q'('register_tensor$i'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:C_update_a_update_fun$ (fun_app$k(compatible$g(?v0), ?v1) ⇒ fun_app$j(compatible$(?v1), ?v0))
tff(axiom85,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('compatible$g'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$j'('compatible$'(A__questionmark_v1),A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$h(?v0, ?v1) ⇒ compatible$f(?v1, ?v0))
tff(axiom86,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$h'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$f'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$(?v0), ?v1) ⇒ fun_app$k(compatible$g(?v1), ?v0))
tff(axiom87,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$k'('compatible$g'(A__questionmark_v1),A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$f(?v0, ?v1) ⇒ compatible$h(?v1, ?v0))
tff(axiom88,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$h'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$i(?v0, ?v1) ⇒ compatible$a(?v1, ?v0))
tff(axiom89,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$i'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$a'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$j(?v0, ?v1) ⇒ compatible$b(?v1, ?v0))
tff(axiom90,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$j'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$b'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_a_update_fun$ (compatible$k(?v0, ?v1) ⇒ fun_app$j(compatible$d(?v1), ?v0))
tff(axiom91,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$'] :
      ( 'compatible$k'(A__questionmark_v0,A__questionmark_v1)
     => 'fun_app$j'('compatible$d'(A__questionmark_v1),A__questionmark_v0) ) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:A_update_a_update_fun$ (compatible$l(?v0, ?v1) ⇒ compatible$e(?v1, ?v0))
tff(axiom92,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$'] :
      ( 'compatible$l'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$e'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$a(?v0, ?v1) ⇒ compatible$i(?v1, ?v0))
tff(axiom93,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$i'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ (compatible$b(?v0, ?v1) ⇒ compatible$j(?v1, ?v0))
tff(axiom94,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$'] :
      ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
     => 'compatible$j'(A__questionmark_v1,A__questionmark_v0) ) ).

%% register$c(fun_app$be(fun_app$bf(comp$, f$), g$))
tff(axiom95,axiom,
    'register$c'('fun_app$be'('fun_app$bf'('comp$','f$'),'g$')) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ (fun_app$k(register$, ?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$u(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v1, ?v3)), fun_app$u(?v0, ?v2))))) ⇒ fun_app$k(compatible$m(?v0), ?v1))
tff(axiom96,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) )
     => 'fun_app$k'('compatible$m'(A__questionmark_v0),A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$c(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$q(?v0, ?v2))))) ⇒ compatible$n(?v0, ?v1))
tff(axiom97,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$n'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$c(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:C_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$q(?v0, ?v2))))) ⇒ compatible$i(?v0, ?v1))
tff(axiom98,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$i'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$a(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:A_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ compatible$a(?v0, ?v1))
tff(axiom99,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$a'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:A_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ compatible$c(?v0, ?v1))
tff(axiom100,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$c'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$a(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:A_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ compatible$o(?v0, ?v1))
tff(axiom101,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$o'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$g(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:D_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ compatible$h(?v0, ?v1))
tff(axiom102,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$h'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$g(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:D_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ compatible$p(?v0, ?v1))
tff(axiom103,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$p'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$g(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:D_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ compatible$q(?v0, ?v1))
tff(axiom104,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'compatible$q'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ (fun_app$j(register$e, ?v1) ∧ ∀ ?v2:C_update$ ?v3:D_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$u(?v0, ?v2))))) ⇒ fun_app$j(compatible$(?v0), ?v1))
tff(axiom105,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$j'('register$e',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) )
     => 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ (fun_app$k(compatible$m(?v0), ?v1) = (fun_app$k(register$, ?v0) ∧ (fun_app$k(register$, ?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$u(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v1, ?v3)), fun_app$u(?v0, ?v2))))))
tff(axiom106,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('compatible$m'(A__questionmark_v0),A__questionmark_v1)
    <=> ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$n(?v0, ?v1) = (register$c(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$q(?v0, ?v2))))))
tff(axiom107,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$n'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$i(?v0, ?v1) = (register$c(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:C_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$q(?v0, ?v2))))))
tff(axiom108,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$i'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$a(?v0, ?v1) = (register$a(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:A_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$ae(?v0, ?v2))))))
tff(axiom109,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$c(?v0, ?v1) = (register$a(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:A_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$ae(?v0, ?v2))))))
tff(axiom110,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$o(?v0, ?v1) = (register$a(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:A_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$ae(?v0, ?v2))))))
tff(axiom111,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$a'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$h(?v0, ?v1) = (register$g(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:D_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$m(?v0, ?v2))))))
tff(axiom112,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$h'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$g'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$p(?v0, ?v1) = (register$g(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:D_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$m(?v0, ?v2))))))
tff(axiom113,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$p'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$g'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$q(?v0, ?v1) = (register$g(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:D_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$m(?v0, ?v2))))))
tff(axiom114,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$q'(A__questionmark_v0,A__questionmark_v1)
    <=> ( 'register$g'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$(?v0), ?v1) = (fun_app$k(register$, ?v0) ∧ (fun_app$j(register$e, ?v1) ∧ ∀ ?v2:C_update$ ?v3:D_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$u(?v0, ?v2))))))
tff(axiom115,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
    <=> ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$j'('register$e',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ (fun_app$k(register$, ?v0) ⇒ (fun_app$u(?v0, id_update$b) = id_update$))
tff(axiom116,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('register$',A__questionmark_v0)
     => ( 'fun_app$u'(A__questionmark_v0,'id_update$b') = 'id_update$' ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ (fun_app$q(?v0, id_update$b) = id_update$c))
tff(axiom117,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => ( 'fun_app$q'(A__questionmark_v0,'id_update$b') = 'id_update$c' ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ (register$a(?v0) ⇒ (fun_app$ae(?v0, id_update$) = id_update$c))
tff(axiom118,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$'] :
      ( 'register$a'(A__questionmark_v0)
     => ( 'fun_app$ae'(A__questionmark_v0,'id_update$') = 'id_update$c' ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ (register$g(?v0) ⇒ (fun_app$m(?v0, id_update$a) = id_update$c))
tff(axiom119,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$'] :
      ( 'register$g'(A__questionmark_v0)
     => ( 'fun_app$m'(A__questionmark_v0,'id_update$a') = 'id_update$c' ) ) ).

%% ∀ ?v0:D_update_d_update_fun$ (register$r(?v0) ⇒ (fun_app$bg(?v0, id_update$a) = id_update$a))
tff(axiom120,axiom,
    ! [A__questionmark_v0: 'D_update_d_update_fun$'] :
      ( 'register$r'(A__questionmark_v0)
     => ( 'fun_app$bg'(A__questionmark_v0,'id_update$a') = 'id_update$a' ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ (fun_app$j(register$e, ?v0) ⇒ (fun_app$au(?v0, id_update$a) = id_update$))
tff(axiom121,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('register$e',A__questionmark_v0)
     => ( 'fun_app$au'(A__questionmark_v0,'id_update$a') = 'id_update$' ) ) ).

%% ∀ ?v0:D_update_c_update_fun$ (register$s(?v0) ⇒ (fun_app$bh(?v0, id_update$a) = id_update$b))
tff(axiom122,axiom,
    ! [A__questionmark_v0: 'D_update_c_update_fun$'] :
      ( 'register$s'(A__questionmark_v0)
     => ( 'fun_app$bh'(A__questionmark_v0,'id_update$a') = 'id_update$b' ) ) ).

%% ∀ ?v0:B_update_d_update_fun$ (register$t(?v0) ⇒ (fun_app$bi(?v0, id_update$c) = id_update$a))
tff(axiom123,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun$'] :
      ( 'register$t'(A__questionmark_v0)
     => ( 'fun_app$bi'(A__questionmark_v0,'id_update$c') = 'id_update$a' ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ (register$d(?v0) ⇒ (fun_app$x(?v0, id_update$c) = id_update$c))
tff(axiom124,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$'] :
      ( 'register$d'(A__questionmark_v0)
     => ( 'fun_app$x'(A__questionmark_v0,'id_update$c') = 'id_update$c' ) ) ).

%% ∀ ?v0:B_update_a_update_fun$ (register$f(?v0) ⇒ (fun_app$az(?v0, id_update$c) = id_update$))
tff(axiom125,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$'] :
      ( 'register$f'(A__questionmark_v0)
     => ( 'fun_app$az'(A__questionmark_v0,'id_update$c') = 'id_update$' ) ) ).

%% preregister$(fun_app$bj(fun_app$bk(comp$a, f$), register_pair$(g$, h$)))
tff(axiom126,axiom,
    'preregister$'('fun_app$bj'('fun_app$bk'('comp$a','f$'),'register_pair$'('g$','h$'))) ).

%% ∀ ?v0:C_update_a_update_fun$ (fun_app$k(register$, ?v0) ⇒ fun_app$k(preregister$a, ?v0))
tff(axiom127,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('register$',A__questionmark_v0)
     => 'fun_app$k'('preregister$a',A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ preregister$b(?v0))
tff(axiom128,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => 'preregister$b'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_b_update_fun$ (register$a(?v0) ⇒ preregister$c(?v0))
tff(axiom129,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$'] :
      ( 'register$a'(A__questionmark_v0)
     => 'preregister$c'(A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_b_update_fun$ (register$g(?v0) ⇒ preregister$d(?v0))
tff(axiom130,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$'] :
      ( 'register$g'(A__questionmark_v0)
     => 'preregister$d'(A__questionmark_v0) ) ).

%% ∀ ?v0:C_d_prod_update_b_update_fun$ (register$u(?v0) ⇒ preregister$(?v0))
tff(axiom131,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_b_update_fun$'] :
      ( 'register$u'(A__questionmark_v0)
     => 'preregister$'(A__questionmark_v0) ) ).

%% ∀ ?v0:B_update_a_update_fun$ (register$f(?v0) ⇒ preregister$e(?v0))
tff(axiom132,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$'] :
      ( 'register$f'(A__questionmark_v0)
     => 'preregister$e'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_d_update_fun$ (register$v(?v0) ⇒ preregister$f(?v0))
tff(axiom133,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$'] :
      ( 'register$v'(A__questionmark_v0)
     => 'preregister$f'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_c_update_fun$ (register$w(?v0) ⇒ preregister$g(?v0))
tff(axiom134,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$'] :
      ( 'register$w'(A__questionmark_v0)
     => 'preregister$g'(A__questionmark_v0) ) ).

%% ∀ ?v0:A_update_a_update_fun$ (register$b(?v0) ⇒ preregister$h(?v0))
tff(axiom135,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$'] :
      ( 'register$b'(A__questionmark_v0)
     => 'preregister$h'(A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_a_update_fun$ (fun_app$j(register$e, ?v0) ⇒ fun_app$j(preregister$i, ?v0))
tff(axiom136,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('register$e',A__questionmark_v0)
     => 'fun_app$j'('preregister$i',A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:C_update$ ((fun_app$k(register$, ?v0) ∧ fun_app$k(register$, ?v1)) ⇒ (fun_app$bl(register_tensor$(?v0, ?v1), tensor_update$l(?v2, ?v3)) = fun_app$h(tensor_update$d(fun_app$u(?v0, ?v2)), fun_app$u(?v1, ?v3))))
tff(axiom137,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => ( 'fun_app$bl'('register_tensor$'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$h'('tensor_update$d'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_b_update_fun$ ?v2:C_update$ ?v3:C_update$ ((fun_app$k(register$, ?v0) ∧ register$c(?v1)) ⇒ (fun_app$bm(register_tensor$a(?v0, ?v1), tensor_update$l(?v2, ?v3)) = fun_app$g(tensor_update$c(fun_app$u(?v0, ?v2)), fun_app$q(?v1, ?v3))))
tff(axiom138,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => ( 'fun_app$bm'('register_tensor$a'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$g'('tensor_update$c'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update$ ?v3:A_update$ ((fun_app$k(register$, ?v0) ∧ register$a(?v1)) ⇒ (fun_app$bn(register_tensor$b(?v0, ?v1), tensor_update$m(?v2, ?v3)) = fun_app$g(tensor_update$c(fun_app$u(?v0, ?v2)), fun_app$ae(?v1, ?v3))))
tff(axiom139,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => ( 'fun_app$bn'('register_tensor$b'(A__questionmark_v0,A__questionmark_v1),'tensor_update$m'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$g'('tensor_update$c'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update$ ?v3:D_update$ ((fun_app$k(register$, ?v0) ∧ register$g(?v1)) ⇒ (fun_app$bo(register_tensor$c(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$g(tensor_update$c(fun_app$u(?v0, ?v2)), fun_app$m(?v1, ?v3))))
tff(axiom140,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => ( 'fun_app$bo'('register_tensor$c'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$g'('tensor_update$c'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:C_update$ ((register$c(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ (fun_app$bp(register_tensor$d(?v0, ?v1), tensor_update$l(?v2, ?v3)) = fun_app$a(tensor_update$(fun_app$q(?v0, ?v2)), fun_app$u(?v1, ?v3))))
tff(axiom141,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => ( 'fun_app$bp'('register_tensor$d'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$a'('tensor_update$'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:C_update$ ?v3:C_update$ ((register$c(?v0) ∧ register$c(?v1)) ⇒ (fun_app$bq(register_tensor$e(?v0, ?v1), tensor_update$l(?v2, ?v3)) = tensor_update$f(fun_app$q(?v0, ?v2), fun_app$q(?v1, ?v3))))
tff(axiom142,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => ( 'fun_app$bq'('register_tensor$e'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$f'('fun_app$q'(A__questionmark_v0,A__questionmark_v2),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update$ ?v3:A_update$ ((register$c(?v0) ∧ register$a(?v1)) ⇒ (fun_app$br(register_tensor$f(?v0, ?v1), tensor_update$m(?v2, ?v3)) = tensor_update$f(fun_app$q(?v0, ?v2), fun_app$ae(?v1, ?v3))))
tff(axiom143,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => ( 'fun_app$br'('register_tensor$f'(A__questionmark_v0,A__questionmark_v1),'tensor_update$m'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$f'('fun_app$q'(A__questionmark_v0,A__questionmark_v2),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update$ ?v3:D_update$ ((register$c(?v0) ∧ register$g(?v1)) ⇒ (fun_app$bs(register_tensor$g(?v0, ?v1), tensor_update$h(?v2, ?v3)) = tensor_update$f(fun_app$q(?v0, ?v2), fun_app$m(?v1, ?v3))))
tff(axiom144,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => ( 'fun_app$bs'('register_tensor$g'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$f'('fun_app$q'(A__questionmark_v0,A__questionmark_v2),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update$ ?v3:C_update$ ((register$a(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ (fun_app$bt(register_tensor$h(?v0, ?v1), fun_app$e(tensor_update$b(?v2), ?v3)) = fun_app$a(tensor_update$(fun_app$ae(?v0, ?v2)), fun_app$u(?v1, ?v3))))
tff(axiom145,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => ( 'fun_app$bt'('register_tensor$h'(A__questionmark_v0,A__questionmark_v1),'fun_app$e'('tensor_update$b'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$a'('tensor_update$'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update$ ?v3:C_update$ ((register$a(?v0) ∧ register$c(?v1)) ⇒ (fun_app$bu(register_tensor$i(?v0, ?v1), fun_app$e(tensor_update$b(?v2), ?v3)) = tensor_update$f(fun_app$ae(?v0, ?v2), fun_app$q(?v1, ?v3))))
tff(axiom146,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => ( 'fun_app$bu'('register_tensor$i'(A__questionmark_v0,A__questionmark_v1),'fun_app$e'('tensor_update$b'(A__questionmark_v2),A__questionmark_v3)) = 'tensor_update$f'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_a_update_fun$ ((fun_app$j(compatible$d(?v0), ?v1) ∧ fun_app$k(register$, ?v2)) ⇒ fun_app$j(compatible$(comp$b(?v0, ?v2)), ?v1))
tff(axiom147,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$b'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_b_update_fun$ ((fun_app$j(compatible$r(?v0), ?v1) ∧ register$c(?v2)) ⇒ fun_app$j(compatible$(comp$c(?v0, ?v2)), ?v1))
tff(axiom148,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$'] :
      ( ( 'fun_app$j'('compatible$r'(A__questionmark_v0),A__questionmark_v1)
        & 'register$c'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$c'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update_a_update_fun$ ((compatible$o(?v0, ?v1) ∧ fun_app$k(register$, ?v2)) ⇒ compatible$f(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), ?v1))
tff(axiom149,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] :
      ( ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2) )
     => 'compatible$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update_b_update_fun$ ((compatible$s(?v0, ?v1) ∧ register$c(?v2)) ⇒ compatible$f(comp$d(?v0, ?v2), ?v1))
tff(axiom150,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$'] :
      ( ( 'compatible$s'(A__questionmark_v0,A__questionmark_v1)
        & 'register$c'(A__questionmark_v2) )
     => 'compatible$f'('comp$d'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_c_update_fun$ ((fun_app$j(compatible$(?v0), ?v1) ∧ register$x(?v2)) ⇒ fun_app$j(compatible$(comp$e(?v0, ?v2)), ?v1))
tff(axiom151,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] :
      ( ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
        & 'register$x'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$e'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update_c_update_fun$ ((compatible$f(?v0, ?v1) ∧ register$x(?v2)) ⇒ compatible$f(comp$f(?v0, ?v2), ?v1))
tff(axiom152,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] :
      ( ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
        & 'register$x'(A__questionmark_v2) )
     => 'compatible$f'('comp$f'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update_b_update_fun$ ((compatible$t(?v0, ?v1) ∧ register$a(?v2)) ⇒ compatible$a(comp$g(?v0, ?v2), ?v1))
tff(axiom153,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'compatible$t'(A__questionmark_v0,A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$a'('comp$g'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update_d_update_fun$ ((compatible$h(?v0, ?v1) ∧ register$v(?v2)) ⇒ compatible$a(comp$h(?v0, ?v2), ?v1))
tff(axiom154,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update_d_update_fun$'] :
      ( ( 'compatible$h'(A__questionmark_v0,A__questionmark_v1)
        & 'register$v'(A__questionmark_v2) )
     => 'compatible$a'('comp$h'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update_c_update_fun$ ((compatible$n(?v0, ?v1) ∧ register$w(?v2)) ⇒ compatible$a(comp$i(?v0, ?v2), ?v1))
tff(axiom155,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update_c_update_fun$'] :
      ( ( 'compatible$n'(A__questionmark_v0,A__questionmark_v1)
        & 'register$w'(A__questionmark_v2) )
     => 'compatible$a'('comp$i'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:A_update_b_update_fun$ ((compatible$u(?v0, ?v1) ∧ register$a(?v2)) ⇒ compatible$b(comp$g(?v0, ?v2), ?v1))
tff(axiom156,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'compatible$u'(A__questionmark_v0,A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$b'('comp$g'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% register$a(f$)
tff(axiom157,axiom,
    'register$a'('f$') ).

%% register$g(fun_app$bv(fun_app$bw(comp$j, f$), h$))
tff(axiom158,axiom,
    'register$g'('fun_app$bv'('fun_app$bw'('comp$j','f$'),'h$')) ).

%% compatible$f(fun_app$be(fun_app$bf(comp$, f$), g$), fun_app$bv(fun_app$bw(comp$j, f$), h$))
tff(axiom159,axiom,
    'compatible$f'('fun_app$be'('fun_app$bf'('comp$','f$'),'g$'),'fun_app$bv'('fun_app$bw'('comp$j','f$'),'h$')) ).

%% ∀ ?v0:B_update$ (fun_app$x(comp_update$a(id_update$c), ?v0) = ?v0)
tff(axiom160,axiom,
    ! [A__questionmark_v0: 'B_update$'] : 'fun_app$x'('comp_update$a'('id_update$c'),A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:A_update$ (fun_app$bd(comp_update$(id_update$), ?v0) = ?v0)
tff(axiom161,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$bd'('comp_update$'('id_update$'),A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:D_update$ (fun_app$bg(comp_update$b(id_update$a), ?v0) = ?v0)
tff(axiom162,axiom,
    ! [A__questionmark_v0: 'D_update$'] : 'fun_app$bg'('comp_update$b'('id_update$a'),A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:C_update$ (fun_app$bx(comp_update$c(id_update$b), ?v0) = ?v0)
tff(axiom163,axiom,
    ! [A__questionmark_v0: 'C_update$'] : 'fun_app$bx'('comp_update$c'('id_update$b'),A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:B_update$ (fun_app$x(comp_update$a(?v0), id_update$c) = ?v0)
tff(axiom164,axiom,
    ! [A__questionmark_v0: 'B_update$'] : 'fun_app$x'('comp_update$a'(A__questionmark_v0),'id_update$c') = A__questionmark_v0 ).

%% ∀ ?v0:A_update$ (fun_app$bd(comp_update$(?v0), id_update$) = ?v0)
tff(axiom165,axiom,
    ! [A__questionmark_v0: 'A_update$'] : 'fun_app$bd'('comp_update$'(A__questionmark_v0),'id_update$') = A__questionmark_v0 ).

%% ∀ ?v0:D_update$ (fun_app$bg(comp_update$b(?v0), id_update$a) = ?v0)
tff(axiom166,axiom,
    ! [A__questionmark_v0: 'D_update$'] : 'fun_app$bg'('comp_update$b'(A__questionmark_v0),'id_update$a') = A__questionmark_v0 ).

%% ∀ ?v0:C_update$ (fun_app$bx(comp_update$c(?v0), id_update$b) = ?v0)
tff(axiom167,axiom,
    ! [A__questionmark_v0: 'C_update$'] : 'fun_app$bx'('comp_update$c'(A__questionmark_v0),'id_update$b') = A__questionmark_v0 ).

%% preregister$(register_pair$a(fun_app$be(fun_app$bf(comp$, f$), g$), fun_app$bv(fun_app$bw(comp$j, f$), h$)))
tff(axiom168,axiom,
    'preregister$'('register_pair$a'('fun_app$be'('fun_app$bf'('comp$','f$'),'g$'),'fun_app$bv'('fun_app$bw'('comp$j','f$'),'h$'))) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ((compatible$c(?v0, ?v1) ∧ (fun_app$j(register$e, ?v2) ∧ fun_app$j(register$e, ?v3))) ⇒ (comp$k(register_pair$b(?v0, ?v1), register_tensor$j(?v2, ?v3)) = register_pair$c(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3))))
tff(axiom169,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'fun_app$j'('register$e',A__questionmark_v3) )
     => ( 'comp$k'('register_pair$b'(A__questionmark_v0,A__questionmark_v1),'register_tensor$j'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$c'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((compatible$c(?v0, ?v1) ∧ (fun_app$j(register$e, ?v2) ∧ fun_app$k(register$, ?v3))) ⇒ (comp$l(register_pair$b(?v0, ?v1), register_tensor$k(?v2, ?v3)) = register_pair$d(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom170,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$l'('register_pair$b'(A__questionmark_v0,A__questionmark_v1),'register_tensor$k'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$d'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_b_update_fun$ ((compatible$b(?v0, ?v1) ∧ (fun_app$j(register$e, ?v2) ∧ register$c(?v3))) ⇒ (comp$m(register_pair$e(?v0, ?v1), register_tensor$l(?v2, ?v3)) = register_pair$d(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), comp$d(?v1, ?v3))))
tff(axiom171,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_b_update_fun$'] :
      ( ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'register$c'(A__questionmark_v3) )
     => ( 'comp$m'('register_pair$e'(A__questionmark_v0,A__questionmark_v1),'register_tensor$l'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$d'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'comp$d'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((compatible$b(?v0, ?v1) ∧ (fun_app$j(register$e, ?v2) ∧ register$a(?v3))) ⇒ (comp$n(register_pair$e(?v0, ?v1), register_tensor$m(?v2, ?v3)) = register_pair$f(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), comp$g(?v1, ?v3))))
tff(axiom172,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'register$a'(A__questionmark_v3) )
     => ( 'comp$n'('register_pair$e'(A__questionmark_v0,A__questionmark_v1),'register_tensor$m'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$f'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'comp$g'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_b_update_fun$ ((compatible$b(?v0, ?v1) ∧ (fun_app$j(register$e, ?v2) ∧ register$g(?v3))) ⇒ (comp$o(register_pair$e(?v0, ?v1), register_tensor$n(?v2, ?v3)) = register_pair$c(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), comp$p(?v1, ?v3))))
tff(axiom173,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_b_update_fun$'] :
      ( ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'register$g'(A__questionmark_v3) )
     => ( 'comp$o'('register_pair$e'(A__questionmark_v0,A__questionmark_v1),'register_tensor$n'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$c'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'comp$p'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((compatible$c(?v0, ?v1) ∧ (fun_app$k(register$, ?v2) ∧ fun_app$k(register$, ?v3))) ⇒ (comp$q(register_pair$b(?v0, ?v1), register_tensor$(?v2, ?v3)) = register_pair$g(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom174,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$q'('register_pair$b'(A__questionmark_v0,A__questionmark_v1),'register_tensor$'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$g'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_b_update_fun$ ((compatible$b(?v0, ?v1) ∧ (fun_app$k(register$, ?v2) ∧ register$c(?v3))) ⇒ (comp$r(register_pair$e(?v0, ?v1), register_tensor$a(?v2, ?v3)) = register_pair$g(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), comp$d(?v1, ?v3))))
tff(axiom175,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_b_update_fun$'] :
      ( ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'register$c'(A__questionmark_v3) )
     => ( 'comp$r'('register_pair$e'(A__questionmark_v0,A__questionmark_v1),'register_tensor$a'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$g'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'comp$d'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((compatible$b(?v0, ?v1) ∧ (fun_app$k(register$, ?v2) ∧ register$a(?v3))) ⇒ (comp$s(register_pair$e(?v0, ?v1), register_tensor$b(?v2, ?v3)) = register_pair$h(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), comp$g(?v1, ?v3))))
tff(axiom176,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'register$a'(A__questionmark_v3) )
     => ( 'comp$s'('register_pair$e'(A__questionmark_v0,A__questionmark_v1),'register_tensor$b'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$h'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'comp$g'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_b_update_fun$ ?v3:C_update_a_update_fun$ ((compatible$j(?v0, ?v1) ∧ (register$c(?v2) ∧ fun_app$k(register$, ?v3))) ⇒ (comp$t(register_pair$i(?v0, ?v1), register_tensor$d(?v2, ?v3)) = register_pair$g(comp$d(?v0, ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom177,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'compatible$j'(A__questionmark_v0,A__questionmark_v1)
        & 'register$c'(A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$t'('register_pair$i'(A__questionmark_v0,A__questionmark_v1),'register_tensor$d'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$g'('comp$d'(A__questionmark_v0,A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ((compatible$j(?v0, ?v1) ∧ (register$a(?v2) ∧ fun_app$j(register$e, ?v3))) ⇒ (comp$u(register_pair$i(?v0, ?v1), register_tensor$o(?v2, ?v3)) = register_pair$j(comp$g(?v0, ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3))))
tff(axiom178,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'compatible$j'(A__questionmark_v0,A__questionmark_v1)
        & 'register$a'(A__questionmark_v2)
        & 'fun_app$j'('register$e',A__questionmark_v3) )
     => ( 'comp$u'('register_pair$i'(A__questionmark_v0,A__questionmark_v1),'register_tensor$o'(A__questionmark_v2,A__questionmark_v3)) = 'register_pair$j'('comp$g'(A__questionmark_v0,A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update$ ?v3:C_update$ (compatible$a(?v0, ?v1) ⇒ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$ae(?v0, ?v2))))
tff(axiom179,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:A_update$ ?v3:B_update$ (compatible$b(?v0, ?v1) ⇒ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$x(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$x(?v1, ?v3)), fun_app$ae(?v0, ?v2))))
tff(axiom180,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'B_update$'] :
      ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$x'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$x'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update$ ?v3:A_update$ (compatible$c(?v0, ?v1) ⇒ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$ae(?v0, ?v2))))
tff(axiom181,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update$ ?v3:D_update$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ (fun_app$bd(comp_update$(fun_app$bd(?v0, ?v2)), fun_app$au(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$bd(?v0, ?v2))))
tff(axiom182,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$bd'('comp_update$'('fun_app$bd'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$bd'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:B_update_a_update_fun$ ?v2:A_update$ ?v3:B_update$ (compatible$e(?v0, ?v1) ⇒ (fun_app$bd(comp_update$(fun_app$bd(?v0, ?v2)), fun_app$az(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$az(?v1, ?v3)), fun_app$bd(?v0, ?v2))))
tff(axiom183,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'B_update_a_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'B_update$'] :
      ( 'compatible$e'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$bd'('comp_update$'('fun_app$bd'(A__questionmark_v0,A__questionmark_v2)),'fun_app$az'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$az'(A__questionmark_v1,A__questionmark_v3)),'fun_app$bd'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update$ ?v3:D_update$ (fun_app$j(compatible$(?v0), ?v1) ⇒ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$u(?v0, ?v2))))
tff(axiom184,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update$ ?v3:D_update$ (compatible$f(?v0, ?v1) ⇒ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$q(?v0, ?v2))))
tff(axiom185,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ register$y(register_pair$k(?v0, ?v1)))
tff(axiom186,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => 'register$y'('register_pair$k'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$o(?v0, ?v1) ⇒ register$z(register_pair$j(?v0, ?v1)))
tff(axiom187,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
     => 'register$z'('register_pair$j'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (compatible$a(?v0, ?v1) ⇒ register$aa(register_pair$l(?v0, ?v1)))
tff(axiom188,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
     => 'register$aa'('register_pair$l'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:B_update_b_update_fun$ (compatible$b(?v0, ?v1) ⇒ register$ab(register_pair$e(?v0, ?v1)))
tff(axiom189,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$'] :
      ( 'compatible$b'(A__questionmark_v0,A__questionmark_v1)
     => 'register$ab'('register_pair$e'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (compatible$c(?v0, ?v1) ⇒ register$ac(register_pair$b(?v0, ?v1)))
tff(axiom190,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( 'compatible$c'(A__questionmark_v0,A__questionmark_v1)
     => 'register$ac'('register_pair$b'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:B_update_a_update_fun$ (compatible$e(?v0, ?v1) ⇒ register$ad(register_pair$m(?v0, ?v1)))
tff(axiom191,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'B_update_a_update_fun$'] :
      ( 'compatible$e'(A__questionmark_v0,A__questionmark_v1)
     => 'register$ad'('register_pair$m'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ (fun_app$j(compatible$(?v0), ?v1) ⇒ fun_app$i(register$ae, register_pair$(?v0, ?v1)))
tff(axiom192,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => 'fun_app$i'('register$ae','register_pair$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ (compatible$f(?v0, ?v1) ⇒ register$u(register_pair$a(?v0, ?v1)))
tff(axiom193,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => 'register$u'('register_pair$a'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$k(preregister$a, ?v0) ∧ preregister$c(?v1)) ⇒ preregister$b(fun_app$be(fun_app$bf(comp$, ?v1), ?v0)))
tff(axiom194,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('preregister$a',A__questionmark_v0)
        & 'preregister$c'(A__questionmark_v1) )
     => 'preregister$b'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$j(preregister$i, ?v0) ∧ preregister$c(?v1)) ⇒ preregister$d(fun_app$bv(fun_app$bw(comp$j, ?v1), ?v0)))
tff(axiom195,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$j'('preregister$i',A__questionmark_v0)
        & 'preregister$c'(A__questionmark_v1) )
     => 'preregister$d'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v0)) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$i(preregister$j, ?v0) ∧ preregister$c(?v1)) ⇒ preregister$(fun_app$bj(fun_app$bk(comp$a, ?v1), ?v0)))
tff(axiom196,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$i'('preregister$j',A__questionmark_v0)
        & 'preregister$c'(A__questionmark_v1) )
     => 'preregister$'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v0)) ) ).

%% ∀ ?v0:C_d_prod_update_b_update_fun$ ?v1:B_update_b_update_fun$ ((preregister$(?v0) ∧ preregister$k(?v1)) ⇒ preregister$(comp$v(?v1, ?v0)))
tff(axiom197,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$'] :
      ( ( 'preregister$'(A__questionmark_v0)
        & 'preregister$k'(A__questionmark_v1) )
     => 'preregister$'('comp$v'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_d_prod_update_c_d_prod_update_fun$ ?v1:C_d_prod_update_b_update_fun$ ((preregister$l(?v0) ∧ preregister$(?v1)) ⇒ preregister$(comp$w(?v1, ?v0)))
tff(axiom198,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_c_d_prod_update_fun$',A__questionmark_v1: 'C_d_prod_update_b_update_fun$'] :
      ( ( 'preregister$l'(A__questionmark_v0)
        & 'preregister$'(A__questionmark_v1) )
     => 'preregister$'('comp$w'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_d_update_fun$ ?v1:D_update_a_update_fun$ ((preregister$m(?v0) ∧ fun_app$j(preregister$i, ?v1)) ⇒ fun_app$j(preregister$i, comp$x(?v1, ?v0)))
tff(axiom199,axiom,
    ! [A__questionmark_v0: 'D_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( ( 'preregister$m'(A__questionmark_v0)
        & 'fun_app$j'('preregister$i',A__questionmark_v1) )
     => 'fun_app$j'('preregister$i','comp$x'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_d_update_fun$ ?v1:D_update_a_update_fun$ ((preregister$n(?v0) ∧ fun_app$j(preregister$i, ?v1)) ⇒ fun_app$k(preregister$a, comp$y(?v1, ?v0)))
tff(axiom200,axiom,
    ! [A__questionmark_v0: 'C_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( ( 'preregister$n'(A__questionmark_v0)
        & 'fun_app$j'('preregister$i',A__questionmark_v1) )
     => 'fun_app$k'('preregister$a','comp$y'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((preregister$o(?v0) ∧ preregister$b(?v1)) ⇒ preregister$b(comp$f(?v1, ?v0)))
tff(axiom201,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'preregister$o'(A__questionmark_v0)
        & 'preregister$b'(A__questionmark_v1) )
     => 'preregister$b'('comp$f'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((preregister$p(?v0) ∧ preregister$b(?v1)) ⇒ preregister$k(comp$z(?v1, ?v0)))
tff(axiom202,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'preregister$p'(A__questionmark_v0)
        & 'preregister$b'(A__questionmark_v1) )
     => 'preregister$k'('comp$z'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((preregister$g(?v0) ∧ preregister$b(?v1)) ⇒ preregister$c(comp$i(?v1, ?v0)))
tff(axiom203,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'preregister$g'(A__questionmark_v0)
        & 'preregister$b'(A__questionmark_v1) )
     => 'preregister$c'('comp$i'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update$ ?v1:B_update$ ?v2:B_update$ (fun_app$x(comp_update$a(fun_app$x(comp_update$a(?v0), ?v1)), ?v2) = fun_app$x(comp_update$a(?v0), fun_app$x(comp_update$a(?v1), ?v2)))
tff(axiom204,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'B_update$'] : 'fun_app$x'('comp_update$a'('fun_app$x'('comp_update$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$x'('comp_update$a'(A__questionmark_v0),'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_update$ ?v1:A_update$ ?v2:A_update$ (fun_app$bd(comp_update$(fun_app$bd(comp_update$(?v0), ?v1)), ?v2) = fun_app$bd(comp_update$(?v0), fun_app$bd(comp_update$(?v1), ?v2)))
tff(axiom205,axiom,
    ! [A__questionmark_v0: 'A_update$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'A_update$'] : 'fun_app$bd'('comp_update$'('fun_app$bd'('comp_update$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$bd'('comp_update$'(A__questionmark_v0),'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:D_update$ ?v1:D_update$ ?v2:D_update$ (fun_app$bg(comp_update$b(fun_app$bg(comp_update$b(?v0), ?v1)), ?v2) = fun_app$bg(comp_update$b(?v0), fun_app$bg(comp_update$b(?v1), ?v2)))
tff(axiom206,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'D_update$'] : 'fun_app$bg'('comp_update$b'('fun_app$bg'('comp_update$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$bg'('comp_update$b'(A__questionmark_v0),'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:C_update$ ?v1:C_update$ ?v2:C_update$ (fun_app$bx(comp_update$c(fun_app$bx(comp_update$c(?v0), ?v1)), ?v2) = fun_app$bx(comp_update$c(?v0), fun_app$bx(comp_update$c(?v1), ?v2)))
tff(axiom207,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'C_update$',A__questionmark_v2: 'C_update$'] : 'fun_app$bx'('comp_update$c'('fun_app$bx'('comp_update$c'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$bx'('comp_update$c'(A__questionmark_v0),'fun_app$bx'('comp_update$c'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update$ ?v3:D_update$ (fun_app$j(compatible$(?v0), ?v1) ⇒ (fun_app$by(register_pair$(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3))))
tff(axiom208,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$by'('register_pair$'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update$ ?v3:D_update$ (compatible$f(?v0, ?v1) ⇒ (fun_app$bz(register_pair$a(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$m(?v1, ?v3))))
tff(axiom209,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$bz'('register_pair$a'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$j(?v0, ?v1) ⇒ (fun_app$ca(register_pair$i(?v0, ?v1), fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$x(?v0, ?v2)), fun_app$ae(?v1, ?v3))))
tff(axiom210,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$j'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$ca'('register_pair$i'(A__questionmark_v0,A__questionmark_v1),'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$x'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$l(?v0, ?v1) ⇒ (register_pair$n(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bd(comp_update$(fun_app$az(?v0, ?v2)), fun_app$bd(?v1, ?v3))))
tff(axiom211,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$l'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$n'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$az'(A__questionmark_v0,A__questionmark_v2)),'fun_app$bd'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_d_update_fun$ ?v1:A_update_d_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$v(?v0, ?v1) ⇒ (register_pair$o(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bg(comp_update$b(fun_app$bi(?v0, ?v2)), fun_app$aa(?v1, ?v3))))
tff(axiom212,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun$',A__questionmark_v1: 'A_update_d_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$v'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$o'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bg'('comp_update$b'('fun_app$bi'(A__questionmark_v0,A__questionmark_v2)),'fun_app$aa'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update_c_update_fun$ ?v1:A_update_c_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$w(?v0, ?v1) ⇒ (register_pair$p(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bx(comp_update$c(fun_app$cb(?v0, ?v2)), fun_app$ac(?v1, ?v3))))
tff(axiom213,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun$',A__questionmark_v1: 'A_update_c_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$w'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$p'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bx'('comp_update$c'('fun_app$cb'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ac'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update$ ?v3:D_update$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ (fun_app$cc(register_pair$k(?v0, ?v1), fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bd(comp_update$(fun_app$bd(?v0, ?v2)), fun_app$au(?v1, ?v3))))
tff(axiom214,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$cc'('register_pair$k'(A__questionmark_v0,A__questionmark_v1),'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$bd'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_d_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$x(?v0, ?v1) ⇒ (register_pair$q(?v0, ?v1, fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bg(comp_update$b(fun_app$aa(?v0, ?v2)), fun_app$bg(?v1, ?v3))))
tff(axiom215,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$x'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$q'(A__questionmark_v0,A__questionmark_v1,'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bg'('comp_update$b'('fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),'fun_app$bg'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:D_update_c_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$y(?v0, ?v1) ⇒ (register_pair$r(?v0, ?v1, fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bx(comp_update$c(fun_app$ac(?v0, ?v2)), fun_app$bh(?v1, ?v3))))
tff(axiom216,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$y'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$r'(A__questionmark_v0,A__questionmark_v1,'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bx'('comp_update$c'('fun_app$ac'(A__questionmark_v0,A__questionmark_v2)),'fun_app$bh'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$o(?v0, ?v1) ⇒ (fun_app$cd(register_pair$j(?v0, ?v1), fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$m(?v1, ?v3))))
tff(axiom217,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$cd'('register_pair$j'(A__questionmark_v0,A__questionmark_v1),'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:B_update$ ?v1:B_update$ ?v2:B_update$ ?v3:B_update$ (comp_update$d(tensor_update$f(?v0, ?v1), tensor_update$f(?v2, ?v3)) = tensor_update$f(fun_app$x(comp_update$a(?v0), ?v2), fun_app$x(comp_update$a(?v1), ?v3)))
tff(axiom218,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'B_update$'] : 'comp_update$d'('tensor_update$f'(A__questionmark_v0,A__questionmark_v1),'tensor_update$f'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$f'('fun_app$x'('comp_update$a'(A__questionmark_v0),A__questionmark_v2),'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:B_update$ ?v1:D_update$ ?v2:B_update$ ?v3:D_update$ (comp_update$e(tensor_update$e(?v0, ?v1), tensor_update$e(?v2, ?v3)) = tensor_update$e(fun_app$x(comp_update$a(?v0), ?v2), fun_app$bg(comp_update$b(?v1), ?v3)))
tff(axiom219,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'D_update$'] : 'comp_update$e'('tensor_update$e'(A__questionmark_v0,A__questionmark_v1),'tensor_update$e'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$e'('fun_app$x'('comp_update$a'(A__questionmark_v0),A__questionmark_v2),'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:B_update$ ?v1:C_update$ ?v2:B_update$ ?v3:C_update$ (comp_update$f(tensor_update$n(?v0, ?v1), tensor_update$n(?v2, ?v3)) = tensor_update$n(fun_app$x(comp_update$a(?v0), ?v2), fun_app$bx(comp_update$c(?v1), ?v3)))
tff(axiom220,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'C_update$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'C_update$'] : 'comp_update$f'('tensor_update$n'(A__questionmark_v0,A__questionmark_v1),'tensor_update$n'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$n'('fun_app$x'('comp_update$a'(A__questionmark_v0),A__questionmark_v2),'fun_app$bx'('comp_update$c'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update$ ?v1:B_update$ ?v2:D_update$ ?v3:B_update$ (comp_update$g(tensor_update$i(?v0, ?v1), tensor_update$i(?v2, ?v3)) = tensor_update$i(fun_app$bg(comp_update$b(?v0), ?v2), fun_app$x(comp_update$a(?v1), ?v3)))
tff(axiom221,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'B_update$'] : 'comp_update$g'('tensor_update$i'(A__questionmark_v0,A__questionmark_v1),'tensor_update$i'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$i'('fun_app$bg'('comp_update$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update$ ?v1:A_update$ ?v2:D_update$ ?v3:A_update$ (comp_update$h(tensor_update$j(?v0, ?v1), tensor_update$j(?v2, ?v3)) = tensor_update$j(fun_app$bg(comp_update$b(?v0), ?v2), fun_app$bd(comp_update$(?v1), ?v3)))
tff(axiom222,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update$'] : 'comp_update$h'('tensor_update$j'(A__questionmark_v0,A__questionmark_v1),'tensor_update$j'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$j'('fun_app$bg'('comp_update$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update$ ?v1:D_update$ ?v2:D_update$ ?v3:D_update$ (comp_update$i(tensor_update$g(?v0, ?v1), tensor_update$g(?v2, ?v3)) = tensor_update$g(fun_app$bg(comp_update$b(?v0), ?v2), fun_app$bg(comp_update$b(?v1), ?v3)))
tff(axiom223,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update$'] : 'comp_update$i'('tensor_update$g'(A__questionmark_v0,A__questionmark_v1),'tensor_update$g'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$g'('fun_app$bg'('comp_update$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update$ ?v1:C_update$ ?v2:D_update$ ?v3:C_update$ (comp_update$j(tensor_update$k(?v0, ?v1), tensor_update$k(?v2, ?v3)) = tensor_update$k(fun_app$bg(comp_update$b(?v0), ?v2), fun_app$bx(comp_update$c(?v1), ?v3)))
tff(axiom224,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'C_update$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update$'] : 'comp_update$j'('tensor_update$k'(A__questionmark_v0,A__questionmark_v1),'tensor_update$k'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$k'('fun_app$bg'('comp_update$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$bx'('comp_update$c'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update$ ?v1:B_update$ ?v2:C_update$ ?v3:B_update$ (comp_update$k(tensor_update$o(?v0, ?v1), tensor_update$o(?v2, ?v3)) = tensor_update$o(fun_app$bx(comp_update$c(?v0), ?v2), fun_app$x(comp_update$a(?v1), ?v3)))
tff(axiom225,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'B_update$'] : 'comp_update$k'('tensor_update$o'(A__questionmark_v0,A__questionmark_v1),'tensor_update$o'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$o'('fun_app$bx'('comp_update$c'(A__questionmark_v0),A__questionmark_v2),'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update$ ?v1:A_update$ ?v2:C_update$ ?v3:A_update$ (comp_update$l(tensor_update$m(?v0, ?v1), tensor_update$m(?v2, ?v3)) = tensor_update$m(fun_app$bx(comp_update$c(?v0), ?v2), fun_app$bd(comp_update$(?v1), ?v3)))
tff(axiom226,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] : 'comp_update$l'('tensor_update$m'(A__questionmark_v0,A__questionmark_v1),'tensor_update$m'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$m'('fun_app$bx'('comp_update$c'(A__questionmark_v0),A__questionmark_v2),'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update$ ?v1:D_update$ ?v2:C_update$ ?v3:D_update$ (fun_app$ce(comp_update$m(tensor_update$h(?v0, ?v1)), tensor_update$h(?v2, ?v3)) = tensor_update$h(fun_app$bx(comp_update$c(?v0), ?v2), fun_app$bg(comp_update$b(?v1), ?v3)))
tff(axiom227,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$ce'('comp_update$m'('tensor_update$h'(A__questionmark_v0,A__questionmark_v1)),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'tensor_update$h'('fun_app$bx'('comp_update$c'(A__questionmark_v0),A__questionmark_v2),'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update$ ?v3:D_update$ (fun_app$j(compatible$(?v0), ?v1) ⇒ (fun_app$by(register_pair$(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$u(?v0, ?v2))))
tff(axiom228,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$by'('register_pair$'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:C_update$ ?v3:D_update$ (compatible$f(?v0, ?v1) ⇒ (fun_app$bz(register_pair$a(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$q(?v0, ?v2))))
tff(axiom229,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$bz'('register_pair$a'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$j(?v0, ?v1) ⇒ (fun_app$ca(register_pair$i(?v0, ?v1), fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$x(?v0, ?v2))))
tff(axiom230,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$j'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$ca'('register_pair$i'(A__questionmark_v0,A__questionmark_v1),'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$x'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$l(?v0, ?v1) ⇒ (register_pair$n(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bd(comp_update$(fun_app$bd(?v1, ?v3)), fun_app$az(?v0, ?v2))))
tff(axiom231,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$l'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$n'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$bd'(A__questionmark_v1,A__questionmark_v3)),'fun_app$az'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_d_update_fun$ ?v1:A_update_d_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$v(?v0, ?v1) ⇒ (register_pair$o(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bg(comp_update$b(fun_app$aa(?v1, ?v3)), fun_app$bi(?v0, ?v2))))
tff(axiom232,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun$',A__questionmark_v1: 'A_update_d_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$v'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$o'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bg'('comp_update$b'('fun_app$aa'(A__questionmark_v1,A__questionmark_v3)),'fun_app$bi'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_c_update_fun$ ?v1:A_update_c_update_fun$ ?v2:B_update$ ?v3:A_update$ (compatible$w(?v0, ?v1) ⇒ (register_pair$p(?v0, ?v1, fun_app$a(tensor_update$(?v2), ?v3)) = fun_app$bx(comp_update$c(fun_app$ac(?v1, ?v3)), fun_app$cb(?v0, ?v2))))
tff(axiom233,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun$',A__questionmark_v1: 'A_update_c_update_fun$',A__questionmark_v2: 'B_update$',A__questionmark_v3: 'A_update$'] :
      ( 'compatible$w'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$p'(A__questionmark_v0,A__questionmark_v1,'fun_app$a'('tensor_update$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bx'('comp_update$c'('fun_app$ac'(A__questionmark_v1,A__questionmark_v3)),'fun_app$cb'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update$ ?v3:D_update$ (fun_app$j(compatible$d(?v0), ?v1) ⇒ (fun_app$cc(register_pair$k(?v0, ?v1), fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$bd(?v0, ?v2))))
tff(axiom234,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'fun_app$j'('compatible$d'(A__questionmark_v0),A__questionmark_v1)
     => ( 'fun_app$cc'('register_pair$k'(A__questionmark_v0,A__questionmark_v1),'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$bd'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_d_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$x(?v0, ?v1) ⇒ (register_pair$q(?v0, ?v1, fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bg(comp_update$b(fun_app$bg(?v1, ?v3)), fun_app$aa(?v0, ?v2))))
tff(axiom235,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$x'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$q'(A__questionmark_v0,A__questionmark_v1,'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bg'('comp_update$b'('fun_app$bg'(A__questionmark_v1,A__questionmark_v3)),'fun_app$aa'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:D_update_c_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$y(?v0, ?v1) ⇒ (register_pair$r(?v0, ?v1, fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$bx(comp_update$c(fun_app$bh(?v1, ?v3)), fun_app$ac(?v0, ?v2))))
tff(axiom236,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$y'(A__questionmark_v0,A__questionmark_v1)
     => ( 'register_pair$r'(A__questionmark_v0,A__questionmark_v1,'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$bx'('comp_update$c'('fun_app$bh'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ac'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update$ ?v3:D_update$ (compatible$o(?v0, ?v1) ⇒ (fun_app$cd(register_pair$j(?v0, ?v1), fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$ae(?v0, ?v2))))
tff(axiom237,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
     => ( 'fun_app$cd'('register_pair$j'(A__questionmark_v0,A__questionmark_v1),'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:C_update$ ((fun_app$k(register$, ?v0) ∧ (fun_app$k(register$, ?v1) ∧ ∀ ?v4:C_update$ ?v5:C_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v4)), fun_app$u(?v1, ?v5)) = fun_app$bd(comp_update$(fun_app$u(?v1, ?v5)), fun_app$u(?v0, ?v4))))) ⇒ (fun_app$cf(register_pair$s(?v0, ?v1), tensor_update$l(?v2, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$u(?v1, ?v3))))
tff(axiom238,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1)
        & ! [A__questionmark_v4: 'C_update$',A__questionmark_v5: 'C_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v4)),'fun_app$u'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v1,A__questionmark_v5)),'fun_app$u'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cf'('register_pair$s'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:C_update$ ?v3:C_update$ ((register$c(?v0) ∧ (register$c(?v1) ∧ ∀ ?v4:C_update$ ?v5:C_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v4)), fun_app$q(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v5)), fun_app$q(?v0, ?v4))))) ⇒ (fun_app$cg(register_pair$g(?v0, ?v1), tensor_update$l(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$q(?v1, ?v3))))
tff(axiom239,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'C_update$',A__questionmark_v5: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v4)),'fun_app$q'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v5)),'fun_app$q'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cg'('register_pair$g'(A__questionmark_v0,A__questionmark_v1),'tensor_update$l'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update$ ?v3:A_update$ ((register$c(?v0) ∧ (register$a(?v1) ∧ ∀ ?v4:C_update$ ?v5:A_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v4)), fun_app$ae(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v5)), fun_app$q(?v0, ?v4))))) ⇒ (fun_app$ch(register_pair$h(?v0, ?v1), tensor_update$m(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$ae(?v1, ?v3))))
tff(axiom240,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'C_update$',A__questionmark_v5: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v4)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v5)),'fun_app$q'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$ch'('register_pair$h'(A__questionmark_v0,A__questionmark_v1),'tensor_update$m'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update$ ?v3:C_update$ ((register$a(?v0) ∧ (register$c(?v1) ∧ ∀ ?v4:A_update$ ?v5:C_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v4)), fun_app$q(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v5)), fun_app$ae(?v0, ?v4))))) ⇒ (fun_app$ci(register_pair$l(?v0, ?v1), fun_app$e(tensor_update$b(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$q(?v1, ?v3))))
tff(axiom241,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v4)),'fun_app$q'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v5)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$ci'('register_pair$l'(A__questionmark_v0,A__questionmark_v1),'fun_app$e'('tensor_update$b'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update$ ?v3:A_update$ ((register$a(?v0) ∧ (register$a(?v1) ∧ ∀ ?v4:A_update$ ?v5:A_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v4)), fun_app$ae(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v5)), fun_app$ae(?v0, ?v4))))) ⇒ (fun_app$cj(register_pair$b(?v0, ?v1), fun_app$h(tensor_update$d(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$ae(?v1, ?v3))))
tff(axiom242,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'A_update$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v4)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v5)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cj'('register_pair$b'(A__questionmark_v0,A__questionmark_v1),'fun_app$h'('tensor_update$d'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update$ ?v3:D_update$ ((register$a(?v0) ∧ (register$g(?v1) ∧ ∀ ?v4:A_update$ ?v5:D_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v4)), fun_app$m(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v5)), fun_app$ae(?v0, ?v4))))) ⇒ (fun_app$cd(register_pair$j(?v0, ?v1), fun_app$c(tensor_update$a(?v2), ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$m(?v1, ?v3))))
tff(axiom243,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v4)),'fun_app$m'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v5)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cd'('register_pair$j'(A__questionmark_v0,A__questionmark_v1),'fun_app$c'('tensor_update$a'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:D_update$ ?v3:C_update$ ((register$g(?v0) ∧ (register$c(?v1) ∧ ∀ ?v4:D_update$ ?v5:C_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v4)), fun_app$q(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v5)), fun_app$m(?v0, ?v4))))) ⇒ (fun_app$ck(register_pair$d(?v0, ?v1), tensor_update$k(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$q(?v1, ?v3))))
tff(axiom244,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'D_update$',A__questionmark_v5: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v4)),'fun_app$q'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v5)),'fun_app$m'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$ck'('register_pair$d'(A__questionmark_v0,A__questionmark_v1),'tensor_update$k'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update$ ?v3:A_update$ ((register$g(?v0) ∧ (register$a(?v1) ∧ ∀ ?v4:D_update$ ?v5:A_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v4)), fun_app$ae(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v5)), fun_app$m(?v0, ?v4))))) ⇒ (fun_app$cl(register_pair$f(?v0, ?v1), tensor_update$j(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$ae(?v1, ?v3))))
tff(axiom245,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'D_update$',A__questionmark_v5: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v4)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v5)),'fun_app$m'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cl'('register_pair$f'(A__questionmark_v0,A__questionmark_v1),'tensor_update$j'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:D_update$ ?v3:D_update$ ((register$g(?v0) ∧ (register$g(?v1) ∧ ∀ ?v4:D_update$ ?v5:D_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v4)), fun_app$m(?v1, ?v5)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v5)), fun_app$m(?v0, ?v4))))) ⇒ (fun_app$cm(register_pair$c(?v0, ?v1), tensor_update$g(?v2, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$m(?v1, ?v3))))
tff(axiom246,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'D_update$',A__questionmark_v5: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v4)),'fun_app$m'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v5)),'fun_app$m'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$cm'('register_pair$c'(A__questionmark_v0,A__questionmark_v1),'tensor_update$g'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update$ ?v3:D_update$ ((fun_app$k(register$, ?v0) ∧ (fun_app$j(register$e, ?v1) ∧ ∀ ?v4:C_update$ ?v5:D_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v4)), fun_app$au(?v1, ?v5)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v5)), fun_app$u(?v0, ?v4))))) ⇒ (fun_app$by(register_pair$(?v0, ?v1), tensor_update$h(?v2, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3))))
tff(axiom247,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$j'('register$e',A__questionmark_v1)
        & ! [A__questionmark_v4: 'C_update$',A__questionmark_v5: 'D_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v4)),'fun_app$au'(A__questionmark_v1,A__questionmark_v5)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v5)),'fun_app$u'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'fun_app$by'('register_pair$'(A__questionmark_v0,A__questionmark_v1),'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_d_prod_update_b_update_fun$ ?v1:C_d_prod_update_b_update_fun$ ((preregister$(?v0) ∧ (preregister$(?v1) ∧ ∀ ?v2:C_update$ ?v3:D_update$ (fun_app$bz(?v0, tensor_update$h(?v2, ?v3)) = fun_app$bz(?v1, tensor_update$h(?v2, ?v3))))) ⇒ (?v0 = ?v1))
tff(axiom248,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_b_update_fun$'] :
      ( ( 'preregister$'(A__questionmark_v0)
        & 'preregister$'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$bz'(A__questionmark_v0,'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$bz'(A__questionmark_v1,'tensor_update$h'(A__questionmark_v2,A__questionmark_v3)) )
     => ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$j(register$e, ?v2) ∧ fun_app$j(register$e, ?v3)))) ⇒ (comp$aa(register_tensor$p(?v0, ?v1), register_tensor$j(?v2, ?v3)) = register_tensor$q(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3))))
tff(axiom249,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'fun_app$j'('register$e',A__questionmark_v3) )
     => ( 'comp$aa'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$j'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$j(register$e, ?v2) ∧ fun_app$k(register$, ?v3)))) ⇒ (comp$ab(register_tensor$p(?v0, ?v1), register_tensor$k(?v2, ?v3)) = register_tensor$r(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom250,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$ab'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$k'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$r'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$k(register$, ?v2) ∧ fun_app$j(register$e, ?v3)))) ⇒ (comp$ac(register_tensor$p(?v0, ?v1), register_tensor$s(?v2, ?v3)) = register_tensor$g(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3))))
tff(axiom251,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'fun_app$j'('register$e',A__questionmark_v3) )
     => ( 'comp$ac'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$s'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$g'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$k(register$, ?v2) ∧ fun_app$k(register$, ?v3)))) ⇒ (comp$ad(register_tensor$p(?v0, ?v1), register_tensor$(?v2, ?v3)) = register_tensor$e(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom252,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$ad'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$e'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:D_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$i(register$ae, ?v2) ∧ fun_app$j(register$e, ?v3)))) ⇒ (comp$ae(register_tensor$p(?v0, ?v1), register_tensor$t(?v2, ?v3)) = register_tensor$u(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3))))
tff(axiom253,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$i'('register$ae',A__questionmark_v2)
        & 'fun_app$j'('register$e',A__questionmark_v3) )
     => ( 'comp$ae'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$t'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$u'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$j(register$e, ?v2) ∧ fun_app$i(register$ae, ?v3)))) ⇒ (comp$af(register_tensor$p(?v0, ?v1), register_tensor$v(?v2, ?v3)) = register_tensor$w(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3))))
tff(axiom254,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2)
        & 'fun_app$i'('register$ae',A__questionmark_v3) )
     => ( 'comp$af'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$v'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$w'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$i(register$ae, ?v2) ∧ fun_app$k(register$, ?v3)))) ⇒ (comp$ag(register_tensor$p(?v0, ?v1), register_tensor$x(?v2, ?v3)) = register_tensor$y(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3))))
tff(axiom255,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$i'('register$ae',A__questionmark_v2)
        & 'fun_app$k'('register$',A__questionmark_v3) )
     => ( 'comp$ag'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$x'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$y'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$k(register$, ?v2) ∧ fun_app$i(register$ae, ?v3)))) ⇒ (comp$ah(register_tensor$p(?v0, ?v1), register_tensor$z(?v2, ?v3)) = register_tensor$aa(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3))))
tff(axiom256,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2)
        & 'fun_app$i'('register$ae',A__questionmark_v3) )
     => ( 'comp$ah'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$z'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$aa'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ (fun_app$i(register$ae, ?v2) ∧ fun_app$i(register$ae, ?v3)))) ⇒ (comp$ai(register_tensor$p(?v0, ?v1), register_tensor$ab(?v2, ?v3)) = register_tensor$ac(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3))))
tff(axiom257,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & 'fun_app$i'('register$ae',A__questionmark_v2)
        & 'fun_app$i'('register$ae',A__questionmark_v3) )
     => ( 'comp$ai'('register_tensor$p'(A__questionmark_v0,A__questionmark_v1),'register_tensor$ab'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$ac'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_c_update_fun$ ?v3:A_update_c_update_fun$ ((fun_app$k(register$, ?v0) ∧ (fun_app$k(register$, ?v1) ∧ (register$w(?v2) ∧ register$w(?v3)))) ⇒ (comp$aj(register_tensor$(?v0, ?v1), register_tensor$ad(?v2, ?v3)) = register_tensor$ae(comp$ak(?v0, ?v2), comp$ak(?v1, ?v3))))
tff(axiom258,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_c_update_fun$',A__questionmark_v3: 'A_update_c_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1)
        & 'register$w'(A__questionmark_v2)
        & 'register$w'(A__questionmark_v3) )
     => ( 'comp$aj'('register_tensor$'(A__questionmark_v0,A__questionmark_v1),'register_tensor$ad'(A__questionmark_v2,A__questionmark_v3)) = 'register_tensor$ae'('comp$ak'(A__questionmark_v0,A__questionmark_v2),'comp$ak'(A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ (fun_app$k(register$, ?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$u(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$u(?v1, ?v3)), fun_app$u(?v0, ?v2))))) ⇒ register$af(register_pair$s(?v0, ?v1)))
tff(axiom259,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$af'('register_pair$s'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$c(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:C_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$q(?v0, ?v2))))) ⇒ register$ag(register_pair$g(?v0, ?v1)))
tff(axiom260,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$ag'('register_pair$g'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$c(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:C_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$q(?v0, ?v2))))) ⇒ register$ah(register_pair$h(?v0, ?v1)))
tff(axiom261,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$ah'('register_pair$h'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$a(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:A_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ register$aa(register_pair$l(?v0, ?v1)))
tff(axiom262,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$aa'('register_pair$l'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$a(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:A_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ register$ac(register_pair$b(?v0, ?v1)))
tff(axiom263,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$ac'('register_pair$b'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$a(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:A_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$ae(?v0, ?v2))))) ⇒ register$z(register_pair$j(?v0, ?v1)))
tff(axiom264,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'A_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$z'('register_pair$j'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$g(?v0) ∧ (register$c(?v1) ∧ ∀ ?v2:D_update$ ?v3:C_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$q(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$q(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ register$ai(register_pair$d(?v0, ?v1)))
tff(axiom265,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$q'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$ai'('register_pair$d'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$g(?v0) ∧ (register$a(?v1) ∧ ∀ ?v2:D_update$ ?v3:A_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$ae(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$ae(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ register$aj(register_pair$f(?v0, ?v1)))
tff(axiom266,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$ae'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$aj'('register_pair$f'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$g(?v0) ∧ (register$g(?v1) ∧ ∀ ?v2:D_update$ ?v3:D_update$ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v2)), fun_app$m(?v1, ?v3)) = fun_app$x(comp_update$a(fun_app$m(?v1, ?v3)), fun_app$m(?v0, ?v2))))) ⇒ register$ak(register_pair$c(?v0, ?v1)))
tff(axiom267,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$g'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v2)),'fun_app$m'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v1,A__questionmark_v3)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) )
     => 'register$ak'('register_pair$c'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ (fun_app$j(register$e, ?v1) ∧ ∀ ?v2:C_update$ ?v3:D_update$ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v2)), fun_app$au(?v1, ?v3)) = fun_app$bd(comp_update$(fun_app$au(?v1, ?v3)), fun_app$u(?v0, ?v2))))) ⇒ fun_app$i(register$ae, register_pair$(?v0, ?v1)))
tff(axiom268,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$j'('register$e',A__questionmark_v1)
        & ! [A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update$'] : 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v2)),'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v1,A__questionmark_v3)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) )
     => 'fun_app$i'('register$ae','register_pair$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_c_update_fun$ ?v1:C_update_a_update_fun$ ((register$x(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ fun_app$k(register$, comp$e(?v1, ?v0)))
tff(axiom269,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$x'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'fun_app$k'('register$','comp$e'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((register$x(?v0) ∧ register$c(?v1)) ⇒ register$c(comp$f(?v1, ?v0)))
tff(axiom270,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$x'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$c'('comp$f'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((register$w(?v0) ∧ register$c(?v1)) ⇒ register$a(comp$i(?v1, ?v0)))
tff(axiom271,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$w'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$a'('comp$i'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_c_update_fun$ ?v1:C_update_b_update_fun$ ((register$s(?v0) ∧ register$c(?v1)) ⇒ register$g(comp$al(?v1, ?v0)))
tff(axiom272,axiom,
    ! [A__questionmark_v0: 'D_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$s'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'register$g'('comp$al'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((register$b(?v0) ∧ register$a(?v1)) ⇒ register$a(comp$am(?v1, ?v0)))
tff(axiom273,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$b'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'register$a'('comp$am'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$j(register$e, ?v0) ∧ register$a(?v1)) ⇒ register$g(fun_app$bv(fun_app$bw(comp$j, ?v1), ?v0)))
tff(axiom274,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$j'('register$e',A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'register$g'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_d_update_fun$ ?v1:D_update_b_update_fun$ ((register$al(?v0) ∧ register$g(?v1)) ⇒ register$c(comp$an(?v1, ?v0)))
tff(axiom275,axiom,
    ! [A__questionmark_v0: 'C_update_d_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$al'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'register$c'('comp$an'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_b_update_fun$ ((register$v(?v0) ∧ register$g(?v1)) ⇒ register$a(comp$h(?v1, ?v0)))
tff(axiom276,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$v'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'register$a'('comp$h'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_d_update_fun$ ?v1:D_update_b_update_fun$ ((register$r(?v0) ∧ register$g(?v1)) ⇒ register$g(comp$ao(?v1, ?v0)))
tff(axiom277,axiom,
    ! [A__questionmark_v0: 'D_update_d_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$r'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'register$g'('comp$ao'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$b(?v1)) ⇒ fun_app$k(register$, comp$b(?v1, ?v0)))
tff(axiom278,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$b'(A__questionmark_v1) )
     => 'fun_app$k'('register$','comp$b'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update$ ?v2:C_update$ (fun_app$k(register$, ?v0) ⇒ (fun_app$bd(comp_update$(fun_app$u(?v0, ?v1)), fun_app$u(?v0, ?v2)) = fun_app$u(?v0, fun_app$bx(comp_update$c(?v1), ?v2))))
tff(axiom279,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update$',A__questionmark_v2: 'C_update$'] :
      ( 'fun_app$k'('register$',A__questionmark_v0)
     => ( 'fun_app$bd'('comp_update$'('fun_app$u'(A__questionmark_v0,A__questionmark_v1)),'fun_app$u'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$u'(A__questionmark_v0,'fun_app$bx'('comp_update$c'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update$ ?v2:C_update$ (register$c(?v0) ⇒ (fun_app$x(comp_update$a(fun_app$q(?v0, ?v1)), fun_app$q(?v0, ?v2)) = fun_app$q(?v0, fun_app$bx(comp_update$c(?v1), ?v2))))
tff(axiom280,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update$',A__questionmark_v2: 'C_update$'] :
      ( 'register$c'(A__questionmark_v0)
     => ( 'fun_app$x'('comp_update$a'('fun_app$q'(A__questionmark_v0,A__questionmark_v1)),'fun_app$q'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$q'(A__questionmark_v0,'fun_app$bx'('comp_update$c'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update$ ?v2:A_update$ (register$a(?v0) ⇒ (fun_app$x(comp_update$a(fun_app$ae(?v0, ?v1)), fun_app$ae(?v0, ?v2)) = fun_app$ae(?v0, fun_app$bd(comp_update$(?v1), ?v2))))
tff(axiom281,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'A_update$'] :
      ( 'register$a'(A__questionmark_v0)
     => ( 'fun_app$x'('comp_update$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v1)),'fun_app$ae'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v0,'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:D_update_b_update_fun$ ?v1:D_update$ ?v2:D_update$ (register$g(?v0) ⇒ (fun_app$x(comp_update$a(fun_app$m(?v0, ?v1)), fun_app$m(?v0, ?v2)) = fun_app$m(?v0, fun_app$bg(comp_update$b(?v1), ?v2))))
tff(axiom282,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'D_update$'] :
      ( 'register$g'(A__questionmark_v0)
     => ( 'fun_app$x'('comp_update$a'('fun_app$m'(A__questionmark_v0,A__questionmark_v1)),'fun_app$m'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$m'(A__questionmark_v0,'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:B_update$ ?v2:B_update$ (register$d(?v0) ⇒ (fun_app$x(comp_update$a(fun_app$x(?v0, ?v1)), fun_app$x(?v0, ?v2)) = fun_app$x(?v0, fun_app$x(comp_update$a(?v1), ?v2))))
tff(axiom283,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'B_update$'] :
      ( 'register$d'(A__questionmark_v0)
     => ( 'fun_app$x'('comp_update$a'('fun_app$x'(A__questionmark_v0,A__questionmark_v1)),'fun_app$x'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$x'(A__questionmark_v0,'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_a_update_fun$ ?v1:B_update$ ?v2:B_update$ (register$f(?v0) ⇒ (fun_app$bd(comp_update$(fun_app$az(?v0, ?v1)), fun_app$az(?v0, ?v2)) = fun_app$az(?v0, fun_app$x(comp_update$a(?v1), ?v2))))
tff(axiom284,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'B_update$'] :
      ( 'register$f'(A__questionmark_v0)
     => ( 'fun_app$bd'('comp_update$'('fun_app$az'(A__questionmark_v0,A__questionmark_v1)),'fun_app$az'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$az'(A__questionmark_v0,'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update$ ?v2:A_update$ (register$b(?v0) ⇒ (fun_app$bd(comp_update$(fun_app$bd(?v0, ?v1)), fun_app$bd(?v0, ?v2)) = fun_app$bd(?v0, fun_app$bd(comp_update$(?v1), ?v2))))
tff(axiom285,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'A_update$'] :
      ( 'register$b'(A__questionmark_v0)
     => ( 'fun_app$bd'('comp_update$'('fun_app$bd'(A__questionmark_v0,A__questionmark_v1)),'fun_app$bd'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v0,'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update$ ?v2:D_update$ (fun_app$j(register$e, ?v0) ⇒ (fun_app$bd(comp_update$(fun_app$au(?v0, ?v1)), fun_app$au(?v0, ?v2)) = fun_app$au(?v0, fun_app$bg(comp_update$b(?v1), ?v2))))
tff(axiom286,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update$',A__questionmark_v2: 'D_update$'] :
      ( 'fun_app$j'('register$e',A__questionmark_v0)
     => ( 'fun_app$bd'('comp_update$'('fun_app$au'(A__questionmark_v0,A__questionmark_v1)),'fun_app$au'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$au'(A__questionmark_v0,'fun_app$bg'('comp_update$b'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:B_update_d_update_fun$ ?v1:B_update$ ?v2:B_update$ (register$t(?v0) ⇒ (fun_app$bg(comp_update$b(fun_app$bi(?v0, ?v1)), fun_app$bi(?v0, ?v2)) = fun_app$bi(?v0, fun_app$x(comp_update$a(?v1), ?v2))))
tff(axiom287,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun$',A__questionmark_v1: 'B_update$',A__questionmark_v2: 'B_update$'] :
      ( 'register$t'(A__questionmark_v0)
     => ( 'fun_app$bg'('comp_update$b'('fun_app$bi'(A__questionmark_v0,A__questionmark_v1)),'fun_app$bi'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$bi'(A__questionmark_v0,'fun_app$x'('comp_update$a'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:A_update$ ?v2:A_update$ (register$v(?v0) ⇒ (fun_app$bg(comp_update$b(fun_app$aa(?v0, ?v1)), fun_app$aa(?v0, ?v2)) = fun_app$aa(?v0, fun_app$bd(comp_update$(?v1), ?v2))))
tff(axiom288,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'A_update$',A__questionmark_v2: 'A_update$'] :
      ( 'register$v'(A__questionmark_v0)
     => ( 'fun_app$bg'('comp_update$b'('fun_app$aa'(A__questionmark_v0,A__questionmark_v1)),'fun_app$aa'(A__questionmark_v0,A__questionmark_v2)) = 'fun_app$aa'(A__questionmark_v0,'fun_app$bd'('comp_update$'(A__questionmark_v1),A__questionmark_v2)) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:B_update_a_update_fun$ ?v2:D_update_b_update_fun$ ((compatible$z(?v0, ?v1) ∧ register$g(?v2)) ⇒ fun_app$j(compatible$(?v0), comp$ap(?v1, ?v2)))
tff(axiom289,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'B_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$'] :
      ( ( 'compatible$z'(A__questionmark_v0,A__questionmark_v1)
        & 'register$g'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'(A__questionmark_v0),'comp$ap'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ((compatible$i(?v0, ?v1) ∧ fun_app$j(register$e, ?v2)) ⇒ compatible$f(?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2)))
tff(axiom290,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] :
      ( ( 'compatible$i'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$j'('register$e',A__questionmark_v2) )
     => 'compatible$f'(A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:B_update_b_update_fun$ ?v2:D_update_b_update_fun$ ((compatible$aa(?v0, ?v1) ∧ register$g(?v2)) ⇒ compatible$f(?v0, comp$p(?v1, ?v2)))
tff(axiom291,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'B_update_b_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$'] :
      ( ( 'compatible$aa'(A__questionmark_v0,A__questionmark_v1)
        & 'register$g'(A__questionmark_v2) )
     => 'compatible$f'(A__questionmark_v0,'comp$p'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_d_update_fun$ ((fun_app$j(compatible$(?v0), ?v1) ∧ register$r(?v2)) ⇒ fun_app$j(compatible$(?v0), comp$x(?v1, ?v2)))
tff(axiom292,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_d_update_fun$'] :
      ( ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
        & 'register$r'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'(A__questionmark_v0),'comp$x'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:D_update_d_update_fun$ ((compatible$f(?v0, ?v1) ∧ register$r(?v2)) ⇒ compatible$f(?v0, comp$ao(?v1, ?v2)))
tff(axiom293,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'D_update_d_update_fun$'] :
      ( ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
        & 'register$r'(A__questionmark_v2) )
     => 'compatible$f'(A__questionmark_v0,'comp$ao'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update_d_update_fun$ ((compatible$o(?v0, ?v1) ∧ register$v(?v2)) ⇒ compatible$c(?v0, comp$h(?v1, ?v2)))
tff(axiom294,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update_d_update_fun$'] :
      ( ( 'compatible$o'(A__questionmark_v0,A__questionmark_v1)
        & 'register$v'(A__questionmark_v2) )
     => 'compatible$c'(A__questionmark_v0,'comp$h'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_a_update_fun$ ((compatible$ab(?v0, ?v1) ∧ register$f(?v2)) ⇒ compatible$e(?v0, comp$aq(?v1, ?v2)))
tff(axiom295,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$'] :
      ( ( 'compatible$ab'(A__questionmark_v0,A__questionmark_v1)
        & 'register$f'(A__questionmark_v2) )
     => 'compatible$e'(A__questionmark_v0,'comp$aq'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_d_update_fun$ ((fun_app$j(compatible$(?v0), ?v1) ∧ register$v(?v2)) ⇒ compatible$ac(?v0, comp$ar(?v1, ?v2)))
tff(axiom296,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_d_update_fun$'] :
      ( ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
        & 'register$v'(A__questionmark_v2) )
     => 'compatible$ac'(A__questionmark_v0,'comp$ar'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update_d_update_fun$ ((compatible$f(?v0, ?v1) ∧ register$v(?v2)) ⇒ compatible$i(?v0, comp$h(?v1, ?v2)))
tff(axiom297,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update_d_update_fun$'] :
      ( ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
        & 'register$v'(A__questionmark_v2) )
     => 'compatible$i'(A__questionmark_v0,'comp$h'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:C_update_c_update_fun$ ((compatible$a(?v0, ?v1) ∧ register$x(?v2)) ⇒ compatible$a(?v0, comp$f(?v1, ?v2)))
tff(axiom298,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] :
      ( ( 'compatible$a'(A__questionmark_v0,A__questionmark_v1)
        & 'register$x'(A__questionmark_v2) )
     => 'compatible$a'(A__questionmark_v0,'comp$f'(A__questionmark_v1,A__questionmark_v2)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ((fun_app$k(compatible$m(?v0), ?v1) ∧ register$a(?v2)) ⇒ compatible$n(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v2), ?v1)))
tff(axiom299,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('compatible$m'(A__questionmark_v0),A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$n'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ((fun_app$k(compatible$g(?v0), ?v1) ∧ register$a(?v2)) ⇒ compatible$h(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v2), ?v1)))
tff(axiom300,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('compatible$g'(A__questionmark_v0),A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ((fun_app$j(compatible$ad(?v0), ?v1) ∧ register$a(?v2)) ⇒ compatible$q(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v1)))
tff(axiom301,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$j'('compatible$ad'(A__questionmark_v0),A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_c_update_fun$ ?v1:D_update_c_update_fun$ ?v2:C_update_a_update_fun$ ((compatible$ae(?v0, ?v1) ∧ fun_app$k(register$, ?v2)) ⇒ fun_app$j(compatible$(comp$e(?v2, ?v0)), comp$as(?v2, ?v1)))
tff(axiom302,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] :
      ( ( 'compatible$ae'(A__questionmark_v0,A__questionmark_v1)
        & 'fun_app$k'('register$',A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$e'(A__questionmark_v2,A__questionmark_v0)),'comp$as'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_c_update_fun$ ?v1:D_update_c_update_fun$ ?v2:C_update_b_update_fun$ ((compatible$ae(?v0, ?v1) ∧ register$c(?v2)) ⇒ compatible$f(comp$f(?v2, ?v0), comp$al(?v2, ?v1)))
tff(axiom303,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$'] :
      ( ( 'compatible$ae'(A__questionmark_v0,A__questionmark_v1)
        & 'register$c'(A__questionmark_v2) )
     => 'compatible$f'('comp$f'(A__questionmark_v2,A__questionmark_v0),'comp$al'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_d_update_fun$ ?v1:D_update_d_update_fun$ ?v2:D_update_b_update_fun$ ((compatible$af(?v0, ?v1) ∧ register$g(?v2)) ⇒ compatible$f(comp$an(?v2, ?v0), comp$ao(?v2, ?v1)))
tff(axiom304,axiom,
    ! [A__questionmark_v0: 'C_update_d_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$'] :
      ( ( 'compatible$af'(A__questionmark_v0,A__questionmark_v1)
        & 'register$g'(A__questionmark_v2) )
     => 'compatible$f'('comp$an'(A__questionmark_v2,A__questionmark_v0),'comp$ao'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_a_update_fun$ ((fun_app$j(compatible$(?v0), ?v1) ∧ register$b(?v2)) ⇒ fun_app$j(compatible$(comp$b(?v2, ?v0)), comp$at(?v2, ?v1)))
tff(axiom305,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$'] :
      ( ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
        & 'register$b'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$b'(A__questionmark_v2,A__questionmark_v0)),'comp$at'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ((fun_app$j(compatible$(?v0), ?v1) ∧ register$a(?v2)) ⇒ compatible$f(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v1)))
tff(axiom306,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$j'('compatible$'(A__questionmark_v0),A__questionmark_v1)
        & 'register$a'(A__questionmark_v2) )
     => 'compatible$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:B_update_a_update_fun$ ((compatible$f(?v0, ?v1) ∧ register$f(?v2)) ⇒ fun_app$j(compatible$(comp$c(?v2, ?v0)), comp$ap(?v2, ?v1)))
tff(axiom307,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$'] :
      ( ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
        & 'register$f'(A__questionmark_v2) )
     => 'fun_app$j'('compatible$'('comp$c'(A__questionmark_v2,A__questionmark_v0)),'comp$ap'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ?v2:B_update_b_update_fun$ ((compatible$f(?v0, ?v1) ∧ register$d(?v2)) ⇒ compatible$f(comp$d(?v2, ?v0), comp$p(?v2, ?v1)))
tff(axiom308,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$'] :
      ( ( 'compatible$f'(A__questionmark_v0,A__questionmark_v1)
        & 'register$d'(A__questionmark_v2) )
     => 'compatible$f'('comp$d'(A__questionmark_v2,A__questionmark_v0),'comp$p'(A__questionmark_v2,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ (fun_app$cn(comp$au(?v0, ?v1), ?v2) = fun_app$co(?v0, fun_app$cp(?v1, ?v2)))
tff(axiom309,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$'] : 'fun_app$cn'('comp$au'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ (fun_app$cq(comp$av(?v0, ?v1), ?v2) = fun_app$co(?v0, fun_app$cr(?v1, ?v2)))
tff(axiom310,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$'] : 'fun_app$cq'('comp$av'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_d_prod_update_fun$ (fun_app$cs(comp$aw(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cu(?v1, ?v2)))
tff(axiom311,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_d_prod_update_fun$'] : 'fun_app$cs'('comp$aw'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ (fun_app$cv(comp$ax(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cp(?v1, ?v2)))
tff(axiom312,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$'] : 'fun_app$cv'('comp$ax'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ (fun_app$cw(comp$ay(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cr(?v1, ?v2)))
tff(axiom313,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$'] : 'fun_app$cw'('comp$ay'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$u(?v1, ?v2)))
tff(axiom314,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$'] : 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$by(?v1, ?v2)))
tff(axiom315,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$'] : 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$au(?v1, ?v2)))
tff(axiom316,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$'] : 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ (comp$d(?v0, fun_app$be(fun_app$bf(comp$, ?v1), ?v2)) = fun_app$be(fun_app$bf(comp$, comp$g(?v0, ?v1)), ?v2))
tff(axiom317,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] : 'comp$d'(A__questionmark_v0,'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$be'('fun_app$bf'('comp$','comp$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ (comp$p(?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2)) = fun_app$bv(fun_app$bw(comp$j, comp$g(?v0, ?v1)), ?v2))
tff(axiom318,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] : 'comp$p'(A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_c_update_fun$ (fun_app$be(fun_app$bf(comp$, ?v0), comp$e(?v1, ?v2)) = comp$f(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2))
tff(axiom319,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$e'(A__questionmark_v1,A__questionmark_v2)) = 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_d_update_fun$ (fun_app$be(fun_app$bf(comp$, ?v0), comp$y(?v1, ?v2)) = comp$an(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2))
tff(axiom320,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_d_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$y'(A__questionmark_v1,A__questionmark_v2)) = 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:C_update_a_update_fun$ (fun_app$be(fun_app$bf(comp$, ?v0), comp$b(?v1, ?v2)) = fun_app$be(fun_app$bf(comp$, comp$am(?v0, ?v1)), ?v2))
tff(axiom321,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$b'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_c_update_fun$ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$as(?v1, ?v2)) = comp$al(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2))
tff(axiom322,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_c_update_fun$'] : 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$as'(A__questionmark_v1,A__questionmark_v2)) = 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_d_update_fun$ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$x(?v1, ?v2)) = comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2))
tff(axiom323,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_d_update_fun$'] : 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$x'(A__questionmark_v1,A__questionmark_v2)) = 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:D_update_a_update_fun$ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$at(?v1, ?v2)) = fun_app$bv(fun_app$bw(comp$j, comp$am(?v0, ?v1)), ?v2))
tff(axiom324,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] : 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$at'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ (comp$v(?v0, fun_app$bj(fun_app$bk(comp$a, ?v1), ?v2)) = fun_app$bj(fun_app$bk(comp$a, comp$g(?v0, ?v1)), ?v2))
tff(axiom325,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$'] : 'comp$v'(A__questionmark_v0,'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$bj'('fun_app$bk'('comp$a','comp$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_update_c_d_prod_update_fun$ (fun_app$be(fun_app$bf(comp$, ?v0), comp$az(?v1, ?v2)) = comp$ba(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2))
tff(axiom326,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_update_c_d_prod_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$az'(A__questionmark_v1,A__questionmark_v2)) = 'comp$ba'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ (fun_app$cn(comp$au(?v0, ?v1), ?v2) = fun_app$co(?v0, fun_app$cp(?v1, ?v2)))
tff(axiom327,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$'] : 'fun_app$cn'('comp$au'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ (fun_app$cq(comp$av(?v0, ?v1), ?v2) = fun_app$co(?v0, fun_app$cr(?v1, ?v2)))
tff(axiom328,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$'] : 'fun_app$cq'('comp$av'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_d_prod_update_fun$ (fun_app$cs(comp$aw(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cu(?v1, ?v2)))
tff(axiom329,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_d_prod_update_fun$'] : 'fun_app$cs'('comp$aw'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ (fun_app$cv(comp$ax(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cp(?v1, ?v2)))
tff(axiom330,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$'] : 'fun_app$cv'('comp$ax'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ (fun_app$cw(comp$ay(?v0, ?v1), ?v2) = fun_app$ct(?v0, fun_app$cr(?v1, ?v2)))
tff(axiom331,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$'] : 'fun_app$cw'('comp$ay'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$u(?v1, ?v2)))
tff(axiom332,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$'] : 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$by(?v1, ?v2)))
tff(axiom333,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$'] : 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$ae(?v0, fun_app$au(?v1, ?v2)))
tff(axiom334,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$'] : 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_c_update_fun$ (comp$f(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$be(fun_app$bf(comp$, ?v0), comp$e(?v1, ?v2)))
tff(axiom335,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] : 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$e'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_c_update_fun$ (comp$al(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$bv(fun_app$bw(comp$j, ?v0), comp$as(?v1, ?v2)))
tff(axiom336,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_c_update_fun$'] : 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$as'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_d_update_fun$ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$be(fun_app$bf(comp$, ?v0), comp$y(?v1, ?v2)))
tff(axiom337,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_d_update_fun$'] : 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$y'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_d_update_fun$ (comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$bv(fun_app$bw(comp$j, ?v0), comp$x(?v1, ?v2)))
tff(axiom338,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_d_update_fun$'] : 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$x'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ (fun_app$be(fun_app$bf(comp$, comp$g(?v0, ?v1)), ?v2) = comp$d(?v0, fun_app$be(fun_app$bf(comp$, ?v1), ?v2)))
tff(axiom339,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$','comp$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'comp$d'(A__questionmark_v0,'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:C_update_a_update_fun$ (fun_app$be(fun_app$bf(comp$, comp$am(?v0, ?v1)), ?v2) = fun_app$be(fun_app$bf(comp$, ?v0), comp$b(?v1, ?v2)))
tff(axiom340,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] : 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$b'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ (fun_app$bv(fun_app$bw(comp$j, comp$g(?v0, ?v1)), ?v2) = comp$p(?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2)))
tff(axiom341,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] : 'fun_app$bv'('fun_app$bw'('comp$j','comp$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'comp$p'(A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:D_update_a_update_fun$ (fun_app$bv(fun_app$bw(comp$j, comp$am(?v0, ?v1)), ?v2) = fun_app$bv(fun_app$bw(comp$j, ?v0), comp$at(?v1, ?v2)))
tff(axiom342,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] : 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$at'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_d_prod_update_c_update_fun$ (comp$bb(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$bj(fun_app$bk(comp$a, ?v0), comp$bc(?v1, ?v2)))
tff(axiom343,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update_c_update_fun$'] : 'comp$bb'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),'comp$bc'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_update_c_d_prod_update_fun$ (comp$ba(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$be(fun_app$bf(comp$, ?v0), comp$az(?v1, ?v2)))
tff(axiom344,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_update_c_d_prod_update_fun$'] : 'comp$ba'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$az'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v4:B_update_d_update_fun$ ((comp$au(?v0, ?v1) = comp$au(?v2, ?v3)) ⇒ (fun_app$co(?v0, fun_app$cp(?v1, ?v4)) = fun_app$co(?v2, fun_app$cp(?v3, ?v4))))
tff(axiom345,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v4: 'B_update_d_update_fun$'] :
      ( ( 'comp$au'(A__questionmark_v0,A__questionmark_v1) = 'comp$au'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$co'(A__questionmark_v2,'fun_app$cp'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v4:B_update_c_update_fun$ ((comp$av(?v0, ?v1) = comp$av(?v2, ?v3)) ⇒ (fun_app$co(?v0, fun_app$cr(?v1, ?v4)) = fun_app$co(?v2, fun_app$cr(?v3, ?v4))))
tff(axiom346,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v4: 'B_update_c_update_fun$'] :
      ( ( 'comp$av'(A__questionmark_v0,A__questionmark_v1) = 'comp$av'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$co'(A__questionmark_v2,'fun_app$cr'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v4:B_update_c_d_prod_update_fun$ ((comp$aw(?v0, ?v1) = comp$aw(?v2, ?v3)) ⇒ (fun_app$ct(?v0, fun_app$cu(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cu(?v3, ?v4))))
tff(axiom347,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v4: 'B_update_c_d_prod_update_fun$'] :
      ( ( 'comp$aw'(A__questionmark_v0,A__questionmark_v1) = 'comp$aw'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cu'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v4:B_update_d_update_fun$ ((comp$ax(?v0, ?v1) = comp$ax(?v2, ?v3)) ⇒ (fun_app$ct(?v0, fun_app$cp(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cp(?v3, ?v4))))
tff(axiom348,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v4: 'B_update_d_update_fun$'] :
      ( ( 'comp$ax'(A__questionmark_v0,A__questionmark_v1) = 'comp$ax'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cp'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v4:B_update_c_update_fun$ ((comp$ay(?v0, ?v1) = comp$ay(?v2, ?v3)) ⇒ (fun_app$ct(?v0, fun_app$cr(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cr(?v3, ?v4))))
tff(axiom349,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v4: 'B_update_c_update_fun$'] :
      ( ( 'comp$ay'(A__questionmark_v0,A__questionmark_v1) = 'comp$ay'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cr'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) ⇒ (fun_app$ae(?v0, fun_app$u(?v1, ?v4)) = fun_app$ae(?v2, fun_app$u(?v3, ?v4))))
tff(axiom350,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$u'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:C_d_prod_update$ ((fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)) ⇒ (fun_app$ae(?v0, fun_app$by(?v1, ?v4)) = fun_app$ae(?v2, fun_app$by(?v3, ?v4))))
tff(axiom351,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update$'] :
      ( ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$by'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) ⇒ (fun_app$ae(?v0, fun_app$au(?v1, ?v4)) = fun_app$ae(?v2, fun_app$au(?v3, ?v4))))
tff(axiom352,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$au'(A__questionmark_v3,A__questionmark_v4)) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_d_update_fun_a_update_a_update_fun_fun$ (((comp$au(?v0, ?v1) = comp$au(?v2, ?v3)) ∧ (∀ ?v4:B_update_d_update_fun$ (fun_app$co(?v0, fun_app$cp(?v1, ?v4)) = fun_app$co(?v2, fun_app$cp(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom353,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( 'comp$au'(A__questionmark_v0,A__questionmark_v1) = 'comp$au'(A__questionmark_v2,A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'B_update_d_update_fun$'] : 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$co'(A__questionmark_v2,'fun_app$cp'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_c_update_fun_a_update_a_update_fun_fun$ (((comp$av(?v0, ?v1) = comp$av(?v2, ?v3)) ∧ (∀ ?v4:B_update_c_update_fun$ (fun_app$co(?v0, fun_app$cr(?v1, ?v4)) = fun_app$co(?v2, fun_app$cr(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom354,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( 'comp$av'(A__questionmark_v0,A__questionmark_v1) = 'comp$av'(A__questionmark_v2,A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'B_update_c_update_fun$'] : 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$co'(A__questionmark_v2,'fun_app$cr'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ (((comp$aw(?v0, ?v1) = comp$aw(?v2, ?v3)) ∧ (∀ ?v4:B_update_c_d_prod_update_fun$ (fun_app$ct(?v0, fun_app$cu(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cu(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom355,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( 'comp$aw'(A__questionmark_v0,A__questionmark_v1) = 'comp$aw'(A__questionmark_v2,A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'B_update_c_d_prod_update_fun$'] : 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cu'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_d_update_fun_a_update_a_update_fun_fun$ (((comp$ax(?v0, ?v1) = comp$ax(?v2, ?v3)) ∧ (∀ ?v4:B_update_d_update_fun$ (fun_app$ct(?v0, fun_app$cp(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cp(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom356,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( 'comp$ax'(A__questionmark_v0,A__questionmark_v1) = 'comp$ax'(A__questionmark_v2,A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'B_update_d_update_fun$'] : 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cp'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_update_fun_a_update_a_update_fun_fun$ (((comp$ay(?v0, ?v1) = comp$ay(?v2, ?v3)) ∧ (∀ ?v4:B_update_c_update_fun$ (fun_app$ct(?v0, fun_app$cr(?v1, ?v4)) = fun_app$ct(?v2, fun_app$cr(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom357,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( ( 'comp$ay'(A__questionmark_v0,A__questionmark_v1) = 'comp$ay'(A__questionmark_v2,A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'B_update_c_update_fun$'] : 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ct'(A__questionmark_v2,'fun_app$cr'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) ∧ (∀ ?v4:C_update$ (fun_app$ae(?v0, fun_app$u(?v1, ?v4)) = fun_app$ae(?v2, fun_app$u(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom358,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'C_update$'] : 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$u'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (((fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)) ∧ (∀ ?v4:C_d_prod_update$ (fun_app$ae(?v0, fun_app$by(?v1, ?v4)) = fun_app$ae(?v2, fun_app$by(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom359,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'C_d_prod_update$'] : 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$by'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) ∧ (∀ ?v4:D_update$ (fun_app$ae(?v0, fun_app$au(?v1, ?v4)) = fun_app$ae(?v2, fun_app$au(?v3, ?v4))) ⇒ false)) ⇒ false)
tff(axiom360,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) )
        & ( ! [A__questionmark_v4: 'D_update$'] : 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$ae'(A__questionmark_v2,'fun_app$au'(A__questionmark_v3,A__questionmark_v4))
         => $false ) )
     => $false ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:A_update_b_update_fun$ ?v4:C_update_a_update_fun$ ?v5:C_update$ ((fun_app$ae(?v0, fun_app$u(?v1, ?v2)) = fun_app$ae(?v3, fun_app$u(?v4, ?v5))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, ?v3), ?v4), ?v5)))
tff(axiom361,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'C_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:A_update_b_update_fun$ ?v4:D_update_a_update_fun$ ?v5:D_update$ ((fun_app$ae(?v0, fun_app$u(?v1, ?v2)) = fun_app$ae(?v3, fun_app$au(?v4, ?v5))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v4), ?v5)))
tff(axiom362,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'D_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:A_update_b_update_fun$ ?v4:C_update_a_update_fun$ ?v5:C_update$ ((fun_app$ae(?v0, fun_app$au(?v1, ?v2)) = fun_app$ae(?v3, fun_app$u(?v4, ?v5))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, ?v3), ?v4), ?v5)))
tff(axiom363,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'C_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:A_update_b_update_fun$ ?v4:D_update_a_update_fun$ ?v5:D_update$ ((fun_app$ae(?v0, fun_app$au(?v1, ?v2)) = fun_app$ae(?v3, fun_app$au(?v4, ?v5))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v4), ?v5)))
tff(axiom364,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'D_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:A_update_b_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:C_d_prod_update$ ((fun_app$ae(?v0, fun_app$u(?v1, ?v2)) = fun_app$ae(?v3, fun_app$by(?v4, ?v5))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v4), ?v5)))
tff(axiom365,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'C_d_prod_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$by'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ ?v3:A_update_b_update_fun$ ?v4:C_update_a_update_fun$ ?v5:C_update$ ((fun_app$ae(?v0, fun_app$by(?v1, ?v2)) = fun_app$ae(?v3, fun_app$u(?v4, ?v5))) ⇒ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, ?v3), ?v4), ?v5)))
tff(axiom366,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'C_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ ?v3:A_update_b_update_fun$ ?v4:D_update_a_update_fun$ ?v5:D_update$ ((fun_app$ae(?v0, fun_app$by(?v1, ?v2)) = fun_app$ae(?v3, fun_app$au(?v4, ?v5))) ⇒ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v4), ?v5)))
tff(axiom367,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'D_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:A_update_b_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:C_d_prod_update$ ((fun_app$ae(?v0, fun_app$au(?v1, ?v2)) = fun_app$ae(?v3, fun_app$by(?v4, ?v5))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v4), ?v5)))
tff(axiom368,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'C_d_prod_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$by'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ ?v3:A_update_b_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:C_d_prod_update$ ((fun_app$ae(?v0, fun_app$by(?v1, ?v2)) = fun_app$ae(?v3, fun_app$by(?v4, ?v5))) ⇒ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v4), ?v5)))
tff(axiom369,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'C_d_prod_update$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$by'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ ?v3:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v4:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v5:B_update_d_update_fun$ ((fun_app$co(?v0, fun_app$cp(?v1, ?v2)) = fun_app$co(?v3, fun_app$cp(?v4, ?v5))) ⇒ (fun_app$cn(comp$au(?v0, ?v1), ?v2) = fun_app$cn(comp$au(?v3, ?v4), ?v5)))
tff(axiom370,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v5: 'B_update_d_update_fun$'] :
      ( ( 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$co'(A__questionmark_v3,'fun_app$cp'(A__questionmark_v4,A__questionmark_v5)) )
     => ( 'fun_app$cn'('comp$au'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cn'('comp$au'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_d_update_fun$ ((comp$au(?v0, ?v1) = ?v2) ⇒ (fun_app$co(?v0, fun_app$cp(?v1, ?v3)) = fun_app$cn(?v2, ?v3)))
tff(axiom371,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun$'] :
      ( ( 'comp$au'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$cn'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun_d_update_b_update_fun_fun$ ?v3:B_update_c_update_fun$ ((comp$av(?v0, ?v1) = ?v2) ⇒ (fun_app$co(?v0, fun_app$cr(?v1, ?v3)) = fun_app$cq(?v2, ?v3)))
tff(axiom372,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun_d_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun$'] :
      ( ( 'comp$av'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$cq'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_d_prod_update_fun$ ((comp$aw(?v0, ?v1) = ?v2) ⇒ (fun_app$ct(?v0, fun_app$cu(?v1, ?v3)) = fun_app$cs(?v2, ?v3)))
tff(axiom373,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_d_prod_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_d_prod_update_fun$'] :
      ( ( 'comp$aw'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$cs'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_d_update_fun$ ((comp$ax(?v0, ?v1) = ?v2) ⇒ (fun_app$ct(?v0, fun_app$cp(?v1, ?v3)) = fun_app$cv(?v2, ?v3)))
tff(axiom374,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_d_update_fun$'] :
      ( ( 'comp$ax'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$cv'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun_c_update_b_update_fun_fun$ ?v3:B_update_c_update_fun$ ((comp$ay(?v0, ?v1) = ?v2) ⇒ (fun_app$ct(?v0, fun_app$cr(?v1, ?v3)) = fun_app$cw(?v2, ?v3)))
tff(axiom375,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun_c_update_b_update_fun_fun$',A__questionmark_v3: 'B_update_c_update_fun$'] :
      ( ( 'comp$ay'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$cw'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_b_update_fun$ ?v3:C_update$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = ?v2) ⇒ (fun_app$ae(?v0, fun_app$u(?v1, ?v3)) = fun_app$q(?v2, ?v3)))
tff(axiom376,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'C_update$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$q'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update_b_update_fun$ ?v3:C_d_prod_update$ ((fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1) = ?v2) ⇒ (fun_app$ae(?v0, fun_app$by(?v1, ?v3)) = fun_app$bz(?v2, ?v3)))
tff(axiom377,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update$'] :
      ( ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bz'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_b_update_fun$ ?v3:D_update$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = ?v2) ⇒ (fun_app$ae(?v0, fun_app$au(?v1, ?v3)) = fun_app$m(?v2, ?v3)))
tff(axiom378,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$',A__questionmark_v3: 'D_update$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$m'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_d_prod_update$ ?v1:C_d_prod_update_bool_fun$ (member$(?v0, collect$(?v1)) = fun_app$ag(?v1, ?v0))
tff(axiom379,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update$',A__questionmark_v1: 'C_d_prod_update_bool_fun$'] :
      ( 'member$'(A__questionmark_v0,'collect$'(A__questionmark_v1))
    <=> 'fun_app$ag'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:D_update$ ?v1:D_update_bool_fun$ (member$a(?v0, collect$a(?v1)) = fun_app$ah(?v1, ?v0))
tff(axiom380,axiom,
    ! [A__questionmark_v0: 'D_update$',A__questionmark_v1: 'D_update_bool_fun$'] :
      ( 'member$a'(A__questionmark_v0,'collect$a'(A__questionmark_v1))
    <=> 'fun_app$ah'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update$ ?v1:C_update_bool_fun$ (member$b(?v0, collect$b(?v1)) = fun_app$ai(?v1, ?v0))
tff(axiom381,axiom,
    ! [A__questionmark_v0: 'C_update$',A__questionmark_v1: 'C_update_bool_fun$'] :
      ( 'member$b'(A__questionmark_v0,'collect$b'(A__questionmark_v1))
    <=> 'fun_app$ai'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_update$ ?v1:A_update_bool_fun$ (member$c(?v0, collect$c(?v1)) = fun_app$aj(?v1, ?v0))
tff(axiom382,axiom,
    ! [A__questionmark_v0: 'A_update$',A__questionmark_v1: 'A_update_bool_fun$'] :
      ( 'member$c'(A__questionmark_v0,'collect$c'(A__questionmark_v1))
    <=> 'fun_app$aj'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_a_update_fun_bool_fun$ (member$e(?v0, collect$d(?v1)) = fun_app$j(?v1, ?v0))
tff(axiom383,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun_bool_fun$'] :
      ( 'member$e'(A__questionmark_v0,'collect$d'(A__questionmark_v1))
    <=> 'fun_app$j'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_a_update_fun_bool_fun$ (member$d(?v0, collect$e(?v1)) = fun_app$i(?v1, ?v0))
tff(axiom384,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun_bool_fun$'] :
      ( 'member$d'(A__questionmark_v0,'collect$e'(A__questionmark_v1))
    <=> 'fun_app$i'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun_bool_fun$ (member$f(?v0, collect$f(?v1)) = fun_app$k(?v1, ?v0))
tff(axiom385,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun_bool_fun$'] :
      ( 'member$f'(A__questionmark_v0,'collect$f'(A__questionmark_v1))
    <=> 'fun_app$k'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:C_d_prod_update_set$ (collect$(uu$(?v0)) = ?v0)
tff(axiom386,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_set$'] : 'collect$'('uu$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:D_update_set$ (collect$a(uua$(?v0)) = ?v0)
tff(axiom387,axiom,
    ! [A__questionmark_v0: 'D_update_set$'] : 'collect$a'('uua$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:C_update_set$ (collect$b(uub$(?v0)) = ?v0)
tff(axiom388,axiom,
    ! [A__questionmark_v0: 'C_update_set$'] : 'collect$b'('uub$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_update_set$ (collect$c(uuc$(?v0)) = ?v0)
tff(axiom389,axiom,
    ! [A__questionmark_v0: 'A_update_set$'] : 'collect$c'('uuc$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:D_update_a_update_fun_set$ (collect$d(uud$(?v0)) = ?v0)
tff(axiom390,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun_set$'] : 'collect$d'('uud$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:C_d_prod_update_a_update_fun_set$ (collect$e(uue$(?v0)) = ?v0)
tff(axiom391,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun_set$'] : 'collect$e'('uue$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:C_update_a_update_fun_set$ (collect$f(uuf$(?v0)) = ?v0)
tff(axiom392,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun_set$'] : 'collect$f'('uuf$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:D_update_a_update_fun_bool_fun$ ?v1:D_update_a_update_fun_bool_fun$ (∀ ?v2:D_update_a_update_fun$ (fun_app$j(?v0, ?v2) = fun_app$j(?v1, ?v2)) ⇒ (collect$d(?v0) = collect$d(?v1)))
tff(axiom393,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun_bool_fun$',A__questionmark_v1: 'D_update_a_update_fun_bool_fun$'] :
      ( ! [A__questionmark_v2: 'D_update_a_update_fun$'] :
          ( 'fun_app$j'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$j'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$d'(A__questionmark_v0) = 'collect$d'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun_bool_fun$ ?v1:C_d_prod_update_a_update_fun_bool_fun$ (∀ ?v2:C_d_prod_update_a_update_fun$ (fun_app$i(?v0, ?v2) = fun_app$i(?v1, ?v2)) ⇒ (collect$e(?v0) = collect$e(?v1)))
tff(axiom394,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun_bool_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun_bool_fun$'] :
      ( ! [A__questionmark_v2: 'C_d_prod_update_a_update_fun$'] :
          ( 'fun_app$i'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$i'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$e'(A__questionmark_v0) = 'collect$e'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:C_update_a_update_fun_bool_fun$ ?v1:C_update_a_update_fun_bool_fun$ (∀ ?v2:C_update_a_update_fun$ (fun_app$k(?v0, ?v2) = fun_app$k(?v1, ?v2)) ⇒ (collect$f(?v0) = collect$f(?v1)))
tff(axiom395,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun_bool_fun$',A__questionmark_v1: 'C_update_a_update_fun_bool_fun$'] :
      ( ! [A__questionmark_v2: 'C_update_a_update_fun$'] :
          ( 'fun_app$k'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$k'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$f'(A__questionmark_v0) = 'collect$f'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ ?v3:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v4:B_update_d_update_fun_a_update_a_update_fun_fun$ ((fun_app$co(?v0, fun_app$cp(?v1, ?v2)) = fun_app$co(?v3, fun_app$cp(?v4, ?v2))) ⇒ (fun_app$cn(comp$au(?v0, ?v1), ?v2) = fun_app$cn(comp$au(?v3, ?v4), ?v2)))
tff(axiom396,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( 'fun_app$co'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$co'(A__questionmark_v3,'fun_app$cp'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$cn'('comp$au'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cn'('comp$au'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ ?v3:A_update_a_update_fun_d_update_b_update_fun_fun$ ?v4:B_update_c_update_fun_a_update_a_update_fun_fun$ ((fun_app$co(?v0, fun_app$cr(?v1, ?v2)) = fun_app$co(?v3, fun_app$cr(?v4, ?v2))) ⇒ (fun_app$cq(comp$av(?v0, ?v1), ?v2) = fun_app$cq(comp$av(?v3, ?v4), ?v2)))
tff(axiom397,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_d_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( 'fun_app$co'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$co'(A__questionmark_v3,'fun_app$cr'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$cq'('comp$av'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cq'('comp$av'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_d_prod_update_fun$ ?v3:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v4:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ((fun_app$ct(?v0, fun_app$cu(?v1, ?v2)) = fun_app$ct(?v3, fun_app$cu(?v4, ?v2))) ⇒ (fun_app$cs(comp$aw(?v0, ?v1), ?v2) = fun_app$cs(comp$aw(?v3, ?v4), ?v2)))
tff(axiom398,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_d_prod_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$'] :
      ( ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cu'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ct'(A__questionmark_v3,'fun_app$cu'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$cs'('comp$aw'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cs'('comp$aw'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_d_update_fun$ ?v3:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v4:B_update_d_update_fun_a_update_a_update_fun_fun$ ((fun_app$ct(?v0, fun_app$cp(?v1, ?v2)) = fun_app$ct(?v3, fun_app$cp(?v4, ?v2))) ⇒ (fun_app$cv(comp$ax(?v0, ?v1), ?v2) = fun_app$cv(comp$ax(?v3, ?v4), ?v2)))
tff(axiom399,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_d_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_d_update_fun_a_update_a_update_fun_fun$'] :
      ( ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cp'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ct'(A__questionmark_v3,'fun_app$cp'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$cv'('comp$ax'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cv'('comp$ax'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v1:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v2:B_update_c_update_fun$ ?v3:A_update_a_update_fun_c_update_b_update_fun_fun$ ?v4:B_update_c_update_fun_a_update_a_update_fun_fun$ ((fun_app$ct(?v0, fun_app$cr(?v1, ?v2)) = fun_app$ct(?v3, fun_app$cr(?v4, ?v2))) ⇒ (fun_app$cw(comp$ay(?v0, ?v1), ?v2) = fun_app$cw(comp$ay(?v3, ?v4), ?v2)))
tff(axiom400,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v1: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v2: 'B_update_c_update_fun$',A__questionmark_v3: 'A_update_a_update_fun_c_update_b_update_fun_fun$',A__questionmark_v4: 'B_update_c_update_fun_a_update_a_update_fun_fun$'] :
      ( ( 'fun_app$ct'(A__questionmark_v0,'fun_app$cr'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ct'(A__questionmark_v3,'fun_app$cr'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$cw'('comp$ay'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$cw'('comp$ay'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:A_update_b_update_fun$ ?v4:C_update_a_update_fun$ ((fun_app$ae(?v0, fun_app$u(?v1, ?v2)) = fun_app$ae(?v3, fun_app$u(?v4, ?v2))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, ?v3), ?v4), ?v2)))
tff(axiom401,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ ?v3:A_update_b_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ((fun_app$ae(?v0, fun_app$by(?v1, ?v2)) = fun_app$ae(?v3, fun_app$by(?v4, ?v2))) ⇒ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v4), ?v2)))
tff(axiom402,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$by'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:A_update_b_update_fun$ ?v4:D_update_a_update_fun$ ((fun_app$ae(?v0, fun_app$au(?v1, ?v2)) = fun_app$ae(?v3, fun_app$au(?v4, ?v2))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v4), ?v2)))
tff(axiom403,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$'] :
      ( ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$ae'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_c_update_fun$ ?v2:C_update$ ?v3:A_update_a_update_fun$ ?v4:C_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$u(?v0, fun_app$bx(?v1, ?v2)) = fun_app$bd(?v3, fun_app$u(?v4, ?v2))) ⇒ (fun_app$q(comp$f(fun_app$be(fun_app$bf(comp$, ?v5), ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom404,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_c_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$u'(A__questionmark_v0,'fun_app$bx'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_c_update_fun$ ?v2:D_update$ ?v3:A_update_a_update_fun$ ?v4:D_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$u(?v0, fun_app$bh(?v1, ?v2)) = fun_app$bd(?v3, fun_app$au(?v4, ?v2))) ⇒ (fun_app$m(comp$al(fun_app$be(fun_app$bf(comp$, ?v5), ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom405,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$u'(A__questionmark_v0,'fun_app$bh'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$m'('comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:C_update_d_update_fun$ ?v2:C_update$ ?v3:A_update_a_update_fun$ ?v4:C_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$au(?v0, fun_app$cx(?v1, ?v2)) = fun_app$bd(?v3, fun_app$u(?v4, ?v2))) ⇒ (fun_app$q(comp$an(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom406,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'C_update_d_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$au'(A__questionmark_v0,'fun_app$cx'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_d_update_fun$ ?v2:D_update$ ?v3:A_update_a_update_fun$ ?v4:D_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$au(?v0, fun_app$bg(?v1, ?v2)) = fun_app$bd(?v3, fun_app$au(?v4, ?v2))) ⇒ (fun_app$m(comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v0), ?v1), ?v2) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom407,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$au'(A__questionmark_v0,'fun_app$bg'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$au'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$m'('comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$bd(?v0, fun_app$u(?v1, ?v2)) = fun_app$u(?v3, fun_app$bx(?v4, ?v2))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v0)), ?v1), ?v2) = fun_app$q(comp$f(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v4), ?v2)))
tff(axiom408,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$bd'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$u'(A__questionmark_v3,'fun_app$bx'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$bd(?v0, fun_app$u(?v1, ?v2)) = fun_app$au(?v3, fun_app$cx(?v4, ?v2))) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v0)), ?v1), ?v2) = fun_app$q(comp$an(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v4), ?v2)))
tff(axiom409,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$bd'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$au'(A__questionmark_v3,'fun_app$cx'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$bd(?v0, fun_app$au(?v1, ?v2)) = fun_app$u(?v3, fun_app$bh(?v4, ?v2))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, comp$am(?v5, ?v0)), ?v1), ?v2) = fun_app$m(comp$al(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v4), ?v2)))
tff(axiom410,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$bd'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$u'(A__questionmark_v3,'fun_app$bh'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v5,A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$bd(?v0, fun_app$au(?v1, ?v2)) = fun_app$au(?v3, fun_app$bg(?v4, ?v2))) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, comp$am(?v5, ?v0)), ?v1), ?v2) = fun_app$m(comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v4), ?v2)))
tff(axiom411,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$bd'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$au'(A__questionmark_v3,'fun_app$bg'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v5,A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = 'fun_app$m'('comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_d_prod_update_c_update_fun$ ?v2:C_d_prod_update$ ?v3:A_update_a_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$u(?v0, fun_app$cy(?v1, ?v2)) = fun_app$bd(?v3, fun_app$by(?v4, ?v2))) ⇒ (fun_app$bz(comp$bb(fun_app$be(fun_app$bf(comp$, ?v5), ?v0), ?v1), ?v2) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom412,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_c_update_fun$',A__questionmark_v2: 'C_d_prod_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$u'(A__questionmark_v0,'fun_app$cy'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$by'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$bz'('comp$bb'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_update_c_d_prod_update_fun$ ?v2:C_update$ ?v3:A_update_a_update_fun$ ?v4:C_update_a_update_fun$ ?v5:A_update_b_update_fun$ ((fun_app$by(?v0, fun_app$cz(?v1, ?v2)) = fun_app$bd(?v3, fun_app$u(?v4, ?v2))) ⇒ (fun_app$q(comp$ba(fun_app$bj(fun_app$bk(comp$a, ?v5), ?v0), ?v1), ?v2) = fun_app$q(fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v3)), ?v4), ?v2)))
tff(axiom413,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_update_c_d_prod_update_fun$',A__questionmark_v2: 'C_update$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$by'(A__questionmark_v0,'fun_app$cz'(A__questionmark_v1,A__questionmark_v2)) = 'fun_app$bd'(A__questionmark_v3,'fun_app$u'(A__questionmark_v4,A__questionmark_v2)) )
     => ( 'fun_app$q'('comp$ba'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v5),A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v3)),A__questionmark_v4),A__questionmark_v2) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ((comp$g(?v0, ?v1) = ?v2) ⇒ (comp$d(?v0, fun_app$be(fun_app$bf(comp$, ?v1), ?v3)) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)))
tff(axiom414,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$d'(A__questionmark_v0,'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ((comp$g(?v0, ?v1) = ?v2) ⇒ (comp$p(?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)))
tff(axiom415,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$p'(A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ((comp$am(?v0, ?v1) = ?v2) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$b(?v1, ?v3)) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)))
tff(axiom416,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
      ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$b'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ((comp$am(?v0, ?v1) = ?v2) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$at(?v1, ?v3)) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)))
tff(axiom417,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
      ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$at'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_b_update_fun$ ?v3:C_update_c_update_fun$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = ?v2) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$e(?v1, ?v3)) = comp$f(?v2, ?v3)))
tff(axiom418,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'C_update_c_update_fun$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$e'(A__questionmark_v1,A__questionmark_v3)) = 'comp$f'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_b_update_fun$ ?v3:D_update_c_update_fun$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = ?v2) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$as(?v1, ?v3)) = comp$al(?v2, ?v3)))
tff(axiom419,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'D_update_c_update_fun$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$as'(A__questionmark_v1,A__questionmark_v3)) = 'comp$al'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_b_update_fun$ ?v3:C_update_d_update_fun$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = ?v2) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$y(?v1, ?v3)) = comp$an(?v2, ?v3)))
tff(axiom420,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$',A__questionmark_v3: 'C_update_d_update_fun$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$y'(A__questionmark_v1,A__questionmark_v3)) = 'comp$an'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_b_update_fun$ ?v3:D_update_d_update_fun$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = ?v2) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$x(?v1, ?v3)) = comp$ao(?v2, ?v3)))
tff(axiom421,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$',A__questionmark_v3: 'D_update_d_update_fun$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$x'(A__questionmark_v1,A__questionmark_v3)) = 'comp$ao'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ((comp$g(?v0, ?v1) = ?v2) ⇒ (comp$v(?v0, fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)))
tff(axiom422,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$v'(A__questionmark_v0,'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ((comp$am(?v0, ?v1) = ?v2) ⇒ (fun_app$bj(fun_app$bk(comp$a, ?v0), comp$bd(?v1, ?v3)) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)))
tff(axiom423,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] :
      ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),'comp$bd'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_c_update_fun$ ?v2:A_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:A_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((comp$e(?v0, ?v1) = comp$b(?v2, ?v3)) ∧ (comp$am(?v4, ?v2) = ?v5)) ⇒ (comp$f(fun_app$be(fun_app$bf(comp$, ?v4), ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v5), ?v3)))
tff(axiom424,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_c_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'comp$e'(A__questionmark_v0,A__questionmark_v1) = 'comp$b'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$am'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_c_update_fun$ ?v2:A_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:A_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((comp$as(?v0, ?v1) = comp$at(?v2, ?v3)) ∧ (comp$am(?v4, ?v2) = ?v5)) ⇒ (comp$al(fun_app$be(fun_app$bf(comp$, ?v4), ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3)))
tff(axiom425,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'comp$as'(A__questionmark_v0,A__questionmark_v1) = 'comp$at'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$am'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:C_update_d_update_fun$ ?v2:A_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:A_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((comp$y(?v0, ?v1) = comp$b(?v2, ?v3)) ∧ (comp$am(?v4, ?v2) = ?v5)) ⇒ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v5), ?v3)))
tff(axiom426,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'C_update_d_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'comp$y'(A__questionmark_v0,A__questionmark_v1) = 'comp$b'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$am'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_d_update_fun$ ?v2:A_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:A_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((comp$x(?v0, ?v1) = comp$at(?v2, ?v3)) ∧ (comp$am(?v4, ?v2) = ?v5)) ⇒ (comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3)))
tff(axiom427,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'comp$x'(A__questionmark_v0,A__questionmark_v1) = 'comp$at'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$am'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_c_update_fun$ ?v4:A_update_b_update_fun$ ?v5:C_update_b_update_fun$ (((comp$b(?v0, ?v1) = comp$e(?v2, ?v3)) ∧ (fun_app$be(fun_app$bf(comp$, ?v4), ?v2) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, comp$am(?v4, ?v0)), ?v1) = comp$f(?v5, ?v3)))
tff(axiom428,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_c_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'C_update_b_update_fun$'] :
      ( ( ( 'comp$b'(A__questionmark_v0,A__questionmark_v1) = 'comp$e'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'comp$f'(A__questionmark_v5,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_c_update_fun$ ?v4:A_update_b_update_fun$ ?v5:C_update_b_update_fun$ (((comp$at(?v0, ?v1) = comp$as(?v2, ?v3)) ∧ (fun_app$be(fun_app$bf(comp$, ?v4), ?v2) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, comp$am(?v4, ?v0)), ?v1) = comp$al(?v5, ?v3)))
tff(axiom429,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_c_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'C_update_b_update_fun$'] :
      ( ( ( 'comp$at'(A__questionmark_v0,A__questionmark_v1) = 'comp$as'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'comp$al'(A__questionmark_v5,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_d_update_fun$ ?v4:A_update_b_update_fun$ ?v5:D_update_b_update_fun$ (((comp$b(?v0, ?v1) = comp$y(?v2, ?v3)) ∧ (fun_app$bv(fun_app$bw(comp$j, ?v4), ?v2) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, comp$am(?v4, ?v0)), ?v1) = comp$an(?v5, ?v3)))
tff(axiom430,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_d_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'D_update_b_update_fun$'] :
      ( ( ( 'comp$b'(A__questionmark_v0,A__questionmark_v1) = 'comp$y'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'comp$an'(A__questionmark_v5,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_d_update_fun$ ?v4:A_update_b_update_fun$ ?v5:D_update_b_update_fun$ (((comp$at(?v0, ?v1) = comp$x(?v2, ?v3)) ∧ (fun_app$bv(fun_app$bw(comp$j, ?v4), ?v2) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, comp$am(?v4, ?v0)), ?v1) = comp$ao(?v5, ?v3)))
tff(axiom431,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_d_update_fun$',A__questionmark_v4: 'A_update_b_update_fun$',A__questionmark_v5: 'D_update_b_update_fun$'] :
      ( ( ( 'comp$at'(A__questionmark_v0,A__questionmark_v1) = 'comp$x'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'comp$ao'(A__questionmark_v5,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:B_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) ∧ (comp$g(?v4, ?v2) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, comp$g(?v4, ?v0)), ?v1) = fun_app$be(fun_app$bf(comp$, ?v5), ?v3)))
tff(axiom432,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'B_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$g'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$g'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:B_update_b_update_fun$ ?v5:A_update_b_update_fun$ (((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) ∧ (comp$g(?v4, ?v2) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, comp$g(?v4, ?v0)), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3)))
tff(axiom433,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'B_update_b_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$'] :
      ( ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$g'(A__questionmark_v4,A__questionmark_v2) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j','comp$g'(A__questionmark_v4,A__questionmark_v0)),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_a_update_fun$ ?v4:C_update_a_update_fun$ ?v5:C_update_a_update_fun$ (((comp$g(?v0, ?v1) = comp$am(?v2, ?v3)) ∧ (comp$b(?v3, ?v4) = ?v5)) ⇒ (comp$d(?v0, fun_app$be(fun_app$bf(comp$, ?v1), ?v4)) = fun_app$be(fun_app$bf(comp$, ?v2), ?v5)))
tff(axiom434,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'C_update_a_update_fun$'] :
      ( ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = 'comp$am'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$b'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'comp$d'(A__questionmark_v0,'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v4)) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_a_update_fun$ ?v4:D_update_a_update_fun$ ?v5:D_update_a_update_fun$ (((comp$g(?v0, ?v1) = comp$am(?v2, ?v3)) ∧ (comp$at(?v3, ?v4) = ?v5)) ⇒ (comp$p(?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v4)) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v5)))
tff(axiom435,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'D_update_a_update_fun$'] :
      ( ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = 'comp$am'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$at'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'comp$p'(A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v4)) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_update_a_update_fun$ ?v5:C_update_b_update_fun$ (((comp$am(?v0, ?v1) = comp$g(?v2, ?v3)) ∧ (fun_app$be(fun_app$bf(comp$, ?v3), ?v4) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$b(?v1, ?v4)) = comp$d(?v2, ?v5)))
tff(axiom436,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_a_update_fun$',A__questionmark_v5: 'C_update_b_update_fun$'] :
      ( ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = 'comp$g'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$b'(A__questionmark_v1,A__questionmark_v4)) = 'comp$d'(A__questionmark_v2,A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:A_update_b_update_fun$ ?v4:D_update_a_update_fun$ ?v5:D_update_b_update_fun$ (((comp$am(?v0, ?v1) = comp$g(?v2, ?v3)) ∧ (fun_app$bv(fun_app$bw(comp$j, ?v3), ?v4) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$at(?v1, ?v4)) = comp$p(?v2, ?v5)))
tff(axiom437,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_a_update_fun$',A__questionmark_v5: 'D_update_b_update_fun$'] :
      ( ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = 'comp$g'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$at'(A__questionmark_v1,A__questionmark_v4)) = 'comp$p'(A__questionmark_v2,A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_fun$ ?v5:C_update_a_update_fun$ (((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) ∧ (comp$e(?v3, ?v4) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$e(?v1, ?v4)) = fun_app$be(fun_app$bf(comp$, ?v2), ?v5)))
tff(axiom438,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'C_update_a_update_fun$'] :
      ( ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$e'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$e'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_fun$ ?v5:D_update_a_update_fun$ (((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) ∧ (comp$as(?v3, ?v4) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$as(?v1, ?v4)) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v5)))
tff(axiom439,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'D_update_a_update_fun$'] :
      ( ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$as'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$as'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_fun$ ?v5:C_update_a_update_fun$ (((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) ∧ (comp$y(?v3, ?v4) = ?v5)) ⇒ (fun_app$be(fun_app$bf(comp$, ?v0), comp$y(?v1, ?v4)) = fun_app$be(fun_app$bf(comp$, ?v2), ?v5)))
tff(axiom440,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'C_update_a_update_fun$'] :
      ( ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$y'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),'comp$y'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_fun$ ?v5:D_update_a_update_fun$ (((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) ∧ (comp$x(?v3, ?v4) = ?v5)) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v0), comp$x(?v1, ?v4)) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v5)))
tff(axiom441,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_fun$',A__questionmark_v5: 'D_update_a_update_fun$'] :
      ( ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3) )
        & ( 'comp$x'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),'comp$x'(A__questionmark_v1,A__questionmark_v4)) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:B_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_a_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:C_d_prod_update_a_update_fun$ (((comp$g(?v0, ?v1) = comp$am(?v2, ?v3)) ∧ (comp$bd(?v3, ?v4) = ?v5)) ⇒ (comp$v(?v0, fun_app$bj(fun_app$bk(comp$a, ?v1), ?v4)) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v5)))
tff(axiom442,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'C_d_prod_update_a_update_fun$'] :
      ( ( ( 'comp$g'(A__questionmark_v0,A__questionmark_v1) = 'comp$am'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'comp$bd'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'comp$v'(A__questionmark_v0,'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v4)) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v5) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_d_prod_update_a_update_fun$ ?v5:C_d_prod_update_b_update_fun$ (((comp$am(?v0, ?v1) = comp$g(?v2, ?v3)) ∧ (fun_app$bj(fun_app$bk(comp$a, ?v3), ?v4) = ?v5)) ⇒ (fun_app$bj(fun_app$bk(comp$a, ?v0), comp$bd(?v1, ?v4)) = comp$v(?v2, ?v5)))
tff(axiom443,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_d_prod_update_a_update_fun$',A__questionmark_v5: 'C_d_prod_update_b_update_fun$'] :
      ( ( ( 'comp$am'(A__questionmark_v0,A__questionmark_v1) = 'comp$g'(A__questionmark_v2,A__questionmark_v3) )
        & ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v4) = A__questionmark_v5 ) )
     => ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),'comp$bd'(A__questionmark_v1,A__questionmark_v4)) = 'comp$v'(A__questionmark_v2,A__questionmark_v5) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_c_update_fun$ ?v2:C_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$e(?v0, ?v1) = ?v2) ⇒ (comp$f(fun_app$be(fun_app$bf(comp$, ?v3), ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v3), ?v2)))
tff(axiom444,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_c_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$e'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_c_update_fun$ ?v2:D_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$as(?v0, ?v1) = ?v2) ⇒ (comp$al(fun_app$be(fun_app$bf(comp$, ?v3), ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v2)))
tff(axiom445,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_c_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$as'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:C_update_d_update_fun$ ?v2:C_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$y(?v0, ?v1) = ?v2) ⇒ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v3), ?v2)))
tff(axiom446,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'C_update_d_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$y'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_d_update_fun$ ?v2:D_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$x(?v0, ?v1) = ?v2) ⇒ (comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v0), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v2)))
tff(axiom447,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_d_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$x'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$b(?v0, ?v1) = ?v2) ⇒ (fun_app$be(fun_app$bf(comp$, comp$am(?v3, ?v0)), ?v1) = fun_app$be(fun_app$bf(comp$, ?v3), ?v2)))
tff(axiom448,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$b'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v3,A__questionmark_v0)),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$at(?v0, ?v1) = ?v2) ⇒ (fun_app$bv(fun_app$bw(comp$j, comp$am(?v3, ?v0)), ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v2)))
tff(axiom449,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$at'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'(A__questionmark_v3,A__questionmark_v0)),A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_b_update_fun$ ?v3:B_update_b_update_fun$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = ?v2) ⇒ (fun_app$be(fun_app$bf(comp$, comp$g(?v3, ?v0)), ?v1) = comp$d(?v3, ?v2)))
tff(axiom450,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$g'(A__questionmark_v3,A__questionmark_v0)),A__questionmark_v1) = 'comp$d'(A__questionmark_v3,A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_b_update_fun$ ?v3:B_update_b_update_fun$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = ?v2) ⇒ (fun_app$bv(fun_app$bw(comp$j, comp$g(?v3, ?v0)), ?v1) = comp$p(?v3, ?v2)))
tff(axiom451,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j','comp$g'(A__questionmark_v3,A__questionmark_v0)),A__questionmark_v1) = 'comp$p'(A__questionmark_v3,A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_d_prod_update_c_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$bc(?v0, ?v1) = ?v2) ⇒ (comp$bb(fun_app$be(fun_app$bf(comp$, ?v3), ?v0), ?v1) = fun_app$bj(fun_app$bk(comp$a, ?v3), ?v2)))
tff(axiom452,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_c_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$bc'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$bb'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_update_c_d_prod_update_fun$ ?v2:C_update_a_update_fun$ ?v3:A_update_b_update_fun$ ((comp$az(?v0, ?v1) = ?v2) ⇒ (comp$ba(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v0), ?v1) = fun_app$be(fun_app$bf(comp$, ?v3), ?v2)))
tff(axiom453,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_update_c_d_prod_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( 'comp$az'(A__questionmark_v0,A__questionmark_v1) = A__questionmark_v2 )
     => ( 'comp$ba'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v0),A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_itself$ ?v1:D_update_set$ (separating$(?v0, ?v1) = ∀ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ((fun_app$j(preregister$i, ?v2) ∧ (fun_app$j(preregister$i, ?v3) ∧ ∀ ?v4:D_update$ (member$a(?v4, ?v1) ⇒ (fun_app$au(?v2, ?v4) = fun_app$au(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom454,axiom,
    ! [A__questionmark_v0: 'A_itself$',A__questionmark_v1: 'D_update_set$'] :
      ( 'separating$'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] :
          ( ( 'fun_app$j'('preregister$i',A__questionmark_v2)
            & 'fun_app$j'('preregister$i',A__questionmark_v3)
            & ! [A__questionmark_v4: 'D_update$'] :
                ( 'member$a'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$au'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$au'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:B_itself$ ?v1:C_update_set$ (separating$a(?v0, ?v1) = ∀ ?v2:C_update_b_update_fun$ ?v3:C_update_b_update_fun$ ((preregister$b(?v2) ∧ (preregister$b(?v3) ∧ ∀ ?v4:C_update$ (member$b(?v4, ?v1) ⇒ (fun_app$q(?v2, ?v4) = fun_app$q(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom455,axiom,
    ! [A__questionmark_v0: 'B_itself$',A__questionmark_v1: 'C_update_set$'] :
      ( 'separating$a'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'C_update_b_update_fun$'] :
          ( ( 'preregister$b'(A__questionmark_v2)
            & 'preregister$b'(A__questionmark_v3)
            & ! [A__questionmark_v4: 'C_update$'] :
                ( 'member$b'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$q'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$q'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:A_itself$ ?v1:C_update_set$ (separating$b(?v0, ?v1) = ∀ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ((fun_app$k(preregister$a, ?v2) ∧ (fun_app$k(preregister$a, ?v3) ∧ ∀ ?v4:C_update$ (member$b(?v4, ?v1) ⇒ (fun_app$u(?v2, ?v4) = fun_app$u(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom456,axiom,
    ! [A__questionmark_v0: 'A_itself$',A__questionmark_v1: 'C_update_set$'] :
      ( 'separating$b'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] :
          ( ( 'fun_app$k'('preregister$a',A__questionmark_v2)
            & 'fun_app$k'('preregister$a',A__questionmark_v3)
            & ! [A__questionmark_v4: 'C_update$'] :
                ( 'member$b'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$u'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$u'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:B_itself$ ?v1:B_update_set$ (separating$c(?v0, ?v1) = ∀ ?v2:B_update_b_update_fun$ ?v3:B_update_b_update_fun$ ((preregister$k(?v2) ∧ (preregister$k(?v3) ∧ ∀ ?v4:B_update$ (member$g(?v4, ?v1) ⇒ (fun_app$x(?v2, ?v4) = fun_app$x(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom457,axiom,
    ! [A__questionmark_v0: 'B_itself$',A__questionmark_v1: 'B_update_set$'] :
      ( 'separating$c'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$'] :
          ( ( 'preregister$k'(A__questionmark_v2)
            & 'preregister$k'(A__questionmark_v3)
            & ! [A__questionmark_v4: 'B_update$'] :
                ( 'member$g'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$x'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$x'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:B_itself$ ?v1:A_update_set$ (separating$d(?v0, ?v1) = ∀ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ ((preregister$c(?v2) ∧ (preregister$c(?v3) ∧ ∀ ?v4:A_update$ (member$c(?v4, ?v1) ⇒ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom458,axiom,
    ! [A__questionmark_v0: 'B_itself$',A__questionmark_v1: 'A_update_set$'] :
      ( 'separating$d'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
          ( ( 'preregister$c'(A__questionmark_v2)
            & 'preregister$c'(A__questionmark_v3)
            & ! [A__questionmark_v4: 'A_update$'] :
                ( 'member$c'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:B_itself$ ?v1:C_d_prod_update_set$ (separating$e(?v0, ?v1) = ∀ ?v2:C_d_prod_update_b_update_fun$ ?v3:C_d_prod_update_b_update_fun$ ((preregister$(?v2) ∧ (preregister$(?v3) ∧ ∀ ?v4:C_d_prod_update$ (member$(?v4, ?v1) ⇒ (fun_app$bz(?v2, ?v4) = fun_app$bz(?v3, ?v4))))) ⇒ (?v2 = ?v3)))
tff(axiom459,axiom,
    ! [A__questionmark_v0: 'B_itself$',A__questionmark_v1: 'C_d_prod_update_set$'] :
      ( 'separating$e'(A__questionmark_v0,A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'C_d_prod_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_b_update_fun$'] :
          ( ( 'preregister$'(A__questionmark_v2)
            & 'preregister$'(A__questionmark_v3)
            & ! [A__questionmark_v4: 'C_d_prod_update$'] :
                ( 'member$'(A__questionmark_v4,A__questionmark_v1)
               => ( 'fun_app$bz'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$bz'(A__questionmark_v3,A__questionmark_v4) ) ) )
         => ( A__questionmark_v2 = A__questionmark_v3 ) ) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ register$am(uug$(?v0)))
tff(axiom460,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => 'register$am'('uug$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ (register$a(?v0) ⇒ register$an(uuh$(?v0)))
tff(axiom461,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$'] :
      ( 'register$a'(A__questionmark_v0)
     => 'register$an'('uuh$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ (register$g(?v0) ⇒ register$ao(uui$(?v0)))
tff(axiom462,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$'] :
      ( 'register$g'(A__questionmark_v0)
     => 'register$ao'('uui$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_b_update_fun$ (register$d(?v0) ⇒ register$ap(uuj$(?v0)))
tff(axiom463,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$'] :
      ( 'register$d'(A__questionmark_v0)
     => 'register$ap'('uuj$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_d_update_fun$ (register$v(?v0) ⇒ register$aq(uuk$(?v0)))
tff(axiom464,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$'] :
      ( 'register$v'(A__questionmark_v0)
     => 'register$aq'('uuk$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_c_update_fun$ (register$w(?v0) ⇒ register$ar(uul$(?v0)))
tff(axiom465,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$'] :
      ( 'register$w'(A__questionmark_v0)
     => 'register$ar'('uul$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ register$as(uum$(?v0)))
tff(axiom466,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => 'register$as'('uum$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ (register$a(?v0) ⇒ register$at(uun$(?v0)))
tff(axiom467,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$'] :
      ( 'register$a'(A__questionmark_v0)
     => 'register$at'('uun$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ (register$g(?v0) ⇒ register$au(uuo$(?v0)))
tff(axiom468,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$'] :
      ( 'register$g'(A__questionmark_v0)
     => 'register$au'('uuo$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_b_update_fun$ (register$d(?v0) ⇒ register$av(uup$(?v0)))
tff(axiom469,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$'] :
      ( 'register$d'(A__questionmark_v0)
     => 'register$av'('uup$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ (fun_app$k(register$, ?v0) ⇒ register$aw(uuq$(?v0)))
tff(axiom470,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$'] :
      ( 'fun_app$k'('register$',A__questionmark_v0)
     => 'register$aw'('uuq$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ register$ax(uur$(?v0)))
tff(axiom471,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => 'register$ax'('uur$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ (register$a(?v0) ⇒ register$ay(uus$(?v0)))
tff(axiom472,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$'] :
      ( 'register$a'(A__questionmark_v0)
     => 'register$ay'('uus$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:D_update_b_update_fun$ (register$g(?v0) ⇒ register$az(uut$(?v0)))
tff(axiom473,axiom,
    ! [A__questionmark_v0: 'D_update_b_update_fun$'] :
      ( 'register$g'(A__questionmark_v0)
     => 'register$az'('uut$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_b_update_fun$ (register$d(?v0) ⇒ register$ba(uuu$(?v0)))
tff(axiom474,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_fun$'] :
      ( 'register$d'(A__questionmark_v0)
     => 'register$ba'('uuu$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_a_update_fun$ (register$f(?v0) ⇒ register$bb(uuv$(?v0)))
tff(axiom475,axiom,
    ! [A__questionmark_v0: 'B_update_a_update_fun$'] :
      ( 'register$f'(A__questionmark_v0)
     => 'register$bb'('uuv$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_d_update_fun$ (register$v(?v0) ⇒ register$aq(uuw$(?v0)))
tff(axiom476,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$'] :
      ( 'register$v'(A__questionmark_v0)
     => 'register$aq'('uuw$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_c_update_fun$ (register$w(?v0) ⇒ register$bc(uux$(?v0)))
tff(axiom477,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$'] :
      ( 'register$w'(A__questionmark_v0)
     => 'register$bc'('uux$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_update_a_update_fun$ (register$b(?v0) ⇒ register$bd(uuy$(?v0)))
tff(axiom478,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$'] :
      ( 'register$b'(A__questionmark_v0)
     => 'register$bd'('uuy$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ (register$c(?v0) ⇒ register$as(uuz$(?v0)))
tff(axiom479,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$'] :
      ( 'register$c'(A__questionmark_v0)
     => 'register$as'('uuz$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v1:A_update_a_update_fun_d_update_b_update_fun_fun$ (fcomp$(?v0, ?v1) = comp$au(?v1, ?v0))
tff(axiom480,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v1: 'A_update_a_update_fun_d_update_b_update_fun_fun$'] : 'fcomp$'(A__questionmark_v0,A__questionmark_v1) = 'comp$au'(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v1:A_update_a_update_fun_d_update_b_update_fun_fun$ (fcomp$a(?v0, ?v1) = comp$av(?v1, ?v0))
tff(axiom481,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v1: 'A_update_a_update_fun_d_update_b_update_fun_fun$'] : 'fcomp$a'(A__questionmark_v0,A__questionmark_v1) = 'comp$av'(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$ ?v1:A_update_a_update_fun_c_update_b_update_fun_fun$ (fcomp$b(?v0, ?v1) = comp$aw(?v1, ?v0))
tff(axiom482,axiom,
    ! [A__questionmark_v0: 'B_update_c_d_prod_update_fun_a_update_a_update_fun_fun$',A__questionmark_v1: 'A_update_a_update_fun_c_update_b_update_fun_fun$'] : 'fcomp$b'(A__questionmark_v0,A__questionmark_v1) = 'comp$aw'(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:B_update_d_update_fun_a_update_a_update_fun_fun$ ?v1:A_update_a_update_fun_c_update_b_update_fun_fun$ (fcomp$c(?v0, ?v1) = comp$ax(?v1, ?v0))
tff(axiom483,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun_a_update_a_update_fun_fun$',A__questionmark_v1: 'A_update_a_update_fun_c_update_b_update_fun_fun$'] : 'fcomp$c'(A__questionmark_v0,A__questionmark_v1) = 'comp$ax'(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:B_update_c_update_fun_a_update_a_update_fun_fun$ ?v1:A_update_a_update_fun_c_update_b_update_fun_fun$ (fcomp$d(?v0, ?v1) = comp$ay(?v1, ?v0))
tff(axiom484,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun_a_update_a_update_fun_fun$',A__questionmark_v1: 'A_update_a_update_fun_c_update_b_update_fun_fun$'] : 'fcomp$d'(A__questionmark_v0,A__questionmark_v1) = 'comp$ay'(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ (fcomp$e(?v0, ?v1) = fun_app$be(fun_app$bf(comp$, ?v1), ?v0))
tff(axiom485,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'fcomp$e'(A__questionmark_v0,A__questionmark_v1) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v0) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ (fcomp$f(?v0, ?v1) = fun_app$bj(fun_app$bk(comp$a, ?v1), ?v0))
tff(axiom486,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'fcomp$f'(A__questionmark_v0,A__questionmark_v1) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v0) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ (fcomp$g(?v0, ?v1) = fun_app$bv(fun_app$bw(comp$j, ?v1), ?v0))
tff(axiom487,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'fcomp$g'(A__questionmark_v0,A__questionmark_v1) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v0) ).

%% register$be(tensor_update$(id_update$c))
tff(axiom488,axiom,
    'register$be'('tensor_update$'('id_update$c')) ).

%% register$bf(tensor_update$a(id_update$))
tff(axiom489,axiom,
    'register$bf'('tensor_update$a'('id_update$')) ).

%% register$bg(tensor_update$b(id_update$))
tff(axiom490,axiom,
    'register$bg'('tensor_update$b'('id_update$')) ).

%% register$bh(tensor_update$c(id_update$))
tff(axiom491,axiom,
    'register$bh'('tensor_update$c'('id_update$')) ).

%% register$bi(tensor_update$d(id_update$))
tff(axiom492,axiom,
    'register$bi'('tensor_update$d'('id_update$')) ).

%% register$bj(uva$)
tff(axiom493,axiom,
    'register$bj'('uva$') ).

%% register$bk(uvb$)
tff(axiom494,axiom,
    'register$bk'('uvb$') ).

%% register$bl(uvc$)
tff(axiom495,axiom,
    'register$bl'('uvc$') ).

%% register$bm(uvd$)
tff(axiom496,axiom,
    'register$bm'('uvd$') ).

%% register$bi(uve$)
tff(axiom497,axiom,
    'register$bi'('uve$') ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_b_update_fun$ (register_tensor$af(?v0, ?v1) = register_pair$t(uun$(?v0), uvf$(?v1)))
tff(axiom498,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] : 'register_tensor$af'(A__questionmark_v0,A__questionmark_v1) = 'register_pair$t'('uun$'(A__questionmark_v0),'uvf$'(A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ (register_tensor$o(?v0, ?v1) = register_pair$u(uvg$(?v0), uvh$(?v1)))
tff(axiom499,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] : 'register_tensor$o'(A__questionmark_v0,A__questionmark_v1) = 'register_pair$u'('uvg$'(A__questionmark_v0),'uvh$'(A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ (register_tensor$i(?v0, ?v1) = register_pair$v(uun$(?v0), uuz$(?v1)))
tff(axiom500,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] : 'register_tensor$i'(A__questionmark_v0,A__questionmark_v1) = 'register_pair$v'('uun$'(A__questionmark_v0),'uuz$'(A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ (register_tensor$h(?v0, ?v1) = register_pair$w(uvg$(?v0), uvi$(?v1)))
tff(axiom501,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] : 'register_tensor$h'(A__questionmark_v0,A__questionmark_v1) = 'register_pair$w'('uvg$'(A__questionmark_v0),'uvi$'(A__questionmark_v1)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ (register_tensor$p(?v0, ?v1) = register_pair$x(uun$(?v0), uvj$(?v1)))
tff(axiom502,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'register_tensor$p'(A__questionmark_v0,A__questionmark_v1) = 'register_pair$x'('uun$'(A__questionmark_v0),'uvj$'(A__questionmark_v1)) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:C_update_c_update_fun$ (comp$be(convol$(?v0, ?v1), ?v2) = convol$(comp$f(?v0, ?v2), comp$f(?v1, ?v2)))
tff(axiom503,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] : 'comp$be'('convol$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$'('comp$f'(A__questionmark_v0,A__questionmark_v2),'comp$f'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update_c_update_fun$ (comp$bf(convol$(?v0, ?v1), ?v2) = convol$a(comp$i(?v0, ?v2), comp$i(?v1, ?v2)))
tff(axiom504,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update_c_update_fun$'] : 'comp$bf'('convol$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$a'('comp$i'(A__questionmark_v0,A__questionmark_v2),'comp$i'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_c_update_fun$ (comp$bg(convol$b(?v0, ?v1), ?v2) = convol$c(comp$as(?v0, ?v2), comp$as(?v1, ?v2)))
tff(axiom505,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_c_update_fun$'] : 'comp$bg'('convol$b'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$c'('comp$as'(A__questionmark_v0,A__questionmark_v2),'comp$as'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_c_update_fun$ (comp$bh(convol$b(?v0, ?v1), ?v2) = convol$b(comp$e(?v0, ?v2), comp$e(?v1, ?v2)))
tff(axiom506,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_c_update_fun$'] : 'comp$bh'('convol$b'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$b'('comp$e'(A__questionmark_v0,A__questionmark_v2),'comp$e'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_a_update_fun$ (comp$bi(convol$a(?v0, ?v1), ?v2) = convol$a(comp$am(?v0, ?v2), comp$am(?v1, ?v2)))
tff(axiom507,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$'] : 'comp$bi'('convol$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$a'('comp$am'(A__questionmark_v0,A__questionmark_v2),'comp$am'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ (comp$bj(convol$a(?v0, ?v1), ?v2) = convol$(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v2)))
tff(axiom508,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] : 'comp$bj'('convol$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ (comp$bk(convol$a(?v0, ?v1), ?v2) = convol$d(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v2)))
tff(axiom509,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$'] : 'comp$bk'('convol$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ (comp$bl(convol$a(?v0, ?v1), ?v2) = convol$e(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2)))
tff(axiom510,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] : 'comp$bl'('convol$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'convol$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$ag(uvk$(?v0), uvl$(?v1)))
tff(axiom511,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$ag'('uvk$'(A__questionmark_v0),'uvl$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$c(?v1)) ⇒ compatible$ah(uvi$(?v0), uvm$(?v1)))
tff(axiom512,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$ah'('uvi$'(A__questionmark_v0),'uvm$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$a(?v1)) ⇒ compatible$ai(uvi$(?v0), uvg$(?v1)))
tff(axiom513,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'compatible$ai'('uvi$'(A__questionmark_v0),'uvg$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$g(?v1)) ⇒ compatible$aj(uvi$(?v0), uvn$(?v1)))
tff(axiom514,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'compatible$aj'('uvi$'(A__questionmark_v0),'uvn$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$c(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$ak(uvo$(?v0), uvp$(?v1)))
tff(axiom515,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$ak'('uvo$'(A__questionmark_v0),'uvp$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$c(?v0) ∧ register$c(?v1)) ⇒ compatible$al(uuz$(?v0), uum$(?v1)))
tff(axiom516,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$al'('uuz$'(A__questionmark_v0),'uum$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$c(?v0) ∧ register$a(?v1)) ⇒ compatible$am(uuz$(?v0), uun$(?v1)))
tff(axiom517,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'compatible$am'('uuz$'(A__questionmark_v0),'uun$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$c(?v0) ∧ register$g(?v1)) ⇒ compatible$an(uuz$(?v0), uuo$(?v1)))
tff(axiom518,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'compatible$an'('uuz$'(A__questionmark_v0),'uuo$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$a(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$ao(uvq$(?v0), uvp$(?v1)))
tff(axiom519,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$ao'('uvq$'(A__questionmark_v0),'uvp$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$a(?v0) ∧ register$c(?v1)) ⇒ compatible$ap(uvj$(?v0), uum$(?v1)))
tff(axiom520,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$ap'('uvj$'(A__questionmark_v0),'uum$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ((fun_app$k(register$, ?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$ag(uvl$(?v0), uvk$(?v1)))
tff(axiom521,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$ag'('uvl$'(A__questionmark_v0),'uvk$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$c(?v1)) ⇒ compatible$ak(uvp$(?v0), uvo$(?v1)))
tff(axiom522,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$ak'('uvp$'(A__questionmark_v0),'uvo$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$a(?v1)) ⇒ compatible$aq(uvp$(?v0), uvq$(?v1)))
tff(axiom523,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'compatible$aq'('uvp$'(A__questionmark_v0),'uvq$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:D_update_b_update_fun$ ((fun_app$k(register$, ?v0) ∧ register$g(?v1)) ⇒ compatible$ar(uvp$(?v0), uvr$(?v1)))
tff(axiom524,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'fun_app$k'('register$',A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'compatible$ar'('uvp$'(A__questionmark_v0),'uvr$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$c(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$ah(uvm$(?v0), uvi$(?v1)))
tff(axiom525,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$ah'('uvm$'(A__questionmark_v0),'uvi$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$c(?v0) ∧ register$c(?v1)) ⇒ compatible$al(uum$(?v0), uuz$(?v1)))
tff(axiom526,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$al'('uum$'(A__questionmark_v0),'uuz$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:A_update_b_update_fun$ ((register$c(?v0) ∧ register$a(?v1)) ⇒ compatible$am(uum$(?v0), uvj$(?v1)))
tff(axiom527,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$a'(A__questionmark_v1) )
     => 'compatible$am'('uum$'(A__questionmark_v0),'uvj$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:C_update_b_update_fun$ ?v1:D_update_b_update_fun$ ((register$c(?v0) ∧ register$g(?v1)) ⇒ compatible$an(uum$(?v0), uvf$(?v1)))
tff(axiom528,axiom,
    ! [A__questionmark_v0: 'C_update_b_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$'] :
      ( ( 'register$c'(A__questionmark_v0)
        & 'register$g'(A__questionmark_v1) )
     => 'compatible$an'('uum$'(A__questionmark_v0),'uvf$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ((register$a(?v0) ∧ fun_app$k(register$, ?v1)) ⇒ compatible$as(uvg$(?v0), uvi$(?v1)))
tff(axiom529,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'fun_app$k'('register$',A__questionmark_v1) )
     => 'compatible$as'('uvg$'(A__questionmark_v0),'uvi$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_b_update_fun$ ((register$a(?v0) ∧ register$c(?v1)) ⇒ compatible$ap(uun$(?v0), uuz$(?v1)))
tff(axiom530,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$'] :
      ( ( 'register$a'(A__questionmark_v0)
        & 'register$c'(A__questionmark_v1) )
     => 'compatible$ap'('uun$'(A__questionmark_v0),'uuz$'(A__questionmark_v1)) ) ).

%% ∀ ?v0:B_update$ ?v1:C_update_a_update_fun$ ?v2:C_update$ (fun_app$q(fun_app$be(fun_app$bf(comp$, uvs$(?v0)), ?v1), ?v2) = ?v0)
tff(axiom531,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update$'] : 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$','uvs$'(A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:B_update$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update$ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, uvs$(?v0)), ?v1), ?v2) = ?v0)
tff(axiom532,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update$'] : 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a','uvs$'(A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:B_update$ ?v1:D_update_a_update_fun$ ?v2:D_update$ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, uvs$(?v0)), ?v1), ?v2) = ?v0)
tff(axiom533,axiom,
    ! [A__questionmark_v0: 'B_update$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update$'] : 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j','uvs$'(A__questionmark_v0)),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:C_d_prod_update_set$ ?v1:C_d_prod_update_b_update_fun$ ?v2:C_d_prod_update_b_update_fun$ ((separating$e(type$, ?v0) ∧ (preregister$(?v1) ∧ (preregister$(?v2) ∧ ∀ ?v3:C_d_prod_update$ (member$(?v3, ?v0) ⇒ (fun_app$bz(?v1, ?v3) = fun_app$bz(?v2, ?v3)))))) ⇒ (?v1 = ?v2))
tff(axiom534,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_set$',A__questionmark_v1: 'C_d_prod_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_b_update_fun$'] :
      ( ( 'separating$e'('type$',A__questionmark_v0)
        & 'preregister$'(A__questionmark_v1)
        & 'preregister$'(A__questionmark_v2)
        & ! [A__questionmark_v3: 'C_d_prod_update$'] :
            ( 'member$'(A__questionmark_v3,A__questionmark_v0)
           => ( 'fun_app$bz'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$bz'(A__questionmark_v2,A__questionmark_v3) ) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (comp$ay(map_fun$(?v0, ?v1), map_fun$a(?v2, ?v3)) = map_fun$b(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom535,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$ay'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'map_fun$a'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$b'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$aw(map_fun$(?v0, ?v1), map_fun$c(?v2, ?v3)) = map_fun$d(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom536,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$aw'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'map_fun$c'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$d'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (comp$ax(map_fun$(?v0, ?v1), map_fun$e(?v2, ?v3)) = map_fun$f(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom537,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$ax'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'map_fun$e'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (comp$bm(map_fun$g(?v0, ?v1), map_fun$a(?v2, ?v3)) = map_fun$h(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom538,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$bm'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'map_fun$a'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$h'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$bn(map_fun$g(?v0, ?v1), map_fun$c(?v2, ?v3)) = map_fun$i(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom539,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$bn'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'map_fun$c'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (comp$bo(map_fun$g(?v0, ?v1), map_fun$e(?v2, ?v3)) = map_fun$j(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom540,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$bo'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'map_fun$e'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$j'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (comp$av(map_fun$k(?v0, ?v1), map_fun$a(?v2, ?v3)) = map_fun$l(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom541,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$av'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'map_fun$a'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$l'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$bp(map_fun$k(?v0, ?v1), map_fun$c(?v2, ?v3)) = map_fun$m(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom542,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$bp'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'map_fun$c'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (comp$au(map_fun$k(?v0, ?v1), map_fun$e(?v2, ?v3)) = map_fun$n(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom543,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$au'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'map_fun$e'(A__questionmark_v2,A__questionmark_v3)) = 'map_fun$n'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ (comp$bq(map_prod$(?v0, ?v1), convol$b(?v2, ?v3)) = convol$(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom544,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$bq'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'convol$b'(A__questionmark_v2,A__questionmark_v3)) = 'convol$'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$br(map_prod$(?v0, ?v1), convol$f(?v2, ?v3)) = convol$d(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom545,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$br'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'convol$f'(A__questionmark_v2,A__questionmark_v3)) = 'convol$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ (comp$bs(map_prod$(?v0, ?v1), convol$c(?v2, ?v3)) = convol$e(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom546,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$bs'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'convol$c'(A__questionmark_v2,A__questionmark_v3)) = 'convol$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_bool_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ (pred_fun$(uvt$, ?v0, fun_app$be(fun_app$bf(comp$, ?v1), ?v2)) = fun_app$k(pred_fun$a(uvt$, comp$bt(?v0, ?v1)), ?v2))
tff(axiom547,axiom,
    ! [A__questionmark_v0: 'B_update_bool_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$'] :
      ( 'pred_fun$'('uvt$',A__questionmark_v0,'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2))
    <=> 'fun_app$k'('pred_fun$a'('uvt$','comp$bt'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ) ).

%% ∀ ?v0:B_update_bool_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ (pred_fun$b(uvu$, ?v0, fun_app$bj(fun_app$bk(comp$a, ?v1), ?v2)) = fun_app$i(pred_fun$c(uvu$, comp$bt(?v0, ?v1)), ?v2))
tff(axiom548,axiom,
    ! [A__questionmark_v0: 'B_update_bool_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$'] :
      ( 'pred_fun$b'('uvu$',A__questionmark_v0,'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v2))
    <=> 'fun_app$i'('pred_fun$c'('uvu$','comp$bt'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ) ).

%% ∀ ?v0:B_update_bool_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ (pred_fun$d(uvv$, ?v0, fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2)) = fun_app$j(pred_fun$e(uvv$, comp$bt(?v0, ?v1)), ?v2))
tff(axiom549,axiom,
    ! [A__questionmark_v0: 'B_update_bool_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$'] :
      ( 'pred_fun$d'('uvv$',A__questionmark_v0,'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2))
    <=> 'fun_app$j'('pred_fun$e'('uvv$','comp$bt'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ fun_app$k(pred_fun$a(uvt$, uvw$(?v2, ?v3)), ?v1)) ⇒ (fun_app$be(fun_app$bf(comp$, ?v2), ?v0) = fun_app$be(fun_app$bf(comp$, ?v3), ?v1)))
tff(axiom550,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & 'fun_app$k'('pred_fun$a'('uvt$','uvw$'(A__questionmark_v2,A__questionmark_v3)),A__questionmark_v1) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ fun_app$i(pred_fun$c(uvu$, uvw$(?v2, ?v3)), ?v1)) ⇒ (fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0) = fun_app$bj(fun_app$bk(comp$a, ?v3), ?v1)))
tff(axiom551,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & 'fun_app$i'('pred_fun$c'('uvu$','uvw$'(A__questionmark_v2,A__questionmark_v3)),A__questionmark_v1) )
     => ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ fun_app$j(pred_fun$e(uvv$, uvw$(?v2, ?v3)), ?v1)) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v1)))
tff(axiom552,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & 'fun_app$j'('pred_fun$e'('uvv$','uvw$'(A__questionmark_v2,A__questionmark_v3)),A__questionmark_v1) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (map_prod$a(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) = comp$bu(map_prod$(?v0, ?v2), map_prod$b(?v1, ?v3)))
tff(axiom553,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'map_prod$a'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3)) = 'comp$bu'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$b'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (map_prod$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)) = comp$bv(map_prod$(?v0, ?v2), map_prod$d(?v1, ?v3)))
tff(axiom554,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'map_prod$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3)) = 'comp$bv'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$d'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (map_prod$e(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) = comp$bw(map_prod$(?v0, ?v2), map_prod$f(?v1, ?v3)))
tff(axiom555,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'map_prod$e'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3)) = 'comp$bw'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$f'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (map_prod$g(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) = comp$bx(map_prod$(?v0, ?v2), map_prod$h(?v1, ?v3)))
tff(axiom556,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'map_prod$g'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3)) = 'comp$bx'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$h'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (map_prod$i(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)) = comp$by(map_prod$(?v0, ?v2), map_prod$j(?v1, ?v3)))
tff(axiom557,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'map_prod$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3)) = 'comp$by'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$j'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (map_prod$k(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) = comp$bz(map_prod$(?v0, ?v2), map_prod$l(?v1, ?v3)))
tff(axiom558,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'map_prod$k'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3)) = 'comp$bz'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$l'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ (map_prod$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), fun_app$be(fun_app$bf(comp$, ?v2), ?v3)) = comp$ca(map_prod$(?v0, ?v2), map_prod$n(?v1, ?v3)))
tff(axiom559,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'map_prod$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v3)) = 'comp$ca'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$n'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (map_prod$o(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), fun_app$bj(fun_app$bk(comp$a, ?v2), ?v3)) = comp$cb(map_prod$(?v0, ?v2), map_prod$p(?v1, ?v3)))
tff(axiom560,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'map_prod$o'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v3)) = 'comp$cb'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$p'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ (map_prod$q(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v3)) = comp$cc(map_prod$(?v0, ?v2), map_prod$r(?v1, ?v3)))
tff(axiom561,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'map_prod$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v3)) = 'comp$cc'('map_prod$'(A__questionmark_v0,A__questionmark_v2),'map_prod$r'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$db(map_prod$b(?v2, ?v3), ?v4)) = fun_app$dc(map_prod$a(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom562,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$db'('map_prod$b'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dc'('map_prod$a'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:C_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dd(map_prod$d(?v2, ?v3), ?v4)) = fun_app$de(map_prod$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom563,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'C_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dd'('map_prod$d'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$de'('map_prod$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$df(map_prod$f(?v2, ?v3), ?v4)) = fun_app$dg(map_prod$e(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom564,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$df'('map_prod$f'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dg'('map_prod$e'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_d_prod_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dh(map_prod$h(?v2, ?v3), ?v4)) = fun_app$di(map_prod$g(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom565,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dh'('map_prod$h'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$di'('map_prod$g'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:C_d_prod_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dj(map_prod$j(?v2, ?v3), ?v4)) = fun_app$dk(map_prod$i(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom566,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dj'('map_prod$j'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dk'('map_prod$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_d_prod_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dl(map_prod$l(?v2, ?v3), ?v4)) = fun_app$dm(map_prod$k(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom567,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dl'('map_prod$l'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dm'('map_prod$k'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dn(map_prod$n(?v2, ?v3), ?v4)) = fun_app$do(map_prod$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom568,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dn'('map_prod$n'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$do'('map_prod$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:D_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dp(map_prod$p(?v2, ?v3), ?v4)) = fun_app$dq(map_prod$o(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom569,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'D_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dp'('map_prod$p'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dq'('map_prod$o'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dr(map_prod$r(?v2, ?v3), ?v4)) = fun_app$ds(map_prod$q(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom570,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dr'('map_prod$r'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$ds'('map_prod$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ (comp$bu(map_prod$(?v0, ?v1), map_prod$b(?v2, ?v3)) = map_prod$a(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom571,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$bu'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$b'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$a'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$bv(map_prod$(?v0, ?v1), map_prod$d(?v2, ?v3)) = map_prod$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom572,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$bv'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$d'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ (comp$bw(map_prod$(?v0, ?v1), map_prod$f(?v2, ?v3)) = map_prod$e(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom573,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$bw'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$f'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$e'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_update_a_update_fun$ (comp$bx(map_prod$(?v0, ?v1), map_prod$h(?v2, ?v3)) = map_prod$g(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom574,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$bx'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$h'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$g'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$by(map_prod$(?v0, ?v1), map_prod$j(?v2, ?v3)) = map_prod$i(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom575,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$by'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$j'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:D_update_a_update_fun$ (comp$bz(map_prod$(?v0, ?v1), map_prod$l(?v2, ?v3)) = map_prod$k(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom576,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$bz'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$l'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$k'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ (comp$ca(map_prod$(?v0, ?v1), map_prod$n(?v2, ?v3)) = map_prod$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)))
tff(axiom577,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$'] : 'comp$ca'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$n'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ (comp$cb(map_prod$(?v0, ?v1), map_prod$p(?v2, ?v3)) = map_prod$o(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)))
tff(axiom578,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$'] : 'comp$cb'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$p'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$o'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ (comp$cc(map_prod$(?v0, ?v1), map_prod$r(?v2, ?v3)) = map_prod$q(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)))
tff(axiom579,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$'] : 'comp$cc'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'map_prod$r'(A__questionmark_v2,A__questionmark_v3)) = 'map_prod$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_b_update_fun$ ?v3:C_update$ ((fun_app$be(fun_app$bf(comp$, ?v0), ?v1) = comp$d(id$, ?v2)) ⇒ (fun_app$ae(?v0, fun_app$u(?v1, ?v3)) = fun_app$q(?v2, ?v3)))
tff(axiom580,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_b_update_fun$',A__questionmark_v3: 'C_update$'] :
      ( ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1) = 'comp$d'('id$',A__questionmark_v2) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$u'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$q'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update_b_update_fun$ ?v3:C_d_prod_update$ ((fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1) = comp$v(id$, ?v2)) ⇒ (fun_app$ae(?v0, fun_app$by(?v1, ?v3)) = fun_app$bz(?v2, ?v3)))
tff(axiom581,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update$'] :
      ( ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1) = 'comp$v'('id$',A__questionmark_v2) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$by'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$bz'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_b_update_fun$ ?v3:D_update$ ((fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1) = comp$p(id$, ?v2)) ⇒ (fun_app$ae(?v0, fun_app$au(?v1, ?v3)) = fun_app$m(?v2, ?v3)))
tff(axiom582,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_b_update_fun$',A__questionmark_v3: 'D_update$'] :
      ( ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1) = 'comp$p'('id$',A__questionmark_v2) )
     => ( 'fun_app$ae'(A__questionmark_v0,'fun_app$au'(A__questionmark_v1,A__questionmark_v3)) = 'fun_app$m'(A__questionmark_v2,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$db(map_prod$b(?v2, ?v3), ?v4)) = fun_app$dc(map_prod$a(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom583,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$db'('map_prod$b'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dc'('map_prod$a'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:C_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dd(map_prod$d(?v2, ?v3), ?v4)) = fun_app$de(map_prod$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom584,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'C_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dd'('map_prod$d'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$de'('map_prod$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$df(map_prod$f(?v2, ?v3), ?v4)) = fun_app$dg(map_prod$e(fun_app$be(fun_app$bf(comp$, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom585,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$df'('map_prod$f'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dg'('map_prod$e'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_d_prod_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dh(map_prod$h(?v2, ?v3), ?v4)) = fun_app$di(map_prod$g(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom586,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dh'('map_prod$h'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$di'('map_prod$g'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:C_d_prod_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dj(map_prod$j(?v2, ?v3), ?v4)) = fun_app$dk(map_prod$i(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom587,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dj'('map_prod$j'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dk'('map_prod$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_d_prod_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dl(map_prod$l(?v2, ?v3), ?v4)) = fun_app$dm(map_prod$k(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom588,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_d_prod_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dl'('map_prod$l'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dm'('map_prod$k'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dn(map_prod$n(?v2, ?v3), ?v4)) = fun_app$do(map_prod$m(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom589,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dn'('map_prod$n'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$do'('map_prod$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:D_update_c_d_prod_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dp(map_prod$p(?v2, ?v3), ?v4)) = fun_app$dq(map_prod$o(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom590,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'D_update_c_d_prod_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dp'('map_prod$p'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dq'('map_prod$o'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_prod$ (fun_app$da(map_prod$(?v0, ?v1), fun_app$dr(map_prod$r(?v2, ?v3), ?v4)) = fun_app$ds(map_prod$q(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v2), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom591,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_prod$'] : 'fun_app$da'('map_prod$'(A__questionmark_v0,A__questionmark_v1),'fun_app$dr'('map_prod$r'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$ds'('map_prod$q'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v2),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:B_update_c_update_fun$ (fun_app$ct(map_fun$(?v0, ?v1), fun_app$cr(map_fun$a(?v2, ?v3), ?v4)) = fun_app$cw(map_fun$b(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom592,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'B_update_c_update_fun$'] : 'fun_app$ct'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'fun_app$cr'('map_fun$a'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$cw'('map_fun$b'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:B_update_c_d_prod_update_fun$ (fun_app$ct(map_fun$(?v0, ?v1), fun_app$cu(map_fun$c(?v2, ?v3), ?v4)) = fun_app$cs(map_fun$d(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom593,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'B_update_c_d_prod_update_fun$'] : 'fun_app$ct'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'fun_app$cu'('map_fun$c'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$cs'('map_fun$d'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:B_update_d_update_fun$ (fun_app$ct(map_fun$(?v0, ?v1), fun_app$cp(map_fun$e(?v2, ?v3), ?v4)) = fun_app$cv(map_fun$f(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom594,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'B_update_d_update_fun$'] : 'fun_app$ct'('map_fun$'(A__questionmark_v0,A__questionmark_v1),'fun_app$cp'('map_fun$e'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$cv'('map_fun$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:B_update_c_update_fun$ (fun_app$dt(map_fun$g(?v0, ?v1), fun_app$cr(map_fun$a(?v2, ?v3), ?v4)) = fun_app$du(map_fun$h(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom595,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'B_update_c_update_fun$'] : 'fun_app$dt'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'fun_app$cr'('map_fun$a'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$du'('map_fun$h'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:B_update_c_d_prod_update_fun$ (fun_app$dt(map_fun$g(?v0, ?v1), fun_app$cu(map_fun$c(?v2, ?v3), ?v4)) = fun_app$dv(map_fun$i(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom596,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'B_update_c_d_prod_update_fun$'] : 'fun_app$dt'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'fun_app$cu'('map_fun$c'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dv'('map_fun$i'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:B_update_d_update_fun$ (fun_app$dt(map_fun$g(?v0, ?v1), fun_app$cp(map_fun$e(?v2, ?v3), ?v4)) = fun_app$dw(map_fun$j(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom597,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'B_update_d_update_fun$'] : 'fun_app$dt'('map_fun$g'(A__questionmark_v0,A__questionmark_v1),'fun_app$cp'('map_fun$e'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dw'('map_fun$j'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_update_a_update_fun$ ?v4:B_update_c_update_fun$ (fun_app$co(map_fun$k(?v0, ?v1), fun_app$cr(map_fun$a(?v2, ?v3), ?v4)) = fun_app$cq(map_fun$l(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$be(fun_app$bf(comp$, ?v1), ?v3)), ?v4))
tff(axiom598,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'B_update_c_update_fun$'] : 'fun_app$co'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'fun_app$cr'('map_fun$a'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$cq'('map_fun$l'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:C_d_prod_update_a_update_fun$ ?v4:B_update_c_d_prod_update_fun$ (fun_app$co(map_fun$k(?v0, ?v1), fun_app$cu(map_fun$c(?v2, ?v3), ?v4)) = fun_app$dx(map_fun$m(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$bj(fun_app$bk(comp$a, ?v1), ?v3)), ?v4))
tff(axiom599,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_fun$',A__questionmark_v4: 'B_update_c_d_prod_update_fun$'] : 'fun_app$co'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'fun_app$cu'('map_fun$c'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$dx'('map_fun$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ ?v3:D_update_a_update_fun$ ?v4:B_update_d_update_fun$ (fun_app$co(map_fun$k(?v0, ?v1), fun_app$cp(map_fun$e(?v2, ?v3), ?v4)) = fun_app$cn(map_fun$n(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), fun_app$bv(fun_app$bw(comp$j, ?v1), ?v3)), ?v4))
tff(axiom600,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'B_update_d_update_fun$'] : 'fun_app$co'('map_fun$k'(A__questionmark_v0,A__questionmark_v1),'fun_app$cp'('map_fun$e'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) = 'fun_app$cn'('map_fun$n'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_c_update_bool_fun_fun$ rel_fun$(rel_fun$a(?v0, ?v1), rel_fun$b(rel_fun$c(?v2, ?v0), rel_fun$d(?v2, ?v1)), comp$, comp$)
tff(axiom601,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_c_update_bool_fun_fun$'] : 'rel_fun$'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$b'('rel_fun$c'(A__questionmark_v2,A__questionmark_v0),'rel_fun$d'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_c_d_prod_update_bool_fun_fun$ rel_fun$e(rel_fun$a(?v0, ?v1), rel_fun$f(rel_fun$g(?v2, ?v0), rel_fun$h(?v2, ?v1)), comp$, comp$a)
tff(axiom602,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$e'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$f'('rel_fun$g'(A__questionmark_v2,A__questionmark_v0),'rel_fun$h'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_d_update_bool_fun_fun$ rel_fun$i(rel_fun$a(?v0, ?v1), rel_fun$j(rel_fun$k(?v2, ?v0), rel_fun$l(?v2, ?v1)), comp$, comp$j)
tff(axiom603,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_d_update_bool_fun_fun$'] : 'rel_fun$i'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$j'('rel_fun$k'(A__questionmark_v2,A__questionmark_v0),'rel_fun$l'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_c_update_bool_fun_fun$ rel_fun$m(rel_fun$a(?v0, ?v1), rel_fun$n(rel_fun$o(?v2, ?v0), rel_fun$p(?v2, ?v1)), comp$a, comp$)
tff(axiom604,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_c_update_bool_fun_fun$'] : 'rel_fun$m'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$n'('rel_fun$o'(A__questionmark_v2,A__questionmark_v0),'rel_fun$p'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_c_d_prod_update_bool_fun_fun$ rel_fun$q(rel_fun$a(?v0, ?v1), rel_fun$r(rel_fun$s(?v2, ?v0), rel_fun$t(?v2, ?v1)), comp$a, comp$a)
tff(axiom605,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$q'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$r'('rel_fun$s'(A__questionmark_v2,A__questionmark_v0),'rel_fun$t'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_d_update_bool_fun_fun$ rel_fun$u(rel_fun$a(?v0, ?v1), rel_fun$v(rel_fun$w(?v2, ?v0), rel_fun$x(?v2, ?v1)), comp$a, comp$j)
tff(axiom606,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_d_update_bool_fun_fun$'] : 'rel_fun$u'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$v'('rel_fun$w'(A__questionmark_v2,A__questionmark_v0),'rel_fun$x'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_c_update_bool_fun_fun$ rel_fun$y(rel_fun$a(?v0, ?v1), rel_fun$z(rel_fun$aa(?v2, ?v0), rel_fun$ab(?v2, ?v1)), comp$j, comp$)
tff(axiom607,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_c_update_bool_fun_fun$'] : 'rel_fun$y'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$z'('rel_fun$aa'(A__questionmark_v2,A__questionmark_v0),'rel_fun$ab'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_c_d_prod_update_bool_fun_fun$ rel_fun$ac(rel_fun$a(?v0, ?v1), rel_fun$ad(rel_fun$ae(?v2, ?v0), rel_fun$af(?v2, ?v1)), comp$j, comp$a)
tff(axiom608,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$ac'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$ad'('rel_fun$ae'(A__questionmark_v2,A__questionmark_v0),'rel_fun$af'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_d_update_bool_fun_fun$ rel_fun$ag(rel_fun$a(?v0, ?v1), rel_fun$ah(rel_fun$ai(?v2, ?v0), rel_fun$aj(?v2, ?v1)), comp$j, comp$j)
tff(axiom609,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_d_update_bool_fun_fun$'] : 'rel_fun$ag'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$ah'('rel_fun$ai'(A__questionmark_v2,A__questionmark_v0),'rel_fun$aj'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ rel_fun$(rel_fun$a(?v0, ?v1), rel_fun$b(rel_fun$c(uvx$, ?v0), rel_fun$d(uvx$, ?v1)), comp$, comp$)
tff(axiom610,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$'] : 'rel_fun$'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$b'('rel_fun$c'('uvx$',A__questionmark_v0),'rel_fun$d'('uvx$',A__questionmark_v1)),'comp$','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ rel_fun$q(rel_fun$a(?v0, ?v1), rel_fun$r(rel_fun$s(uvy$, ?v0), rel_fun$t(uvy$, ?v1)), comp$a, comp$a)
tff(axiom611,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$'] : 'rel_fun$q'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$r'('rel_fun$s'('uvy$',A__questionmark_v0),'rel_fun$t'('uvy$',A__questionmark_v1)),'comp$a','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ rel_fun$ag(rel_fun$a(?v0, ?v1), rel_fun$ah(rel_fun$ai(uvz$, ?v0), rel_fun$aj(uvz$, ?v1)), comp$j, comp$j)
tff(axiom612,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$'] : 'rel_fun$ag'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$ah'('rel_fun$ai'('uvz$',A__questionmark_v0),'rel_fun$aj'('uvz$',A__questionmark_v1)),'comp$j','comp$j') ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_set$ ?v2:C_update_a_update_fun$ ?v3:C_update_set$ ?v4:A_update_b_update_fun$ ((image$b(?v0, ?v1) = image$b(?v2, ?v3)) ⇒ (image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v0), ?v1) = image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v2), ?v3)))
tff(axiom613,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_set$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$b'(A__questionmark_v0,A__questionmark_v1) = 'image$b'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_set$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_set$ ?v4:A_update_b_update_fun$ ((image$b(?v0, ?v1) = image$(?v2, ?v3)) ⇒ (image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v0), ?v1) = image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v2), ?v3)))
tff(axiom614,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_set$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$b'(A__questionmark_v0,A__questionmark_v1) = 'image$'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_set$ ?v2:D_update_a_update_fun$ ?v3:D_update_set$ ?v4:A_update_b_update_fun$ ((image$b(?v0, ?v1) = image$a(?v2, ?v3)) ⇒ (image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v0), ?v1) = image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v2), ?v3)))
tff(axiom615,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_set$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$b'(A__questionmark_v0,A__questionmark_v1) = 'image$a'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_set$ ?v2:C_update_a_update_fun$ ?v3:C_update_set$ ?v4:A_update_b_update_fun$ ((image$(?v0, ?v1) = image$b(?v2, ?v3)) ⇒ (image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v0), ?v1) = image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v2), ?v3)))
tff(axiom616,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_set$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$'(A__questionmark_v0,A__questionmark_v1) = 'image$b'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_set$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_set$ ?v4:A_update_b_update_fun$ ((image$(?v0, ?v1) = image$(?v2, ?v3)) ⇒ (image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v0), ?v1) = image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v2), ?v3)))
tff(axiom617,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_set$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$'(A__questionmark_v0,A__questionmark_v1) = 'image$'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_set$ ?v2:D_update_a_update_fun$ ?v3:D_update_set$ ?v4:A_update_b_update_fun$ ((image$(?v0, ?v1) = image$a(?v2, ?v3)) ⇒ (image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v0), ?v1) = image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v2), ?v3)))
tff(axiom618,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_set$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$'(A__questionmark_v0,A__questionmark_v1) = 'image$a'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_set$ ?v2:C_update_a_update_fun$ ?v3:C_update_set$ ?v4:A_update_b_update_fun$ ((image$a(?v0, ?v1) = image$b(?v2, ?v3)) ⇒ (image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v0), ?v1) = image$c(fun_app$be(fun_app$bf(comp$, ?v4), ?v2), ?v3)))
tff(axiom619,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_set$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$a'(A__questionmark_v0,A__questionmark_v1) = 'image$b'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_set$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_set$ ?v4:A_update_b_update_fun$ ((image$a(?v0, ?v1) = image$(?v2, ?v3)) ⇒ (image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v0), ?v1) = image$d(fun_app$bj(fun_app$bk(comp$a, ?v4), ?v2), ?v3)))
tff(axiom620,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_set$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$a'(A__questionmark_v0,A__questionmark_v1) = 'image$'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_set$ ?v2:D_update_a_update_fun$ ?v3:D_update_set$ ?v4:A_update_b_update_fun$ ((image$a(?v0, ?v1) = image$a(?v2, ?v3)) ⇒ (image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v0), ?v1) = image$e(fun_app$bv(fun_app$bw(comp$j, ?v4), ?v2), ?v3)))
tff(axiom621,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_set$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_set$',A__questionmark_v4: 'A_update_b_update_fun$'] :
      ( ( 'image$a'(A__questionmark_v0,A__questionmark_v1) = 'image$a'(A__questionmark_v2,A__questionmark_v3) )
     => ( 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v0),A__questionmark_v1) = 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v4),A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_set$ (image$f(?v0, image$b(?v1, ?v2)) = image$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), ?v2))
tff(axiom622,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_set$'] : 'image$f'(A__questionmark_v0,'image$b'(A__questionmark_v1,A__questionmark_v2)) = 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:C_d_prod_update_set$ (image$f(?v0, image$(?v1, ?v2)) = image$d(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), ?v2))
tff(axiom623,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'C_d_prod_update_set$'] : 'image$f'(A__questionmark_v0,'image$'(A__questionmark_v1,A__questionmark_v2)) = 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_set$ (image$f(?v0, image$a(?v1, ?v2)) = image$e(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), ?v2))
tff(axiom624,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_set$'] : 'image$f'(A__questionmark_v0,'image$a'(A__questionmark_v1,A__questionmark_v2)) = 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_update_set$ ?v1:A_update_b_update_fun$ (rel_fun$ak(uvx$, grp$(?v0, ?v1)) = grp$a(collect$f(uwa$(?v0)), fun_app$bf(comp$, ?v1)))
tff(axiom625,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'rel_fun$ak'('uvx$','grp$'(A__questionmark_v0,A__questionmark_v1)) = 'grp$a'('collect$f'('uwa$'(A__questionmark_v0)),'fun_app$bf'('comp$',A__questionmark_v1)) ).

%% ∀ ?v0:A_update_set$ ?v1:A_update_b_update_fun$ (rel_fun$al(uvy$, grp$(?v0, ?v1)) = grp$b(collect$e(uwb$(?v0)), fun_app$bk(comp$a, ?v1)))
tff(axiom626,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'rel_fun$al'('uvy$','grp$'(A__questionmark_v0,A__questionmark_v1)) = 'grp$b'('collect$e'('uwb$'(A__questionmark_v0)),'fun_app$bk'('comp$a',A__questionmark_v1)) ).

%% ∀ ?v0:A_update_set$ ?v1:A_update_b_update_fun$ (rel_fun$am(uvz$, grp$(?v0, ?v1)) = grp$c(collect$d(uwc$(?v0)), fun_app$bw(comp$j, ?v1)))
tff(axiom627,axiom,
    ! [A__questionmark_v0: 'A_update_set$',A__questionmark_v1: 'A_update_b_update_fun$'] : 'rel_fun$am'('uvz$','grp$'(A__questionmark_v0,A__questionmark_v1)) = 'grp$c'('collect$d'('uwc$'(A__questionmark_v0)),'fun_app$bw'('comp$j',A__questionmark_v1)) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_set$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((image$b(?v0, ?v1) = top$c) ∧ ∀ ?v4:C_update$ (member$b(?v4, ?v1) ⇒ (fun_app$q(fun_app$be(fun_app$bf(comp$, ?v2), ?v0), ?v4) = fun_app$q(fun_app$be(fun_app$bf(comp$, ?v3), ?v0), ?v4)))) ⇒ (?v2 = ?v3))
tff(axiom628,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_set$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( 'image$b'(A__questionmark_v0,A__questionmark_v1) = 'top$c' )
        & ! [A__questionmark_v4: 'C_update$'] :
            ( 'member$b'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0),A__questionmark_v4) = 'fun_app$q'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v0),A__questionmark_v4) ) ) )
     => ( A__questionmark_v2 = A__questionmark_v3 ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_set$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((image$(?v0, ?v1) = top$c) ∧ ∀ ?v4:C_d_prod_update$ (member$(?v4, ?v1) ⇒ (fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0), ?v4) = fun_app$bz(fun_app$bj(fun_app$bk(comp$a, ?v3), ?v0), ?v4)))) ⇒ (?v2 = ?v3))
tff(axiom629,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_set$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( 'image$'(A__questionmark_v0,A__questionmark_v1) = 'top$c' )
        & ! [A__questionmark_v4: 'C_d_prod_update$'] :
            ( 'member$'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0),A__questionmark_v4) = 'fun_app$bz'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v0),A__questionmark_v4) ) ) )
     => ( A__questionmark_v2 = A__questionmark_v3 ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_set$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((image$a(?v0, ?v1) = top$c) ∧ ∀ ?v4:D_update$ (member$a(?v4, ?v1) ⇒ (fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0), ?v4) = fun_app$m(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v0), ?v4)))) ⇒ (?v2 = ?v3))
tff(axiom630,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_set$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( 'image$a'(A__questionmark_v0,A__questionmark_v1) = 'top$c' )
        & ! [A__questionmark_v4: 'D_update$'] :
            ( 'member$a'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0),A__questionmark_v4) = 'fun_app$m'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v0),A__questionmark_v4) ) ) )
     => ( A__questionmark_v2 = A__questionmark_v3 ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ (((image$b(?v0, top$b) = top$c) ∧ (image$f(?v1, top$c) = top$d)) ⇒ (image$c(fun_app$be(fun_app$bf(comp$, ?v1), ?v0), top$b) = top$d))
tff(axiom631,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( ( 'image$b'(A__questionmark_v0,'top$b') = 'top$c' )
        & ( 'image$f'(A__questionmark_v1,'top$c') = 'top$d' ) )
     => ( 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v0),'top$b') = 'top$d' ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ (((image$(?v0, top$) = top$c) ∧ (image$f(?v1, top$c) = top$d)) ⇒ (image$d(fun_app$bj(fun_app$bk(comp$a, ?v1), ?v0), top$) = top$d))
tff(axiom632,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( ( 'image$'(A__questionmark_v0,'top$') = 'top$c' )
        & ( 'image$f'(A__questionmark_v1,'top$c') = 'top$d' ) )
     => ( 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v0),'top$') = 'top$d' ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ (((image$a(?v0, top$a) = top$c) ∧ (image$f(?v1, top$c) = top$d)) ⇒ (image$e(fun_app$bv(fun_app$bw(comp$j, ?v1), ?v0), top$a) = top$d))
tff(axiom633,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$'] :
      ( ( ( 'image$a'(A__questionmark_v0,'top$a') = 'top$c' )
        & ( 'image$f'(A__questionmark_v1,'top$c') = 'top$d' ) )
     => ( 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v0),'top$a') = 'top$d' ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ ((∀ ?v4:A_update$ ?v5:A_update$ ((member$c(?v4, image$b(?v0, top$b)) ∧ (member$c(?v5, image$b(?v1, top$b)) ∧ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v5)))) ⇒ (?v4 = ?v5)) ∧ (fun_app$be(fun_app$bf(comp$, ?v2), ?v0) = fun_app$be(fun_app$bf(comp$, ?v3), ?v1))) ⇒ (?v0 = ?v1))
tff(axiom634,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'A_update$'] :
            ( ( 'member$c'(A__questionmark_v4,'image$b'(A__questionmark_v0,'top$b'))
              & 'member$c'(A__questionmark_v5,'image$b'(A__questionmark_v1,'top$b'))
              & ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v5) ) )
           => ( A__questionmark_v4 = A__questionmark_v5 ) )
        & ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v1) ) )
     => ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ ((∀ ?v4:A_update$ ?v5:A_update$ ((member$c(?v4, image$(?v0, top$)) ∧ (member$c(?v5, image$(?v1, top$)) ∧ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v5)))) ⇒ (?v4 = ?v5)) ∧ (fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0) = fun_app$bj(fun_app$bk(comp$a, ?v3), ?v1))) ⇒ (?v0 = ?v1))
tff(axiom635,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'A_update$'] :
            ( ( 'member$c'(A__questionmark_v4,'image$'(A__questionmark_v0,'top$'))
              & 'member$c'(A__questionmark_v5,'image$'(A__questionmark_v1,'top$'))
              & ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v5) ) )
           => ( A__questionmark_v4 = A__questionmark_v5 ) )
        & ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v1) ) )
     => ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ ((∀ ?v4:A_update$ ?v5:A_update$ ((member$c(?v4, image$a(?v0, top$a)) ∧ (member$c(?v5, image$a(?v1, top$a)) ∧ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v5)))) ⇒ (?v4 = ?v5)) ∧ (fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v1))) ⇒ (?v0 = ?v1))
tff(axiom636,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ! [A__questionmark_v4: 'A_update$',A__questionmark_v5: 'A_update$'] :
            ( ( 'member$c'(A__questionmark_v4,'image$a'(A__questionmark_v0,'top$a'))
              & 'member$c'(A__questionmark_v5,'image$a'(A__questionmark_v1,'top$a'))
              & ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v5) ) )
           => ( A__questionmark_v4 = A__questionmark_v5 ) )
        & ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v1) ) )
     => ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ (∀ ?v3:A_update$ (member$c(?v3, image$b(?v0, top$b)) ⇒ (fun_app$ae(?v1, ?v3) = fun_app$ae(?v2, ?v3))) ⇒ (fun_app$be(fun_app$bf(comp$, ?v1), ?v0) = fun_app$be(fun_app$bf(comp$, ?v2), ?v0)))
tff(axiom637,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ! [A__questionmark_v3: 'A_update$'] :
          ( 'member$c'(A__questionmark_v3,'image$b'(A__questionmark_v0,'top$b'))
         => ( 'fun_app$ae'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$ae'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v0) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ (∀ ?v3:A_update$ (member$c(?v3, image$(?v0, top$)) ⇒ (fun_app$ae(?v1, ?v3) = fun_app$ae(?v2, ?v3))) ⇒ (fun_app$bj(fun_app$bk(comp$a, ?v1), ?v0) = fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0)))
tff(axiom638,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ! [A__questionmark_v3: 'A_update$'] :
          ( 'member$c'(A__questionmark_v3,'image$'(A__questionmark_v0,'top$'))
         => ( 'fun_app$ae'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$ae'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v0) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:A_update_b_update_fun$ ?v2:A_update_b_update_fun$ (∀ ?v3:A_update$ (member$c(?v3, image$a(?v0, top$a)) ⇒ (fun_app$ae(?v1, ?v3) = fun_app$ae(?v2, ?v3))) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v1), ?v0) = fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0)))
tff(axiom639,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$'] :
      ( ! [A__questionmark_v3: 'A_update$'] :
          ( 'member$c'(A__questionmark_v3,'image$a'(A__questionmark_v0,'top$a'))
         => ( 'fun_app$ae'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$ae'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v0) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:C_update_a_update_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:A_update$ (member$c(?v4, image$b(?v1, top$b)) ⇒ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v4)))) ⇒ (fun_app$be(fun_app$bf(comp$, ?v2), ?v0) = fun_app$be(fun_app$bf(comp$, ?v3), ?v1)))
tff(axiom640,axiom,
    ! [A__questionmark_v0: 'C_update_a_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'A_update$'] :
            ( 'member$c'(A__questionmark_v4,'image$b'(A__questionmark_v1,'top$b'))
           => ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v0) = 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:C_d_prod_update_a_update_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:A_update$ (member$c(?v4, image$(?v1, top$)) ⇒ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v4)))) ⇒ (fun_app$bj(fun_app$bk(comp$a, ?v2), ?v0) = fun_app$bj(fun_app$bk(comp$a, ?v3), ?v1)))
tff(axiom641,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_a_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'A_update$'] :
            ( 'member$c'(A__questionmark_v4,'image$'(A__questionmark_v1,'top$'))
           => ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:D_update_a_update_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:A_update_b_update_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:A_update$ (member$c(?v4, image$a(?v1, top$a)) ⇒ (fun_app$ae(?v2, ?v4) = fun_app$ae(?v3, ?v4)))) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v2), ?v0) = fun_app$bv(fun_app$bw(comp$j, ?v3), ?v1)))
tff(axiom642,axiom,
    ! [A__questionmark_v0: 'D_update_a_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'A_update$'] :
            ( 'member$c'(A__questionmark_v4,'image$a'(A__questionmark_v1,'top$a'))
           => ( 'fun_app$ae'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$ae'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v0) = 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_update_a_update_fun$ (image$c(fun_app$be(fun_app$bf(comp$, ?v0), ?v1), top$b) = image$f(?v0, image$b(?v1, top$b)))
tff(axiom643,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$'] : 'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v0),A__questionmark_v1),'top$b') = 'image$f'(A__questionmark_v0,'image$b'(A__questionmark_v1,'top$b')) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:C_d_prod_update_a_update_fun$ (image$d(fun_app$bj(fun_app$bk(comp$a, ?v0), ?v1), top$) = image$f(?v0, image$(?v1, top$)))
tff(axiom644,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$'] : 'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v0),A__questionmark_v1),'top$') = 'image$f'(A__questionmark_v0,'image$'(A__questionmark_v1,'top$')) ).

%% ∀ ?v0:A_update_b_update_fun$ ?v1:D_update_a_update_fun$ (image$e(fun_app$bv(fun_app$bw(comp$j, ?v0), ?v1), top$a) = image$f(?v0, image$a(?v1, top$a)))
tff(axiom645,axiom,
    ! [A__questionmark_v0: 'A_update_b_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$'] : 'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v0),A__questionmark_v1),'top$a') = 'image$f'(A__questionmark_v0,'image$a'(A__questionmark_v1,'top$a')) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_set$ (fun_app$dy(?v0, image$f(?v1, image$b(?v2, ?v3))) = fun_app$dy(?v0, image$c(fun_app$be(fun_app$bf(comp$, ?v1), ?v2), ?v3)))
tff(axiom646,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$b'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_set$ (fun_app$dy(?v0, image$f(?v1, image$(?v2, ?v3))) = fun_app$dy(?v0, image$d(fun_app$bj(fun_app$bk(comp$a, ?v1), ?v2), ?v3)))
tff(axiom647,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_set$ (fun_app$dy(?v0, image$f(?v1, image$a(?v2, ?v3))) = fun_app$dy(?v0, image$e(fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2), ?v3)))
tff(axiom648,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$a'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_set$ (fun_app$dy(?v0, image$f(?v1, image$b(?v2, ?v3))) = fun_app$dy(?v0, image$c(fun_app$be(fun_app$bf(comp$, ?v1), ?v2), ?v3)))
tff(axiom649,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$b'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$c'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:C_d_prod_update_a_update_fun$ ?v3:C_d_prod_update_set$ (fun_app$dy(?v0, image$f(?v1, image$(?v2, ?v3))) = fun_app$dy(?v0, image$d(fun_app$bj(fun_app$bk(comp$a, ?v1), ?v2), ?v3)))
tff(axiom650,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'C_d_prod_update_a_update_fun$',A__questionmark_v3: 'C_d_prod_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$d'('fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:B_update_set_b_update_fun$ ?v1:A_update_b_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_set$ (fun_app$dy(?v0, image$f(?v1, image$a(?v2, ?v3))) = fun_app$dy(?v0, image$e(fun_app$bv(fun_app$bw(comp$j, ?v1), ?v2), ?v3)))
tff(axiom651,axiom,
    ! [A__questionmark_v0: 'B_update_set_b_update_fun$',A__questionmark_v1: 'A_update_b_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_set$'] : 'fun_app$dy'(A__questionmark_v0,'image$f'(A__questionmark_v1,'image$a'(A__questionmark_v2,A__questionmark_v3))) = 'fun_app$dy'(A__questionmark_v0,'image$e'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:C_update_c_update_bool_fun_fun$ rel_fun$(uwd$, rel_fun$b(rel_fun$c(?v0, uwe$), rel_fun$d(?v0, uwf$)), comp$, comp$)
tff(axiom652,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_bool_fun_fun$'] : 'rel_fun$'('uwd$','rel_fun$b'('rel_fun$c'(A__questionmark_v0,'uwe$'),'rel_fun$d'(A__questionmark_v0,'uwf$')),'comp$','comp$') ).

%% ∀ ?v0:C_update_c_d_prod_update_bool_fun_fun$ rel_fun$e(uwd$, rel_fun$f(rel_fun$g(?v0, uwe$), rel_fun$h(?v0, uwf$)), comp$, comp$a)
tff(axiom653,axiom,
    ! [A__questionmark_v0: 'C_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$e'('uwd$','rel_fun$f'('rel_fun$g'(A__questionmark_v0,'uwe$'),'rel_fun$h'(A__questionmark_v0,'uwf$')),'comp$','comp$a') ).

%% ∀ ?v0:C_update_d_update_bool_fun_fun$ rel_fun$i(uwd$, rel_fun$j(rel_fun$k(?v0, uwe$), rel_fun$l(?v0, uwf$)), comp$, comp$j)
tff(axiom654,axiom,
    ! [A__questionmark_v0: 'C_update_d_update_bool_fun_fun$'] : 'rel_fun$i'('uwd$','rel_fun$j'('rel_fun$k'(A__questionmark_v0,'uwe$'),'rel_fun$l'(A__questionmark_v0,'uwf$')),'comp$','comp$j') ).

%% ∀ ?v0:C_d_prod_update_c_update_bool_fun_fun$ rel_fun$m(uwd$, rel_fun$n(rel_fun$o(?v0, uwe$), rel_fun$p(?v0, uwf$)), comp$a, comp$)
tff(axiom655,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_c_update_bool_fun_fun$'] : 'rel_fun$m'('uwd$','rel_fun$n'('rel_fun$o'(A__questionmark_v0,'uwe$'),'rel_fun$p'(A__questionmark_v0,'uwf$')),'comp$a','comp$') ).

%% ∀ ?v0:C_d_prod_update_c_d_prod_update_bool_fun_fun$ rel_fun$q(uwd$, rel_fun$r(rel_fun$s(?v0, uwe$), rel_fun$t(?v0, uwf$)), comp$a, comp$a)
tff(axiom656,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$q'('uwd$','rel_fun$r'('rel_fun$s'(A__questionmark_v0,'uwe$'),'rel_fun$t'(A__questionmark_v0,'uwf$')),'comp$a','comp$a') ).

%% ∀ ?v0:C_d_prod_update_d_update_bool_fun_fun$ rel_fun$u(uwd$, rel_fun$v(rel_fun$w(?v0, uwe$), rel_fun$x(?v0, uwf$)), comp$a, comp$j)
tff(axiom657,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_d_update_bool_fun_fun$'] : 'rel_fun$u'('uwd$','rel_fun$v'('rel_fun$w'(A__questionmark_v0,'uwe$'),'rel_fun$x'(A__questionmark_v0,'uwf$')),'comp$a','comp$j') ).

%% ∀ ?v0:D_update_c_update_bool_fun_fun$ rel_fun$y(uwd$, rel_fun$z(rel_fun$aa(?v0, uwe$), rel_fun$ab(?v0, uwf$)), comp$j, comp$)
tff(axiom658,axiom,
    ! [A__questionmark_v0: 'D_update_c_update_bool_fun_fun$'] : 'rel_fun$y'('uwd$','rel_fun$z'('rel_fun$aa'(A__questionmark_v0,'uwe$'),'rel_fun$ab'(A__questionmark_v0,'uwf$')),'comp$j','comp$') ).

%% ∀ ?v0:D_update_c_d_prod_update_bool_fun_fun$ rel_fun$ac(uwd$, rel_fun$ad(rel_fun$ae(?v0, uwe$), rel_fun$af(?v0, uwf$)), comp$j, comp$a)
tff(axiom659,axiom,
    ! [A__questionmark_v0: 'D_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$ac'('uwd$','rel_fun$ad'('rel_fun$ae'(A__questionmark_v0,'uwe$'),'rel_fun$af'(A__questionmark_v0,'uwf$')),'comp$j','comp$a') ).

%% ∀ ?v0:D_update_d_update_bool_fun_fun$ rel_fun$ag(uwd$, rel_fun$ah(rel_fun$ai(?v0, uwe$), rel_fun$aj(?v0, uwf$)), comp$j, comp$j)
tff(axiom660,axiom,
    ! [A__questionmark_v0: 'D_update_d_update_bool_fun_fun$'] : 'rel_fun$ag'('uwd$','rel_fun$ah'('rel_fun$ai'(A__questionmark_v0,'uwe$'),'rel_fun$aj'(A__questionmark_v0,'uwf$')),'comp$j','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_c_update_bool_fun_fun$ rel_fun$(rel_fun$a(?v0, ?v1), rel_fun$b(rel_fun$c(?v2, ?v0), rel_fun$d(?v2, ?v1)), comp$, comp$)
tff(axiom661,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_c_update_bool_fun_fun$'] : 'rel_fun$'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$b'('rel_fun$c'(A__questionmark_v2,A__questionmark_v0),'rel_fun$d'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_c_d_prod_update_bool_fun_fun$ rel_fun$e(rel_fun$a(?v0, ?v1), rel_fun$f(rel_fun$g(?v2, ?v0), rel_fun$h(?v2, ?v1)), comp$, comp$a)
tff(axiom662,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$e'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$f'('rel_fun$g'(A__questionmark_v2,A__questionmark_v0),'rel_fun$h'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_update_d_update_bool_fun_fun$ rel_fun$i(rel_fun$a(?v0, ?v1), rel_fun$j(rel_fun$k(?v2, ?v0), rel_fun$l(?v2, ?v1)), comp$, comp$j)
tff(axiom663,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_update_d_update_bool_fun_fun$'] : 'rel_fun$i'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$j'('rel_fun$k'(A__questionmark_v2,A__questionmark_v0),'rel_fun$l'(A__questionmark_v2,A__questionmark_v1)),'comp$','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_c_update_bool_fun_fun$ rel_fun$m(rel_fun$a(?v0, ?v1), rel_fun$n(rel_fun$o(?v2, ?v0), rel_fun$p(?v2, ?v1)), comp$a, comp$)
tff(axiom664,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_c_update_bool_fun_fun$'] : 'rel_fun$m'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$n'('rel_fun$o'(A__questionmark_v2,A__questionmark_v0),'rel_fun$p'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_c_d_prod_update_bool_fun_fun$ rel_fun$q(rel_fun$a(?v0, ?v1), rel_fun$r(rel_fun$s(?v2, ?v0), rel_fun$t(?v2, ?v1)), comp$a, comp$a)
tff(axiom665,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$q'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$r'('rel_fun$s'(A__questionmark_v2,A__questionmark_v0),'rel_fun$t'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:C_d_prod_update_d_update_bool_fun_fun$ rel_fun$u(rel_fun$a(?v0, ?v1), rel_fun$v(rel_fun$w(?v2, ?v0), rel_fun$x(?v2, ?v1)), comp$a, comp$j)
tff(axiom666,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'C_d_prod_update_d_update_bool_fun_fun$'] : 'rel_fun$u'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$v'('rel_fun$w'(A__questionmark_v2,A__questionmark_v0),'rel_fun$x'(A__questionmark_v2,A__questionmark_v1)),'comp$a','comp$j') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_c_update_bool_fun_fun$ rel_fun$y(rel_fun$a(?v0, ?v1), rel_fun$z(rel_fun$aa(?v2, ?v0), rel_fun$ab(?v2, ?v1)), comp$j, comp$)
tff(axiom667,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_c_update_bool_fun_fun$'] : 'rel_fun$y'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$z'('rel_fun$aa'(A__questionmark_v2,A__questionmark_v0),'rel_fun$ab'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_c_d_prod_update_bool_fun_fun$ rel_fun$ac(rel_fun$a(?v0, ?v1), rel_fun$ad(rel_fun$ae(?v2, ?v0), rel_fun$af(?v2, ?v1)), comp$j, comp$a)
tff(axiom668,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_c_d_prod_update_bool_fun_fun$'] : 'rel_fun$ac'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$ad'('rel_fun$ae'(A__questionmark_v2,A__questionmark_v0),'rel_fun$af'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$a') ).

%% ∀ ?v0:A_update_a_update_bool_fun_fun$ ?v1:B_update_b_update_bool_fun_fun$ ?v2:D_update_d_update_bool_fun_fun$ rel_fun$ag(rel_fun$a(?v0, ?v1), rel_fun$ah(rel_fun$ai(?v2, ?v0), rel_fun$aj(?v2, ?v1)), comp$j, comp$j)
tff(axiom669,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_bool_fun_fun$',A__questionmark_v1: 'B_update_b_update_bool_fun_fun$',A__questionmark_v2: 'D_update_d_update_bool_fun_fun$'] : 'rel_fun$ag'('rel_fun$a'(A__questionmark_v0,A__questionmark_v1),'rel_fun$ah'('rel_fun$ai'(A__questionmark_v2,A__questionmark_v0),'rel_fun$aj'(A__questionmark_v2,A__questionmark_v1)),'comp$j','comp$j') ).

%% ∀ ?v0:B_update_b_update_bool_fun_fun$ ?v1:B_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:B_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_c_update_fun$ ?v6:C_update_a_update_fun$ ?v7:A_update_c_update_bool_fun_fun$ ((quotient$(?v0, ?v1, ?v2, ?v3) ∧ quotient$a(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$b(relcompp$(?v3, relcompp$a(?v4, conversep$(?v3))), comp$cd(?v5, ?v1), fun_app$be(fun_app$bf(comp$, ?v2), ?v6), relcompp$b(?v3, ?v7)))
tff(axiom670,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_bool_fun_fun$',A__questionmark_v1: 'B_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'B_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_c_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$',A__questionmark_v7: 'A_update_c_update_bool_fun_fun$'] :
      ( ( 'quotient$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$a'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$b'('relcompp$'(A__questionmark_v3,'relcompp$a'(A__questionmark_v4,'conversep$'(A__questionmark_v3))),'comp$cd'(A__questionmark_v5,A__questionmark_v1),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v2),A__questionmark_v6),'relcompp$b'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:B_update_b_update_bool_fun_fun$ ?v1:B_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:B_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_c_d_prod_update_fun$ ?v6:C_d_prod_update_a_update_fun$ ?v7:A_update_c_d_prod_update_bool_fun_fun$ ((quotient$(?v0, ?v1, ?v2, ?v3) ∧ quotient$c(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$d(relcompp$(?v3, relcompp$a(?v4, conversep$(?v3))), comp$ce(?v5, ?v1), fun_app$bj(fun_app$bk(comp$a, ?v2), ?v6), relcompp$c(?v3, ?v7)))
tff(axiom671,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_bool_fun_fun$',A__questionmark_v1: 'B_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'B_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_c_d_prod_update_fun$',A__questionmark_v6: 'C_d_prod_update_a_update_fun$',A__questionmark_v7: 'A_update_c_d_prod_update_bool_fun_fun$'] :
      ( ( 'quotient$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$c'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$d'('relcompp$'(A__questionmark_v3,'relcompp$a'(A__questionmark_v4,'conversep$'(A__questionmark_v3))),'comp$ce'(A__questionmark_v5,A__questionmark_v1),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v2),A__questionmark_v6),'relcompp$c'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:B_update_b_update_bool_fun_fun$ ?v1:B_update_a_update_fun$ ?v2:A_update_b_update_fun$ ?v3:B_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_d_update_fun$ ?v6:D_update_a_update_fun$ ?v7:A_update_d_update_bool_fun_fun$ ((quotient$(?v0, ?v1, ?v2, ?v3) ∧ quotient$e(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$f(relcompp$(?v3, relcompp$a(?v4, conversep$(?v3))), comp$cf(?v5, ?v1), fun_app$bv(fun_app$bw(comp$j, ?v2), ?v6), relcompp$d(?v3, ?v7)))
tff(axiom672,axiom,
    ! [A__questionmark_v0: 'B_update_b_update_bool_fun_fun$',A__questionmark_v1: 'B_update_a_update_fun$',A__questionmark_v2: 'A_update_b_update_fun$',A__questionmark_v3: 'B_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_d_update_fun$',A__questionmark_v6: 'D_update_a_update_fun$',A__questionmark_v7: 'A_update_d_update_bool_fun_fun$'] :
      ( ( 'quotient$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$e'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$f'('relcompp$'(A__questionmark_v3,'relcompp$a'(A__questionmark_v4,'conversep$'(A__questionmark_v3))),'comp$cf'(A__questionmark_v5,A__questionmark_v1),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v2),A__questionmark_v6),'relcompp$d'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:C_update_c_update_bool_fun_fun$ ?v1:C_update_a_update_fun$ ?v2:A_update_c_update_fun$ ?v3:C_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_b_update_fun$ ?v6:B_update_a_update_fun$ ?v7:A_update_b_update_bool_fun_fun$ ((quotient$g(?v0, ?v1, ?v2, ?v3) ∧ quotient$h(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$i(relcompp$e(?v3, relcompp$f(?v4, conversep$a(?v3))), fun_app$be(fun_app$bf(comp$, ?v5), ?v1), comp$cd(?v2, ?v6), relcompp$g(?v3, ?v7)))
tff(axiom673,axiom,
    ! [A__questionmark_v0: 'C_update_c_update_bool_fun_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'A_update_c_update_fun$',A__questionmark_v3: 'C_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'B_update_a_update_fun$',A__questionmark_v7: 'A_update_b_update_bool_fun_fun$'] :
      ( ( 'quotient$g'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$h'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$i'('relcompp$e'(A__questionmark_v3,'relcompp$f'(A__questionmark_v4,'conversep$a'(A__questionmark_v3))),'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v1),'comp$cd'(A__questionmark_v2,A__questionmark_v6),'relcompp$g'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:C_d_prod_update_c_d_prod_update_bool_fun_fun$ ?v1:C_d_prod_update_a_update_fun$ ?v2:A_update_c_d_prod_update_fun$ ?v3:C_d_prod_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_b_update_fun$ ?v6:B_update_a_update_fun$ ?v7:A_update_b_update_bool_fun_fun$ ((quotient$j(?v0, ?v1, ?v2, ?v3) ∧ quotient$h(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$k(relcompp$h(?v3, relcompp$i(?v4, conversep$b(?v3))), fun_app$bj(fun_app$bk(comp$a, ?v5), ?v1), comp$ce(?v2, ?v6), relcompp$j(?v3, ?v7)))
tff(axiom674,axiom,
    ! [A__questionmark_v0: 'C_d_prod_update_c_d_prod_update_bool_fun_fun$',A__questionmark_v1: 'C_d_prod_update_a_update_fun$',A__questionmark_v2: 'A_update_c_d_prod_update_fun$',A__questionmark_v3: 'C_d_prod_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'B_update_a_update_fun$',A__questionmark_v7: 'A_update_b_update_bool_fun_fun$'] :
      ( ( 'quotient$j'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$h'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$k'('relcompp$h'(A__questionmark_v3,'relcompp$i'(A__questionmark_v4,'conversep$b'(A__questionmark_v3))),'fun_app$bj'('fun_app$bk'('comp$a',A__questionmark_v5),A__questionmark_v1),'comp$ce'(A__questionmark_v2,A__questionmark_v6),'relcompp$j'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:D_update_d_update_bool_fun_fun$ ?v1:D_update_a_update_fun$ ?v2:A_update_d_update_fun$ ?v3:D_update_a_update_bool_fun_fun$ ?v4:A_update_a_update_bool_fun_fun$ ?v5:A_update_b_update_fun$ ?v6:B_update_a_update_fun$ ?v7:A_update_b_update_bool_fun_fun$ ((quotient$l(?v0, ?v1, ?v2, ?v3) ∧ quotient$h(?v4, ?v5, ?v6, ?v7)) ⇒ quotient$m(relcompp$k(?v3, relcompp$l(?v4, conversep$c(?v3))), fun_app$bv(fun_app$bw(comp$j, ?v5), ?v1), comp$cf(?v2, ?v6), relcompp$m(?v3, ?v7)))
tff(axiom675,axiom,
    ! [A__questionmark_v0: 'D_update_d_update_bool_fun_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'A_update_d_update_fun$',A__questionmark_v3: 'D_update_a_update_bool_fun_fun$',A__questionmark_v4: 'A_update_a_update_bool_fun_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'B_update_a_update_fun$',A__questionmark_v7: 'A_update_b_update_bool_fun_fun$'] :
      ( ( 'quotient$l'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)
        & 'quotient$h'(A__questionmark_v4,A__questionmark_v5,A__questionmark_v6,A__questionmark_v7) )
     => 'quotient$m'('relcompp$k'(A__questionmark_v3,'relcompp$l'(A__questionmark_v4,'conversep$c'(A__questionmark_v3))),'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v1),'comp$cf'(A__questionmark_v2,A__questionmark_v6),'relcompp$m'(A__questionmark_v3,A__questionmark_v7)) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:B_update_b_update_fun$ ?v4:C_update_c_update_fun$ ?v5:C_update_c_update_fun$ ?v6:C_update_b_update_fun$ ?v7:A_update_b_update_fun$ ?v8:C_update_a_update_fun$ ((type_definition$(?v0, ?v1, top$c) ∧ (type_definition$a(?v2, ?v3, top$d) ∧ (type_definition$b(?v4, ?v5, top$b) ∧ (comp$f(comp$d(?v3, ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$am(comp$g(?v3, ?v7), ?v0)), comp$e(comp$b(?v1, ?v8), ?v4)))))) ⇒ (fun_app$be(fun_app$bf(comp$, ?v7), ?v8) = ?v6))
tff(axiom676,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'C_update_c_update_fun$',A__questionmark_v6: 'C_update_b_update_fun$',A__questionmark_v7: 'A_update_b_update_fun$',A__questionmark_v8: 'C_update_a_update_fun$'] :
      ( ( 'type_definition$'(A__questionmark_v0,A__questionmark_v1,'top$c')
        & 'type_definition$a'(A__questionmark_v2,A__questionmark_v3,'top$d')
        & 'type_definition$b'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$f'('comp$d'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$am'('comp$g'(A__questionmark_v3,A__questionmark_v7),A__questionmark_v0)),'comp$e'('comp$b'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v7),A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:B_update_b_update_fun$ ?v4:C_update_d_update_fun$ ?v5:D_update_c_update_fun$ ?v6:D_update_b_update_fun$ ?v7:A_update_b_update_fun$ ?v8:D_update_a_update_fun$ ((type_definition$(?v0, ?v1, top$c) ∧ (type_definition$a(?v2, ?v3, top$d) ∧ (type_definition$c(?v4, ?v5, top$a) ∧ (comp$an(comp$p(?v3, ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$am(comp$g(?v3, ?v7), ?v0)), comp$y(comp$at(?v1, ?v8), ?v4)))))) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v7), ?v8) = ?v6))
tff(axiom677,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'D_update_c_update_fun$',A__questionmark_v6: 'D_update_b_update_fun$',A__questionmark_v7: 'A_update_b_update_fun$',A__questionmark_v8: 'D_update_a_update_fun$'] :
      ( ( 'type_definition$'(A__questionmark_v0,A__questionmark_v1,'top$c')
        & 'type_definition$a'(A__questionmark_v2,A__questionmark_v3,'top$d')
        & 'type_definition$c'(A__questionmark_v4,A__questionmark_v5,'top$a')
        & ( 'comp$an'('comp$p'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$am'('comp$g'(A__questionmark_v3,A__questionmark_v7),A__questionmark_v0)),'comp$y'('comp$at'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v7),A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:B_update_b_update_fun$ ?v4:D_update_c_update_fun$ ?v5:C_update_d_update_fun$ ?v6:C_update_b_update_fun$ ?v7:A_update_b_update_fun$ ?v8:C_update_a_update_fun$ ((type_definition$(?v0, ?v1, top$c) ∧ (type_definition$a(?v2, ?v3, top$d) ∧ (type_definition$d(?v4, ?v5, top$b) ∧ (comp$al(comp$d(?v3, ?v6), ?v4) = fun_app$bv(fun_app$bw(comp$j, comp$am(comp$g(?v3, ?v7), ?v0)), comp$as(comp$b(?v1, ?v8), ?v4)))))) ⇒ (fun_app$be(fun_app$bf(comp$, ?v7), ?v8) = ?v6))
tff(axiom678,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'C_update_d_update_fun$',A__questionmark_v6: 'C_update_b_update_fun$',A__questionmark_v7: 'A_update_b_update_fun$',A__questionmark_v8: 'C_update_a_update_fun$'] :
      ( ( 'type_definition$'(A__questionmark_v0,A__questionmark_v1,'top$c')
        & 'type_definition$a'(A__questionmark_v2,A__questionmark_v3,'top$d')
        & 'type_definition$d'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$al'('comp$d'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v4) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'('comp$g'(A__questionmark_v3,A__questionmark_v7),A__questionmark_v0)),'comp$as'('comp$b'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$',A__questionmark_v7),A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_a_update_fun$ ?v1:A_update_a_update_fun$ ?v2:B_update_b_update_fun$ ?v3:B_update_b_update_fun$ ?v4:D_update_d_update_fun$ ?v5:D_update_d_update_fun$ ?v6:D_update_b_update_fun$ ?v7:A_update_b_update_fun$ ?v8:D_update_a_update_fun$ ((type_definition$(?v0, ?v1, top$c) ∧ (type_definition$a(?v2, ?v3, top$d) ∧ (type_definition$e(?v4, ?v5, top$a) ∧ (comp$ao(comp$p(?v3, ?v6), ?v4) = fun_app$bv(fun_app$bw(comp$j, comp$am(comp$g(?v3, ?v7), ?v0)), comp$x(comp$at(?v1, ?v8), ?v4)))))) ⇒ (fun_app$bv(fun_app$bw(comp$j, ?v7), ?v8) = ?v6))
tff(axiom679,axiom,
    ! [A__questionmark_v0: 'A_update_a_update_fun$',A__questionmark_v1: 'A_update_a_update_fun$',A__questionmark_v2: 'B_update_b_update_fun$',A__questionmark_v3: 'B_update_b_update_fun$',A__questionmark_v4: 'D_update_d_update_fun$',A__questionmark_v5: 'D_update_d_update_fun$',A__questionmark_v6: 'D_update_b_update_fun$',A__questionmark_v7: 'A_update_b_update_fun$',A__questionmark_v8: 'D_update_a_update_fun$'] :
      ( ( 'type_definition$'(A__questionmark_v0,A__questionmark_v1,'top$c')
        & 'type_definition$a'(A__questionmark_v2,A__questionmark_v3,'top$d')
        & 'type_definition$e'(A__questionmark_v4,A__questionmark_v5,'top$a')
        & ( 'comp$ao'('comp$p'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v4) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$am'('comp$g'(A__questionmark_v3,A__questionmark_v7),A__questionmark_v0)),'comp$x'('comp$at'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v7),A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_update_c_update_fun$ ?v5:C_update_c_update_fun$ ?v6:C_update_a_update_fun$ ?v7:C_update_a_update_fun$ ?v8:C_update_c_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$b(?v4, ?v5, top$b) ∧ (comp$f(fun_app$be(fun_app$bf(comp$, ?v3), ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$i(fun_app$be(fun_app$bf(comp$, ?v3), ?v7), ?v0)), comp$e(comp$e(?v1, ?v8), ?v4)))))) ⇒ (comp$e(?v7, ?v8) = ?v6))
tff(axiom680,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'C_update_c_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$',A__questionmark_v7: 'C_update_a_update_fun$',A__questionmark_v8: 'C_update_c_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$b'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$e'('comp$e'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$e'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_update_c_update_fun$ ?v5:C_update_c_update_fun$ ?v6:C_update_a_update_fun$ ?v7:D_update_a_update_fun$ ?v8:C_update_d_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$b(?v4, ?v5, top$b) ∧ (comp$f(fun_app$be(fun_app$bf(comp$, ?v3), ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v7), ?v0)), comp$e(comp$y(?v1, ?v8), ?v4)))))) ⇒ (comp$y(?v7, ?v8) = ?v6))
tff(axiom681,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'C_update_c_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$',A__questionmark_v7: 'D_update_a_update_fun$',A__questionmark_v8: 'C_update_d_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$b'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$e'('comp$y'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$y'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:D_update_c_update_fun$ ?v5:C_update_d_update_fun$ ?v6:C_update_a_update_fun$ ?v7:C_update_a_update_fun$ ?v8:C_update_c_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$d(?v4, ?v5, top$b) ∧ (comp$al(fun_app$be(fun_app$bf(comp$, ?v3), ?v6), ?v4) = fun_app$bv(fun_app$bw(comp$j, comp$i(fun_app$be(fun_app$bf(comp$, ?v3), ?v7), ?v0)), comp$as(comp$e(?v1, ?v8), ?v4)))))) ⇒ (comp$e(?v7, ?v8) = ?v6))
tff(axiom682,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'C_update_d_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$',A__questionmark_v7: 'C_update_a_update_fun$',A__questionmark_v8: 'C_update_c_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$d'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$as'('comp$e'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$e'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:D_update_c_update_fun$ ?v5:C_update_d_update_fun$ ?v6:C_update_a_update_fun$ ?v7:D_update_a_update_fun$ ?v8:C_update_d_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$d(?v4, ?v5, top$b) ∧ (comp$al(fun_app$be(fun_app$bf(comp$, ?v3), ?v6), ?v4) = fun_app$bv(fun_app$bw(comp$j, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v7), ?v0)), comp$as(comp$y(?v1, ?v8), ?v4)))))) ⇒ (comp$y(?v7, ?v8) = ?v6))
tff(axiom683,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'C_update_d_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$',A__questionmark_v7: 'D_update_a_update_fun$',A__questionmark_v8: 'C_update_d_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$d'(A__questionmark_v4,A__questionmark_v5,'top$b')
        & ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$as'('comp$y'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$y'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_update_d_update_fun$ ?v5:D_update_c_update_fun$ ?v6:D_update_a_update_fun$ ?v7:C_update_a_update_fun$ ?v8:D_update_c_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$c(?v4, ?v5, top$a) ∧ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$i(fun_app$be(fun_app$bf(comp$, ?v3), ?v7), ?v0)), comp$y(comp$as(?v1, ?v8), ?v4)))))) ⇒ (comp$as(?v7, ?v8) = ?v6))
tff(axiom684,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'D_update_c_update_fun$',A__questionmark_v6: 'D_update_a_update_fun$',A__questionmark_v7: 'C_update_a_update_fun$',A__questionmark_v8: 'D_update_c_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$c'(A__questionmark_v4,A__questionmark_v5,'top$a')
        & ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$y'('comp$as'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$as'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:B_update_a_update_fun$ ?v3:A_update_b_update_fun$ ?v4:C_update_d_update_fun$ ?v5:D_update_c_update_fun$ ?v6:D_update_a_update_fun$ ?v7:D_update_a_update_fun$ ?v8:D_update_d_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (type_definition$g(?v2, ?v3, top$c) ∧ (type_definition$c(?v4, ?v5, top$a) ∧ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v6), ?v4) = fun_app$be(fun_app$bf(comp$, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v3), ?v7), ?v0)), comp$y(comp$x(?v1, ?v8), ?v4)))))) ⇒ (comp$x(?v7, ?v8) = ?v6))
tff(axiom685,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'B_update_a_update_fun$',A__questionmark_v3: 'A_update_b_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'D_update_c_update_fun$',A__questionmark_v6: 'D_update_a_update_fun$',A__questionmark_v7: 'D_update_a_update_fun$',A__questionmark_v8: 'D_update_d_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & 'type_definition$g'(A__questionmark_v2,A__questionmark_v3,'top$c')
        & 'type_definition$c'(A__questionmark_v4,A__questionmark_v5,'top$a')
        & ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v6),A__questionmark_v4) = 'fun_app$be'('fun_app$bf'('comp$','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v3),A__questionmark_v7),A__questionmark_v0)),'comp$y'('comp$x'(A__questionmark_v1,A__questionmark_v8),A__questionmark_v4)) ) )
     => ( 'comp$x'(A__questionmark_v7,A__questionmark_v8) = A__questionmark_v6 ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_c_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (?v2 = comp$e(?v3, ?v4))) ⇒ (comp$f(fun_app$be(fun_app$bf(comp$, ?v5), ?v2), ?v6) = fun_app$be(fun_app$bf(comp$, comp$i(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v0)), comp$e(comp$e(?v1, ?v4), ?v6))))
tff(axiom686,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_c_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & ( A__questionmark_v2 = 'comp$e'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$be'('fun_app$bf'('comp$','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$e'('comp$e'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_c_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (?v2 = comp$y(?v3, ?v4))) ⇒ (comp$f(fun_app$be(fun_app$bf(comp$, ?v5), ?v2), ?v6) = fun_app$be(fun_app$bf(comp$, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v0)), comp$e(comp$y(?v1, ?v4), ?v6))))
tff(axiom687,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_c_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & ( A__questionmark_v2 = 'comp$y'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$f'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$be'('fun_app$bf'('comp$','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$e'('comp$y'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:C_update_c_update_fun$ ?v5:A_update_b_update_fun$ ?v6:D_update_c_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (?v2 = comp$e(?v3, ?v4))) ⇒ (comp$al(fun_app$be(fun_app$bf(comp$, ?v5), ?v2), ?v6) = fun_app$bv(fun_app$bw(comp$j, comp$i(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v0)), comp$as(comp$e(?v1, ?v4), ?v6))))
tff(axiom688,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'C_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'D_update_c_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & ( A__questionmark_v2 = 'comp$e'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$as'('comp$e'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:C_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:C_update_d_update_fun$ ?v5:A_update_b_update_fun$ ?v6:D_update_c_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (?v2 = comp$y(?v3, ?v4))) ⇒ (comp$al(fun_app$be(fun_app$bf(comp$, ?v5), ?v2), ?v6) = fun_app$bv(fun_app$bw(comp$j, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v0)), comp$as(comp$y(?v1, ?v4), ?v6))))
tff(axiom689,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'C_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'C_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'D_update_c_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & ( A__questionmark_v2 = 'comp$y'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$al'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$as'('comp$y'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_d_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (?v2 = comp$as(?v3, ?v4))) ⇒ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v2), ?v6) = fun_app$be(fun_app$bf(comp$, comp$i(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v0)), comp$y(comp$as(?v1, ?v4), ?v6))))
tff(axiom690,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_d_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & ( A__questionmark_v2 = 'comp$as'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$be'('fun_app$bf'('comp$','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$y'('comp$as'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_d_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (?v2 = comp$x(?v3, ?v4))) ⇒ (comp$an(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v2), ?v6) = fun_app$be(fun_app$bf(comp$, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v0)), comp$y(comp$x(?v1, ?v4), ?v6))))
tff(axiom691,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_d_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & ( A__questionmark_v2 = 'comp$x'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$an'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$be'('fun_app$bf'('comp$','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$y'('comp$x'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_c_update_fun$ ?v1:C_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:D_update_c_update_fun$ ?v5:A_update_b_update_fun$ ?v6:D_update_d_update_fun$ ((type_definition$f(?v0, ?v1, top$b) ∧ (?v2 = comp$as(?v3, ?v4))) ⇒ (comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v2), ?v6) = fun_app$bv(fun_app$bw(comp$j, comp$i(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v0)), comp$x(comp$as(?v1, ?v4), ?v6))))
tff(axiom692,axiom,
    ! [A__questionmark_v0: 'A_update_c_update_fun$',A__questionmark_v1: 'C_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'D_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'D_update_d_update_fun$'] :
      ( ( 'type_definition$f'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & ( A__questionmark_v2 = 'comp$as'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$i'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$x'('comp$as'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:A_update_d_update_fun$ ?v1:D_update_a_update_fun$ ?v2:D_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:D_update_d_update_fun$ ?v5:A_update_b_update_fun$ ?v6:D_update_d_update_fun$ ((type_definition$h(?v0, ?v1, top$a) ∧ (?v2 = comp$x(?v3, ?v4))) ⇒ (comp$ao(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v2), ?v6) = fun_app$bv(fun_app$bw(comp$j, comp$h(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v0)), comp$x(comp$x(?v1, ?v4), ?v6))))
tff(axiom693,axiom,
    ! [A__questionmark_v0: 'A_update_d_update_fun$',A__questionmark_v1: 'D_update_a_update_fun$',A__questionmark_v2: 'D_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'D_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'D_update_d_update_fun$'] :
      ( ( 'type_definition$h'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & ( A__questionmark_v2 = 'comp$x'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'comp$ao'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v2),A__questionmark_v6) = 'fun_app$bv'('fun_app$bw'('comp$j','comp$h'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0)),'comp$x'('comp$x'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:B_update_c_update_fun$ ?v1:C_update_b_update_fun$ ?v2:A_update_a_update_fun$ ?v3:C_update_a_update_fun$ ?v4:A_update_c_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_a_update_fun$ ((type_definition$i(?v0, ?v1, top$b) ∧ (?v2 = comp$ak(?v3, ?v4))) ⇒ (fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v2)), ?v6) = comp$d(comp$z(fun_app$be(fun_app$bf(comp$, ?v5), ?v3), ?v0), fun_app$be(fun_app$bf(comp$, comp$i(?v1, ?v4)), ?v6))))
tff(axiom694,axiom,
    ! [A__questionmark_v0: 'B_update_c_update_fun$',A__questionmark_v1: 'C_update_b_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'C_update_a_update_fun$',A__questionmark_v4: 'A_update_c_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$'] :
      ( ( 'type_definition$i'(A__questionmark_v0,A__questionmark_v1,'top$b')
        & ( A__questionmark_v2 = 'comp$ak'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v2)),A__questionmark_v6) = 'comp$d'('comp$z'('fun_app$be'('fun_app$bf'('comp$',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$','comp$i'(A__questionmark_v1,A__questionmark_v4)),A__questionmark_v6)) ) ) ).

%% ∀ ?v0:B_update_d_update_fun$ ?v1:D_update_b_update_fun$ ?v2:A_update_a_update_fun$ ?v3:D_update_a_update_fun$ ?v4:A_update_d_update_fun$ ?v5:A_update_b_update_fun$ ?v6:C_update_a_update_fun$ ((type_definition$j(?v0, ?v1, top$a) ∧ (?v2 = comp$ar(?v3, ?v4))) ⇒ (fun_app$be(fun_app$bf(comp$, comp$am(?v5, ?v2)), ?v6) = comp$d(comp$cg(fun_app$bv(fun_app$bw(comp$j, ?v5), ?v3), ?v0), fun_app$be(fun_app$bf(comp$, comp$h(?v1, ?v4)), ?v6))))
tff(axiom695,axiom,
    ! [A__questionmark_v0: 'B_update_d_update_fun$',A__questionmark_v1: 'D_update_b_update_fun$',A__questionmark_v2: 'A_update_a_update_fun$',A__questionmark_v3: 'D_update_a_update_fun$',A__questionmark_v4: 'A_update_d_update_fun$',A__questionmark_v5: 'A_update_b_update_fun$',A__questionmark_v6: 'C_update_a_update_fun$'] :
      ( ( 'type_definition$j'(A__questionmark_v0,A__questionmark_v1,'top$a')
        & ( A__questionmark_v2 = 'comp$ar'(A__questionmark_v3,A__questionmark_v4) ) )
     => ( 'fun_app$be'('fun_app$bf'('comp$','comp$am'(A__questionmark_v5,A__questionmark_v2)),A__questionmark_v6) = 'comp$d'('comp$cg'('fun_app$bv'('fun_app$bw'('comp$j',A__questionmark_v5),A__questionmark_v3),A__questionmark_v0),'fun_app$be'('fun_app$bf'('comp$','comp$h'(A__questionmark_v1,A__questionmark_v4)),A__questionmark_v6)) ) ) ).

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