Vampire-SAT---5.0.1.SAT-FMo.s

%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : ITP302_10 : TPTP v9.3.1. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n018.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 11:39:18 AM UTC 2026

% Result   : Satisfiable 34.11s 5.47s
% Output   : FiniteModel 34.11s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
tff('declare_$i1',type,
    'fmb_$i_1': $i ).

tff('finite_domain_$i',axiom,
    ! [X: $i] : ( X = 'fmb_$i_1' ) ).

tff('declare_ZF_ZF_ZF_prod_fun$',type,
    'ZF_ZF_ZF_prod_fun$': $tType ).

tff('declare_ZF_ZF_ZF_prod_fun$1',type,
    'fmb_ZF_ZF_ZF_prod_fun$_1': 'ZF_ZF_ZF_prod_fun$' ).

tff('finite_domain_ZF_ZF_ZF_prod_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_prod_fun$'] : ( X = 'fmb_ZF_ZF_ZF_prod_fun$_1' ) ).

tff('declare_B_ZF_fun_set$',type,
    'B_ZF_fun_set$': $tType ).

tff('declare_B_ZF_fun_set$1',type,
    'fmb_B_ZF_fun_set$_1': 'B_ZF_fun_set$' ).

tff('finite_domain_B_ZF_fun_set$',axiom,
    ! [X: 'B_ZF_fun_set$'] : ( X = 'fmb_B_ZF_fun_set$_1' ) ).

tff('declare_Nat_ZF_fun_set$',type,
    'Nat_ZF_fun_set$': $tType ).

tff('declare_Nat_ZF_fun_set$1',type,
    'fmb_Nat_ZF_fun_set$_1': 'Nat_ZF_fun_set$' ).

tff('finite_domain_Nat_ZF_fun_set$',axiom,
    ! [X: 'Nat_ZF_fun_set$'] : ( X = 'fmb_Nat_ZF_fun_set$_1' ) ).

tff('declare_Nat_set_set$',type,
    'Nat_set_set$': $tType ).

tff('declare_Nat_set_set$1',type,
    'fmb_Nat_set_set$_1': 'Nat_set_set$' ).

tff('finite_domain_Nat_set_set$',axiom,
    ! [X: 'Nat_set_set$'] : ( X = 'fmb_Nat_set_set$_1' ) ).

tff('declare_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',type,
    'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$': $tType ).

tff('declare_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$1',type,
    'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).

tff('finite_domain_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',axiom,
    ! [X: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] : ( X = 'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1' ) ).

tff('declare_Nat_ZF_ZF_prod_prod_set$',type,
    'Nat_ZF_ZF_prod_prod_set$': $tType ).

tff('declare_Nat_ZF_ZF_prod_prod_set$1',type,
    'fmb_Nat_ZF_ZF_prod_prod_set$_1': 'Nat_ZF_ZF_prod_prod_set$' ).

tff('finite_domain_Nat_ZF_ZF_prod_prod_set$',axiom,
    ! [X: 'Nat_ZF_ZF_prod_prod_set$'] : ( X = 'fmb_Nat_ZF_ZF_prod_prod_set$_1' ) ).

tff('declare_Nat_nat_ZF_set_ZF_set_prod_fun_fun$',type,
    'Nat_nat_ZF_set_ZF_set_prod_fun_fun$': $tType ).

tff('declare_Nat_nat_ZF_set_ZF_set_prod_fun_fun$1',type,
    'fmb_Nat_nat_ZF_set_ZF_set_prod_fun_fun$_1': 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' ).

tff('finite_domain_Nat_nat_ZF_set_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$'] : ( X = 'fmb_Nat_nat_ZF_set_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$',type,
    'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_1': 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_ZF_set$',type,
    'ZF_set$': $tType ).

tff('declare_ZF_set$1',type,
    'fmb_ZF_set$_1': 'ZF_set$' ).

tff('finite_domain_ZF_set$',axiom,
    ! [X: 'ZF_set$'] : ( X = 'fmb_ZF_set$_1' ) ).

tff('declare_Nat_nat_fun_ZF_set_fun$',type,
    'Nat_nat_fun_ZF_set_fun$': $tType ).

tff('declare_Nat_nat_fun_ZF_set_fun$1',type,
    'fmb_Nat_nat_fun_ZF_set_fun$_1': 'Nat_nat_fun_ZF_set_fun$' ).

tff('finite_domain_Nat_nat_fun_ZF_set_fun$',axiom,
    ! [X: 'Nat_nat_fun_ZF_set_fun$'] : ( X = 'fmb_Nat_nat_fun_ZF_set_fun$_1' ) ).

tff('declare_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',type,
    'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$': $tType ).

tff('declare_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$1',type,
    'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('finite_domain_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',axiom,
    ! [X: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] : ( X = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ) ).

tff('declare_ZF_nat_set_fun$',type,
    'ZF_nat_set_fun$': $tType ).

tff('declare_ZF_nat_set_fun$1',type,
    'fmb_ZF_nat_set_fun$_1': 'ZF_nat_set_fun$' ).

tff('finite_domain_ZF_nat_set_fun$',axiom,
    ! [X: 'ZF_nat_set_fun$'] : ( X = 'fmb_ZF_nat_set_fun$_1' ) ).

tff('declare_Unit_unit_fun$',type,
    'Unit_unit_fun$': $tType ).

tff('declare_Unit_unit_fun$1',type,
    'fmb_Unit_unit_fun$_1': 'Unit_unit_fun$' ).

tff('finite_domain_Unit_unit_fun$',axiom,
    ! [X: 'Unit_unit_fun$'] : ( X = 'fmb_Unit_unit_fun$_1' ) ).

tff('declare_ZF_nat_bool_fun_fun$',type,
    'ZF_nat_bool_fun_fun$': $tType ).

tff('declare_ZF_nat_bool_fun_fun$1',type,
    'fmb_ZF_nat_bool_fun_fun$_1': 'ZF_nat_bool_fun_fun$' ).

tff('finite_domain_ZF_nat_bool_fun_fun$',axiom,
    ! [X: 'ZF_nat_bool_fun_fun$'] : ( X = 'fmb_ZF_nat_bool_fun_fun$_1' ) ).

tff('declare_A_b_b_c_LSCategory_ext_Category_ext$',type,
    'A_b_b_c_LSCategory_ext_Category_ext$': $tType ).

tff('declare_A_b_b_c_LSCategory_ext_Category_ext$1',type,
    'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1': 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('finite_domain_A_b_b_c_LSCategory_ext_Category_ext$',axiom,
    ! [X: 'A_b_b_c_LSCategory_ext_Category_ext$'] : ( X = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ) ).

tff('declare_Nat_set_set_ZF_set_set_fun$',type,
    'Nat_set_set_ZF_set_set_fun$': $tType ).

tff('declare_Nat_set_set_ZF_set_set_fun$1',type,
    'fmb_Nat_set_set_ZF_set_set_fun$_1': 'Nat_set_set_ZF_set_set_fun$' ).

tff('finite_domain_Nat_set_set_ZF_set_set_fun$',axiom,
    ! [X: 'Nat_set_set_ZF_set_set_fun$'] : ( X = 'fmb_Nat_set_set_ZF_set_set_fun$_1' ) ).

tff('declare_ZF_b_set_fun$',type,
    'ZF_b_set_fun$': $tType ).

tff('declare_ZF_b_set_fun$1',type,
    'fmb_ZF_b_set_fun$_1': 'ZF_b_set_fun$' ).

tff('finite_domain_ZF_b_set_fun$',axiom,
    ! [X: 'ZF_b_set_fun$'] : ( X = 'fmb_ZF_b_set_fun$_1' ) ).

tff('declare_Nat_ZF_prod_set$',type,
    'Nat_ZF_prod_set$': $tType ).

tff('declare_Nat_ZF_prod_set$1',type,
    'fmb_Nat_ZF_prod_set$_1': 'Nat_ZF_prod_set$' ).

tff('finite_domain_Nat_ZF_prod_set$',axiom,
    ! [X: 'Nat_ZF_prod_set$'] : ( X = 'fmb_Nat_ZF_prod_set$_1' ) ).

tff('declare_ZF_ZF_prod_set$',type,
    'ZF_ZF_prod_set$': $tType ).

tff('declare_ZF_ZF_prod_set$1',type,
    'fmb_ZF_ZF_prod_set$_1': 'ZF_ZF_prod_set$' ).

tff('finite_domain_ZF_ZF_prod_set$',axiom,
    ! [X: 'ZF_ZF_prod_set$'] : ( X = 'fmb_ZF_ZF_prod_set$_1' ) ).

tff('declare_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$',type,
    'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$1',type,
    'fmb_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_1': 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_set_set_ZF_set_set_fun$',type,
    'ZF_ZF_prod_set_set_ZF_set_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_set_set_ZF_set_set_fun$1',type,
    'fmb_ZF_ZF_prod_set_set_ZF_set_set_fun$_1': 'ZF_ZF_prod_set_set_ZF_set_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_set_set_ZF_set_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_set_set_ZF_set_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_set_set_ZF_set_set_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',type,
    'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$': $tType ).

tff('declare_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$1',type,
    'fmb_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1': 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' ).

tff('finite_domain_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'] : ( X = 'fmb_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1' ) ).

tff('declare_ZF_set_bool_fun_set$',type,
    'ZF_set_bool_fun_set$': $tType ).

tff('declare_ZF_set_bool_fun_set$1',type,
    'fmb_ZF_set_bool_fun_set$_1': 'ZF_set_bool_fun_set$' ).

tff('finite_domain_ZF_set_bool_fun_set$',axiom,
    ! [X: 'ZF_set_bool_fun_set$'] : ( X = 'fmb_ZF_set_bool_fun_set$_1' ) ).

tff('declare_ZF_set_set$',type,
    'ZF_set_set$': $tType ).

tff('declare_ZF_set_set$1',type,
    'fmb_ZF_set_set$_1': 'ZF_set_set$' ).

tff('finite_domain_ZF_set_set$',axiom,
    ! [X: 'ZF_set_set$'] : ( X = 'fmb_ZF_set_set$_1' ) ).

tff('declare_A_bool_fun_set$',type,
    'A_bool_fun_set$': $tType ).

tff('declare_A_bool_fun_set$1',type,
    'fmb_A_bool_fun_set$_1': 'A_bool_fun_set$' ).

tff('finite_domain_A_bool_fun_set$',axiom,
    ! [X: 'A_bool_fun_set$'] : ( X = 'fmb_A_bool_fun_set$_1' ) ).

tff('declare_ZF_set_ZF_set_fun$',type,
    'ZF_set_ZF_set_fun$': $tType ).

tff('declare_ZF_set_ZF_set_fun$1',type,
    'fmb_ZF_set_ZF_set_fun$_1': 'ZF_set_ZF_set_fun$' ).

tff('finite_domain_ZF_set_ZF_set_fun$',axiom,
    ! [X: 'ZF_set_ZF_set_fun$'] : ( X = 'fmb_ZF_set_ZF_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_fun$',type,
    'ZF_ZF_prod_ZF_ZF_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1': 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1' ) ).

tff('declare_ZF_ZF_set_fun$',type,
    'ZF_ZF_set_fun$': $tType ).

tff('declare_ZF_ZF_set_fun$1',type,
    'fmb_ZF_ZF_set_fun$_1': 'ZF_ZF_set_fun$' ).

tff('finite_domain_ZF_ZF_set_fun$',axiom,
    ! [X: 'ZF_ZF_set_fun$'] : ( X = 'fmb_ZF_ZF_set_fun$_1' ) ).

tff('declare_A_b_fun_set$',type,
    'A_b_fun_set$': $tType ).

tff('declare_A_b_fun_set$1',type,
    'fmb_A_b_fun_set$_1': 'A_b_fun_set$' ).

tff('finite_domain_A_b_fun_set$',axiom,
    ! [X: 'A_b_fun_set$'] : ( X = 'fmb_A_b_fun_set$_1' ) ).

tff('declare_ZF_set_ZF_set_prod_set$',type,
    'ZF_set_ZF_set_prod_set$': $tType ).

tff('declare_ZF_set_ZF_set_prod_set$1',type,
    'fmb_ZF_set_ZF_set_prod_set$_1': 'ZF_set_ZF_set_prod_set$' ).

tff('finite_domain_ZF_set_ZF_set_prod_set$',axiom,
    ! [X: 'ZF_set_ZF_set_prod_set$'] : ( X = 'fmb_ZF_set_ZF_set_prod_set$_1' ) ).

tff('declare_ZF_ZF_fun_ZF_set_fun$',type,
    'ZF_ZF_fun_ZF_set_fun$': $tType ).

tff('declare_ZF_ZF_fun_ZF_set_fun$1',type,
    'fmb_ZF_ZF_fun_ZF_set_fun$_1': 'ZF_ZF_fun_ZF_set_fun$' ).

tff('finite_domain_ZF_ZF_fun_ZF_set_fun$',axiom,
    ! [X: 'ZF_ZF_fun_ZF_set_fun$'] : ( X = 'fmb_ZF_ZF_fun_ZF_set_fun$_1' ) ).

tff('declare_Nat_a_fun$',type,
    'Nat_a_fun$': $tType ).

tff('declare_Nat_a_fun$1',type,
    'fmb_Nat_a_fun$_1': 'Nat_a_fun$' ).

tff('finite_domain_Nat_a_fun$',axiom,
    ! [X: 'Nat_a_fun$'] : ( X = 'fmb_Nat_a_fun$_1' ) ).

tff('declare_A_set_set$',type,
    'A_set_set$': $tType ).

tff('declare_A_set_set$1',type,
    'fmb_A_set_set$_1': 'A_set_set$' ).

tff('finite_domain_A_set_set$',axiom,
    ! [X: 'A_set_set$'] : ( X = 'fmb_A_set_set$_1' ) ).

tff('declare_Nat_nat_fun_set$',type,
    'Nat_nat_fun_set$': $tType ).

tff('declare_Nat_nat_fun_set$1',type,
    'fmb_Nat_nat_fun_set$_1': 'Nat_nat_fun_set$' ).

tff('finite_domain_Nat_nat_fun_set$',axiom,
    ! [X: 'Nat_nat_fun_set$'] : ( X = 'fmb_Nat_nat_fun_set$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_fun$',type,
    'ZF_ZF_prod_ZF_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_fun$_1': 'ZF_ZF_prod_ZF_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_fun$_1' ) ).

tff('declare_ZF_nat_ZF_ZF_prod_set_fun_fun$',type,
    'ZF_nat_ZF_ZF_prod_set_fun_fun$': $tType ).

tff('declare_ZF_nat_ZF_ZF_prod_set_fun_fun$1',type,
    'fmb_ZF_nat_ZF_ZF_prod_set_fun_fun$_1': 'ZF_nat_ZF_ZF_prod_set_fun_fun$' ).

tff('finite_domain_ZF_nat_ZF_ZF_prod_set_fun_fun$',axiom,
    ! [X: 'ZF_nat_ZF_ZF_prod_set_fun_fun$'] : ( X = 'fmb_ZF_nat_ZF_ZF_prod_set_fun_fun$_1' ) ).

tff('declare_B_c_LSCategory_ext$',type,
    'B_c_LSCategory_ext$': $tType ).

tff('declare_B_c_LSCategory_ext$1',type,
    'fmb_B_c_LSCategory_ext$_1': 'B_c_LSCategory_ext$' ).

tff('finite_domain_B_c_LSCategory_ext$',axiom,
    ! [X: 'B_c_LSCategory_ext$'] : ( X = 'fmb_B_c_LSCategory_ext$_1' ) ).

tff('declare_Nat_set_set_nat_set_fun$',type,
    'Nat_set_set_nat_set_fun$': $tType ).

tff('declare_Nat_set_set_nat_set_fun$1',type,
    'fmb_Nat_set_set_nat_set_fun$_1': 'Nat_set_set_nat_set_fun$' ).

tff('finite_domain_Nat_set_set_nat_set_fun$',axiom,
    ! [X: 'Nat_set_set_nat_set_fun$'] : ( X = 'fmb_Nat_set_set_nat_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$',type,
    'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$_1': 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',type,
    'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1': 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1' ) ).

tff('declare_B_b_fun$',type,
    'B_b_fun$': $tType ).

tff('declare_B_b_fun$1',type,
    'fmb_B_b_fun$_1': 'B_b_fun$' ).

tff('finite_domain_B_b_fun$',axiom,
    ! [X: 'B_b_fun$'] : ( X = 'fmb_B_b_fun$_1' ) ).

tff('declare_ZF_nat_ZF_set_ZF_set_prod_fun_fun$',type,
    'ZF_nat_ZF_set_ZF_set_prod_fun_fun$': $tType ).

tff('declare_ZF_nat_ZF_set_ZF_set_prod_fun_fun$1',type,
    'fmb_ZF_nat_ZF_set_ZF_set_prod_fun_fun$_1': 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' ).

tff('finite_domain_ZF_nat_ZF_set_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$'] : ( X = 'fmb_ZF_nat_ZF_set_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_ZF_ZF_set_prod_set$',type,
    'ZF_ZF_set_prod_set$': $tType ).

tff('declare_ZF_ZF_set_prod_set$1',type,
    'fmb_ZF_ZF_set_prod_set$_1': 'ZF_ZF_set_prod_set$' ).

tff('finite_domain_ZF_ZF_set_prod_set$',axiom,
    ! [X: 'ZF_ZF_set_prod_set$'] : ( X = 'fmb_ZF_ZF_set_prod_set$_1' ) ).

tff('declare_Nat_ZF_bool_fun_fun$',type,
    'Nat_ZF_bool_fun_fun$': $tType ).

tff('declare_Nat_ZF_bool_fun_fun$1',type,
    'fmb_Nat_ZF_bool_fun_fun$_1': 'Nat_ZF_bool_fun_fun$' ).

tff('finite_domain_Nat_ZF_bool_fun_fun$',axiom,
    ! [X: 'Nat_ZF_bool_fun_fun$'] : ( X = 'fmb_Nat_ZF_bool_fun_fun$_1' ) ).

tff('declare_ZF_nat_prod_ZF_ZF_prod_set_fun$',type,
    'ZF_nat_prod_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_ZF_nat_prod_ZF_ZF_prod_set_fun$1',type,
    'fmb_ZF_nat_prod_ZF_ZF_prod_set_fun$_1': 'ZF_nat_prod_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_ZF_nat_prod_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'ZF_nat_prod_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_ZF_nat_prod_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_set_prod_fun$',type,
    'ZF_ZF_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_ZF_ZF_set_prod_fun$1',type,
    'fmb_ZF_ZF_ZF_set_prod_fun$_1': 'ZF_ZF_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_ZF_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_ZF_ZF_set_prod_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_ZF_prod_fun_fun$',type,
    'ZF_ZF_ZF_ZF_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_ZF_prod_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1': 'ZF_ZF_ZF_ZF_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_ZF_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_ZF_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_prod_set_fun$',type,
    'ZF_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_ZF_ZF_ZF_prod_set_fun$1',type,
    'fmb_ZF_ZF_ZF_prod_set_fun$_1': 'ZF_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_ZF_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_ZF_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_set_fun$',type,
    'ZF_ZF_prod_ZF_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_set_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_set_fun$_1': 'ZF_ZF_prod_ZF_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_set_fun$_1' ) ).

tff('declare_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',type,
    'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).

tff('declare_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$1',type,
    'fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('finite_domain_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',axiom,
    ! [X: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'] : ( X = 'fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1' ) ).

tff('declare_ZF_ZF_prod_nat_set_fun$',type,
    'ZF_ZF_prod_nat_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_nat_set_fun$1',type,
    'fmb_ZF_ZF_prod_nat_set_fun$_1': 'ZF_ZF_prod_nat_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_nat_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_nat_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_nat_set_fun$_1' ) ).

tff('declare_ZF_nat_ZF_set_fun_fun$',type,
    'ZF_nat_ZF_set_fun_fun$': $tType ).

tff('declare_ZF_nat_ZF_set_fun_fun$1',type,
    'fmb_ZF_nat_ZF_set_fun_fun$_1': 'ZF_nat_ZF_set_fun_fun$' ).

tff('finite_domain_ZF_nat_ZF_set_fun_fun$',axiom,
    ! [X: 'ZF_nat_ZF_set_fun_fun$'] : ( X = 'fmb_ZF_nat_ZF_set_fun_fun$_1' ) ).

tff('declare_ZF_ZF_prod$',type,
    'ZF_ZF_prod$': $tType ).

tff('declare_ZF_ZF_prod$1',type,
    'fmb_ZF_ZF_prod$_1': 'ZF_ZF_prod$' ).

tff('finite_domain_ZF_ZF_prod$',axiom,
    ! [X: 'ZF_ZF_prod$'] : ( X = 'fmb_ZF_ZF_prod$_1' ) ).

tff('declare_B_a_set_fun$',type,
    'B_a_set_fun$': $tType ).

tff('declare_B_a_set_fun$1',type,
    'fmb_B_a_set_fun$_1': 'B_a_set_fun$' ).

tff('finite_domain_B_a_set_fun$',axiom,
    ! [X: 'B_a_set_fun$'] : ( X = 'fmb_B_a_set_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',type,
    'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$': $tType ).

tff('declare_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$1',type,
    'fmb_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1': 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' ).

tff('finite_domain_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$'] : ( X = 'fmb_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1' ) ).

tff('declare_B_b_prod_set$',type,
    'B_b_prod_set$': $tType ).

tff('declare_B_b_prod_set$1',type,
    'fmb_B_b_prod_set$_1': 'B_b_prod_set$' ).

tff('finite_domain_B_b_prod_set$',axiom,
    ! [X: 'B_b_prod_set$'] : ( X = 'fmb_B_b_prod_set$_1' ) ).

tff('declare_ZF_ZF_set_set_fun$',type,
    'ZF_ZF_set_set_fun$': $tType ).

tff('declare_ZF_ZF_set_set_fun$1',type,
    'fmb_ZF_ZF_set_set_fun$_1': 'ZF_ZF_set_set_fun$' ).

tff('finite_domain_ZF_ZF_set_set_fun$',axiom,
    ! [X: 'ZF_ZF_set_set_fun$'] : ( X = 'fmb_ZF_ZF_set_set_fun$_1' ) ).

tff('declare_Nat_ZF_set_prod_set$',type,
    'Nat_ZF_set_prod_set$': $tType ).

tff('declare_Nat_ZF_set_prod_set$1',type,
    'fmb_Nat_ZF_set_prod_set$_1': 'Nat_ZF_set_prod_set$' ).

tff('finite_domain_Nat_ZF_set_prod_set$',axiom,
    ! [X: 'Nat_ZF_set_prod_set$'] : ( X = 'fmb_Nat_ZF_set_prod_set$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_set$',type,
    'ZF_ZF_prod_ZF_ZF_prod_prod_set$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_prod_set$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1': 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_prod_prod_set$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_prod_prod_set$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1' ) ).

tff('declare_Nat_nat_prod_set$',type,
    'Nat_nat_prod_set$': $tType ).

tff('declare_Nat_nat_prod_set$1',type,
    'fmb_Nat_nat_prod_set$_1': 'Nat_nat_prod_set$' ).

tff('finite_domain_Nat_nat_prod_set$',axiom,
    ! [X: 'Nat_nat_prod_set$'] : ( X = 'fmb_Nat_nat_prod_set$_1' ) ).

tff('declare_B$',type,
    'B$': $tType ).

tff('declare_B$1',type,
    'fmb_B$_1': 'B$' ).

tff('finite_domain_B$',axiom,
    ! [X: 'B$'] : ( X = 'fmb_B$_1' ) ).

tff('declare_ZF_set_set_bool_fun$',type,
    'ZF_set_set_bool_fun$': $tType ).

tff('declare_ZF_set_set_bool_fun$1',type,
    'fmb_ZF_set_set_bool_fun$_1': 'ZF_set_set_bool_fun$' ).

tff('finite_domain_ZF_set_set_bool_fun$',axiom,
    ! [X: 'ZF_set_set_bool_fun$'] : ( X = 'fmb_ZF_set_set_bool_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_fun_fun$',type,
    'ZF_ZF_ZF_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_fun_fun$_1': 'ZF_ZF_ZF_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_fun_fun$_1' ) ).

tff('declare_A_ZF_set_fun$',type,
    'A_ZF_set_fun$': $tType ).

tff('declare_A_ZF_set_fun$1',type,
    'fmb_A_ZF_set_fun$_1': 'A_ZF_set_fun$' ).

tff('finite_domain_A_ZF_set_fun$',axiom,
    ! [X: 'A_ZF_set_fun$'] : ( X = 'fmb_A_ZF_set_fun$_1' ) ).

tff('declare_B_bool_fun_set$',type,
    'B_bool_fun_set$': $tType ).

tff('declare_B_bool_fun_set$1',type,
    'fmb_B_bool_fun_set$_1': 'B_bool_fun_set$' ).

tff('finite_domain_B_bool_fun_set$',axiom,
    ! [X: 'B_bool_fun_set$'] : ( X = 'fmb_B_bool_fun_set$_1' ) ).

tff('declare_ZF_set_a_fun$',type,
    'ZF_set_a_fun$': $tType ).

tff('declare_ZF_set_a_fun$1',type,
    'fmb_ZF_set_a_fun$_1': 'ZF_set_a_fun$' ).

tff('finite_domain_ZF_set_a_fun$',axiom,
    ! [X: 'ZF_set_a_fun$'] : ( X = 'fmb_ZF_set_a_fun$_1' ) ).

tff('declare_ZF_nat_fun_set$',type,
    'ZF_nat_fun_set$': $tType ).

tff('declare_ZF_nat_fun_set$1',type,
    'fmb_ZF_nat_fun_set$_1': 'ZF_nat_fun_set$' ).

tff('finite_domain_ZF_nat_fun_set$',axiom,
    ! [X: 'ZF_nat_fun_set$'] : ( X = 'fmb_ZF_nat_fun_set$_1' ) ).

tff('declare_B_ZF_set_fun$',type,
    'B_ZF_set_fun$': $tType ).

tff('declare_B_ZF_set_fun$1',type,
    'fmb_B_ZF_set_fun$_1': 'B_ZF_set_fun$' ).

tff('finite_domain_B_ZF_set_fun$',axiom,
    ! [X: 'B_ZF_set_fun$'] : ( X = 'fmb_B_ZF_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$',type,
    'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$1',type,
    'fmb_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_1': 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_set_fun_fun$',type,
    'ZF_ZF_ZF_set_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_set_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_set_fun_fun$_1': 'ZF_ZF_ZF_set_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_set_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_set_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_set_fun_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$',type,
    'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$': $tType ).

tff('declare_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$1',type,
    'fmb_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_1': 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' ).

tff('finite_domain_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$'] : ( X = 'fmb_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_ZF_set_set_ZF_set_bool_fun_fun$',type,
    'ZF_set_set_ZF_set_bool_fun_fun$': $tType ).

tff('declare_ZF_set_set_ZF_set_bool_fun_fun$1',type,
    'fmb_ZF_set_set_ZF_set_bool_fun_fun$_1': 'ZF_set_set_ZF_set_bool_fun_fun$' ).

tff('finite_domain_ZF_set_set_ZF_set_bool_fun_fun$',axiom,
    ! [X: 'ZF_set_set_ZF_set_bool_fun_fun$'] : ( X = 'fmb_ZF_set_set_ZF_set_bool_fun_fun$_1' ) ).

tff('declare_ZF_ZF_set_ZF_set_prod_fun$',type,
    'ZF_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_ZF_ZF_set_ZF_set_prod_fun$_1': 'ZF_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$',type,
    'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$': $tType ).

tff('declare_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$1',type,
    'fmb_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_1': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' ).

tff('finite_domain_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$',axiom,
    ! [X: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] : ( X = 'fmb_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_1' ) ).

tff('declare_Nat_nat_fun$',type,
    'Nat_nat_fun$': $tType ).

tff('declare_Nat_nat_fun$1',type,
    'fmb_Nat_nat_fun$_1': 'Nat_nat_fun$' ).

tff('finite_domain_Nat_nat_fun$',axiom,
    ! [X: 'Nat_nat_fun$'] : ( X = 'fmb_Nat_nat_fun$_1' ) ).

tff('declare_C$',type,
    'C$': $tType ).

tff('declare_C$1',type,
    'fmb_C$_1': 'C$' ).

tff('finite_domain_C$',axiom,
    ! [X: 'C$'] : ( X = 'fmb_C$_1' ) ).

tff('declare_ZF_a_set_fun$',type,
    'ZF_a_set_fun$': $tType ).

tff('declare_ZF_a_set_fun$1',type,
    'fmb_ZF_a_set_fun$_1': 'ZF_a_set_fun$' ).

tff('finite_domain_ZF_a_set_fun$',axiom,
    ! [X: 'ZF_a_set_fun$'] : ( X = 'fmb_ZF_a_set_fun$_1' ) ).

tff('declare_ZF_b_fun$',type,
    'ZF_b_fun$': $tType ).

tff('declare_ZF_b_fun$1',type,
    'fmb_ZF_b_fun$_1': 'ZF_b_fun$' ).

tff('finite_domain_ZF_b_fun$',axiom,
    ! [X: 'ZF_b_fun$'] : ( X = 'fmb_ZF_b_fun$_1' ) ).

tff('declare_ZF_set_set_set_ZF_set_set_fun$',type,
    'ZF_set_set_set_ZF_set_set_fun$': $tType ).

tff('declare_ZF_set_set_set_ZF_set_set_fun$1',type,
    'fmb_ZF_set_set_set_ZF_set_set_fun$_1': 'ZF_set_set_set_ZF_set_set_fun$' ).

tff('finite_domain_ZF_set_set_set_ZF_set_set_fun$',axiom,
    ! [X: 'ZF_set_set_set_ZF_set_set_fun$'] : ( X = 'fmb_ZF_set_set_set_ZF_set_set_fun$_1' ) ).

tff('declare_Nat$',type,
    'Nat$': $tType ).

tff('declare_Nat$1',type,
    'fmb_Nat$_1': 'Nat$' ).

tff('finite_domain_Nat$',axiom,
    ! [X: 'Nat$'] : ( X = 'fmb_Nat$_1' ) ).

tff('declare_Nat_ZF_set_set_fun$',type,
    'Nat_ZF_set_set_fun$': $tType ).

tff('declare_Nat_ZF_set_set_fun$1',type,
    'fmb_Nat_ZF_set_set_fun$_1': 'Nat_ZF_set_set_fun$' ).

tff('finite_domain_Nat_ZF_set_set_fun$',axiom,
    ! [X: 'Nat_ZF_set_set_fun$'] : ( X = 'fmb_Nat_ZF_set_set_fun$_1' ) ).

tff('declare_Nat_set_ZF_set_set_fun$',type,
    'Nat_set_ZF_set_set_fun$': $tType ).

tff('declare_Nat_set_ZF_set_set_fun$1',type,
    'fmb_Nat_set_ZF_set_set_fun$_1': 'Nat_set_ZF_set_set_fun$' ).

tff('finite_domain_Nat_set_ZF_set_set_fun$',axiom,
    ! [X: 'Nat_set_ZF_set_set_fun$'] : ( X = 'fmb_Nat_set_ZF_set_set_fun$_1' ) ).

tff('declare_Nat_nat_prod_ZF_ZF_prod_set_fun$',type,
    'Nat_nat_prod_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_Nat_nat_prod_ZF_ZF_prod_set_fun$1',type,
    'fmb_Nat_nat_prod_ZF_ZF_prod_set_fun$_1': 'Nat_nat_prod_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_Nat_nat_prod_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'Nat_nat_prod_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_Nat_nat_prod_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_B_b_prod_bool_fun$',type,
    'B_b_prod_bool_fun$': $tType ).

tff('declare_B_b_prod_bool_fun$1',type,
    'fmb_B_b_prod_bool_fun$_1': 'B_b_prod_bool_fun$' ).

tff('finite_domain_B_b_prod_bool_fun$',axiom,
    ! [X: 'B_b_prod_bool_fun$'] : ( X = 'fmb_B_b_prod_bool_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_prod_fun$',type,
    'Nat_ZF_ZF_prod_fun$': $tType ).

tff('declare_Nat_ZF_ZF_prod_fun$1',type,
    'fmb_Nat_ZF_ZF_prod_fun$_1': 'Nat_ZF_ZF_prod_fun$' ).

tff('finite_domain_Nat_ZF_ZF_prod_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_prod_fun$'] : ( X = 'fmb_Nat_ZF_ZF_prod_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_fun_set$',type,
    'ZF_ZF_prod_ZF_fun_set$': $tType ).

tff('declare_ZF_ZF_prod_ZF_fun_set$1',type,
    'fmb_ZF_ZF_prod_ZF_fun_set$_1': 'ZF_ZF_prod_ZF_fun_set$' ).

tff('finite_domain_ZF_ZF_prod_ZF_fun_set$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_fun_set$'] : ( X = 'fmb_ZF_ZF_prod_ZF_fun_set$_1' ) ).

tff('declare_ZF_ZF_fun$',type,
    'ZF_ZF_fun$': $tType ).

tff('declare_ZF_ZF_fun$1',type,
    'fmb_ZF_ZF_fun$_1': 'ZF_ZF_fun$' ).

tff('finite_domain_ZF_ZF_fun$',axiom,
    ! [X: 'ZF_ZF_fun$'] : ( X = 'fmb_ZF_ZF_fun$_1' ) ).

tff('declare_ZF_ZF_prod_bool_fun$',type,
    'ZF_ZF_prod_bool_fun$': $tType ).

tff('declare_ZF_ZF_prod_bool_fun$1',type,
    'fmb_ZF_ZF_prod_bool_fun$_1': 'ZF_ZF_prod_bool_fun$' ).

tff('finite_domain_ZF_ZF_prod_bool_fun$',axiom,
    ! [X: 'ZF_ZF_prod_bool_fun$'] : ( X = 'fmb_ZF_ZF_prod_bool_fun$_1' ) ).

tff('declare_ZF_set_set_ZF_set_set_set_fun$',type,
    'ZF_set_set_ZF_set_set_set_fun$': $tType ).

tff('declare_ZF_set_set_ZF_set_set_set_fun$1',type,
    'fmb_ZF_set_set_ZF_set_set_set_fun$_1': 'ZF_set_set_ZF_set_set_set_fun$' ).

tff('finite_domain_ZF_set_set_ZF_set_set_set_fun$',axiom,
    ! [X: 'ZF_set_set_ZF_set_set_set_fun$'] : ( X = 'fmb_ZF_set_set_ZF_set_set_set_fun$_1' ) ).

tff('declare_Nat_set_ZF_set_fun$',type,
    'Nat_set_ZF_set_fun$': $tType ).

tff('declare_Nat_set_ZF_set_fun$1',type,
    'fmb_Nat_set_ZF_set_fun$_1': 'Nat_set_ZF_set_fun$' ).

tff('finite_domain_Nat_set_ZF_set_fun$',axiom,
    ! [X: 'Nat_set_ZF_set_fun$'] : ( X = 'fmb_Nat_set_ZF_set_fun$_1' ) ).

tff('declare_ZF_ZF_fun_set$',type,
    'ZF_ZF_fun_set$': $tType ).

tff('declare_ZF_ZF_fun_set$1',type,
    'fmb_ZF_ZF_fun_set$_1': 'ZF_ZF_fun_set$' ).

tff('finite_domain_ZF_ZF_fun_set$',axiom,
    ! [X: 'ZF_ZF_fun_set$'] : ( X = 'fmb_ZF_ZF_fun_set$_1' ) ).

tff('declare_ZF_ZF_prod_nat_prod_set$',type,
    'ZF_ZF_prod_nat_prod_set$': $tType ).

tff('declare_ZF_ZF_prod_nat_prod_set$1',type,
    'fmb_ZF_ZF_prod_nat_prod_set$_1': 'ZF_ZF_prod_nat_prod_set$' ).

tff('finite_domain_ZF_ZF_prod_nat_prod_set$',axiom,
    ! [X: 'ZF_ZF_prod_nat_prod_set$'] : ( X = 'fmb_ZF_ZF_prod_nat_prod_set$_1' ) ).

tff('declare_B_b_prod_b_fun_set$',type,
    'B_b_prod_b_fun_set$': $tType ).

tff('declare_B_b_prod_b_fun_set$1',type,
    'fmb_B_b_prod_b_fun_set$_1': 'B_b_prod_b_fun_set$' ).

tff('finite_domain_B_b_prod_b_fun_set$',axiom,
    ! [X: 'B_b_prod_b_fun_set$'] : ( X = 'fmb_B_b_prod_b_fun_set$_1' ) ).

tff('declare_Nat_nat_prod_ZF_set_ZF_set_prod_fun$',type,
    'Nat_nat_prod_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_Nat_nat_prod_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_Nat_nat_prod_ZF_set_ZF_set_prod_fun$_1': 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_Nat_nat_prod_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_Nat_nat_prod_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_prod_prod_set$',type,
    'ZF_ZF_ZF_prod_prod_set$': $tType ).

tff('declare_ZF_ZF_ZF_prod_prod_set$1',type,
    'fmb_ZF_ZF_ZF_prod_prod_set$_1': 'ZF_ZF_ZF_prod_prod_set$' ).

tff('finite_domain_ZF_ZF_ZF_prod_prod_set$',axiom,
    ! [X: 'ZF_ZF_ZF_prod_prod_set$'] : ( X = 'fmb_ZF_ZF_ZF_prod_prod_set$_1' ) ).

tff('declare_ZF_set_ZF_prod$',type,
    'ZF_set_ZF_prod$': $tType ).

tff('declare_ZF_set_ZF_prod$1',type,
    'fmb_ZF_set_ZF_prod$_1': 'ZF_set_ZF_prod$' ).

tff('finite_domain_ZF_set_ZF_prod$',axiom,
    ! [X: 'ZF_set_ZF_prod$'] : ( X = 'fmb_ZF_set_ZF_prod$_1' ) ).

tff('declare_Nat_ZF_set_ZF_set_prod_fun$',type,
    'Nat_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_Nat_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_Nat_ZF_set_ZF_set_prod_fun$_1': 'Nat_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_Nat_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'Nat_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_Nat_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_ZF_ZF_prod_set_set$',type,
    'ZF_ZF_prod_set_set$': $tType ).

tff('declare_ZF_ZF_prod_set_set$1',type,
    'fmb_ZF_ZF_prod_set_set$_1': 'ZF_ZF_prod_set_set$' ).

tff('finite_domain_ZF_ZF_prod_set_set$',axiom,
    ! [X: 'ZF_ZF_prod_set_set$'] : ( X = 'fmb_ZF_ZF_prod_set_set$_1' ) ).

tff('declare_B_a_fun$',type,
    'B_a_fun$': $tType ).

tff('declare_B_a_fun$1',type,
    'fmb_B_a_fun$_1': 'B_a_fun$' ).

tff('finite_domain_B_a_fun$',axiom,
    ! [X: 'B_a_fun$'] : ( X = 'fmb_B_a_fun$_1' ) ).

tff('declare_ZF_a_fun$',type,
    'ZF_a_fun$': $tType ).

tff('declare_ZF_a_fun$1',type,
    'fmb_ZF_a_fun$_1': 'ZF_a_fun$' ).

tff('finite_domain_ZF_a_fun$',axiom,
    ! [X: 'ZF_a_fun$'] : ( X = 'fmb_ZF_a_fun$_1' ) ).

tff('declare_ZF_ZF_set_prod$',type,
    'ZF_ZF_set_prod$': $tType ).

tff('declare_ZF_ZF_set_prod$1',type,
    'fmb_ZF_ZF_set_prod$_1': 'ZF_ZF_set_prod$' ).

tff('finite_domain_ZF_ZF_set_prod$',axiom,
    ! [X: 'ZF_ZF_set_prod$'] : ( X = 'fmb_ZF_ZF_set_prod$_1' ) ).

tff('declare_Nat_ZF_set_fun$',type,
    'Nat_ZF_set_fun$': $tType ).

tff('declare_Nat_ZF_set_fun$1',type,
    'fmb_Nat_ZF_set_fun$_1': 'Nat_ZF_set_fun$' ).

tff('finite_domain_Nat_ZF_set_fun$',axiom,
    ! [X: 'Nat_ZF_set_fun$'] : ( X = 'fmb_Nat_ZF_set_fun$_1' ) ).

tff(declare_tlbool,type,
    tlbool: $tType ).

tff(declare_tlbool1,type,
    fmb_tlbool_1: tlbool ).

tff(declare_tlbool2,type,
    fmb_tlbool_2: tlbool ).

tff(finite_domain_tlbool,axiom,
    ! [X: tlbool] :
      ( ( X = fmb_tlbool_1 )
      | ( X = fmb_tlbool_2 ) ) ).

tff(distinct_domain_tlbool,axiom,
    fmb_tlbool_1 != fmb_tlbool_2 ).

tff('declare_ZF_nat_prod_set$',type,
    'ZF_nat_prod_set$': $tType ).

tff('declare_ZF_nat_prod_set$1',type,
    'fmb_ZF_nat_prod_set$_1': 'ZF_nat_prod_set$' ).

tff('finite_domain_ZF_nat_prod_set$',axiom,
    ! [X: 'ZF_nat_prod_set$'] : ( X = 'fmb_ZF_nat_prod_set$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$',type,
    'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$_1': 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_B_b_prod$',type,
    'B_b_prod$': $tType ).

tff('declare_B_b_prod$1',type,
    'fmb_B_b_prod$_1': 'B_b_prod$' ).

tff('finite_domain_B_b_prod$',axiom,
    ! [X: 'B_b_prod$'] : ( X = 'fmb_B_b_prod$_1' ) ).

tff('declare_ZF_set_set_ZF_set_fun$',type,
    'ZF_set_set_ZF_set_fun$': $tType ).

tff('declare_ZF_set_set_ZF_set_fun$1',type,
    'fmb_ZF_set_set_ZF_set_fun$_1': 'ZF_set_set_ZF_set_fun$' ).

tff('finite_domain_ZF_set_set_ZF_set_fun$',axiom,
    ! [X: 'ZF_set_set_ZF_set_fun$'] : ( X = 'fmb_ZF_set_set_ZF_set_fun$_1' ) ).

tff('declare_ZF_ZF_fun_ZF_ZF_fun_fun$',type,
    'ZF_ZF_fun_ZF_ZF_fun_fun$': $tType ).

tff('declare_ZF_ZF_fun_ZF_ZF_fun_fun$1',type,
    'fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1': 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).

tff('finite_domain_ZF_ZF_fun_ZF_ZF_fun_fun$',axiom,
    ! [X: 'ZF_ZF_fun_ZF_ZF_fun_fun$'] : ( X = 'fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1' ) ).

tff('declare_A_set_a_bool_fun_fun$',type,
    'A_set_a_bool_fun_fun$': $tType ).

tff('declare_A_set_a_bool_fun_fun$1',type,
    'fmb_A_set_a_bool_fun_fun$_1': 'A_set_a_bool_fun_fun$' ).

tff('finite_domain_A_set_a_bool_fun_fun$',axiom,
    ! [X: 'A_set_a_bool_fun_fun$'] : ( X = 'fmb_A_set_a_bool_fun_fun$_1' ) ).

tff('declare_Nat_ZF_prod_ZF_ZF_prod_set_fun$',type,
    'Nat_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_Nat_ZF_prod_ZF_ZF_prod_set_fun$1',type,
    'fmb_Nat_ZF_prod_ZF_ZF_prod_set_fun$_1': 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_Nat_ZF_prod_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'Nat_ZF_prod_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_Nat_ZF_prod_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_A_bool_fun$',type,
    'A_bool_fun$': $tType ).

tff('declare_A_bool_fun$1',type,
    'fmb_A_bool_fun$_1': 'A_bool_fun$' ).

tff('finite_domain_A_bool_fun$',axiom,
    ! [X: 'A_bool_fun$'] : ( X = 'fmb_A_bool_fun$_1' ) ).

tff('declare_ZF_nat_fun_ZF_set_fun$',type,
    'ZF_nat_fun_ZF_set_fun$': $tType ).

tff('declare_ZF_nat_fun_ZF_set_fun$1',type,
    'fmb_ZF_nat_fun_ZF_set_fun$_1': 'ZF_nat_fun_ZF_set_fun$' ).

tff('finite_domain_ZF_nat_fun_ZF_set_fun$',axiom,
    ! [X: 'ZF_nat_fun_ZF_set_fun$'] : ( X = 'fmb_ZF_nat_fun_ZF_set_fun$_1' ) ).

tff('declare_A_set$',type,
    'A_set$': $tType ).

tff('declare_A_set$1',type,
    'fmb_A_set$_1': 'A_set$' ).

tff('finite_domain_A_set$',axiom,
    ! [X: 'A_set$'] : ( X = 'fmb_A_set$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$',type,
    'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_1': 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_1' ) ).

tff('declare_A_a_set_fun$',type,
    'A_a_set_fun$': $tType ).

tff('declare_A_a_set_fun$1',type,
    'fmb_A_a_set_fun$_1': 'A_a_set_fun$' ).

tff('finite_domain_A_a_set_fun$',axiom,
    ! [X: 'A_a_set_fun$'] : ( X = 'fmb_A_a_set_fun$_1' ) ).

tff('declare_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',type,
    'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).

tff('declare_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$1',type,
    'fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('finite_domain_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',axiom,
    ! [X: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] : ( X = 'fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1' ) ).

tff('declare_ZF_set_ZF_set_set_fun$',type,
    'ZF_set_ZF_set_set_fun$': $tType ).

tff('declare_ZF_set_ZF_set_set_fun$1',type,
    'fmb_ZF_set_ZF_set_set_fun$_1': 'ZF_set_ZF_set_set_fun$' ).

tff('finite_domain_ZF_set_ZF_set_set_fun$',axiom,
    ! [X: 'ZF_set_ZF_set_set_fun$'] : ( X = 'fmb_ZF_set_ZF_set_set_fun$_1' ) ).

tff('declare_Nat_nat_set_fun$',type,
    'Nat_nat_set_fun$': $tType ).

tff('declare_Nat_nat_set_fun$1',type,
    'fmb_Nat_nat_set_fun$_1': 'Nat_nat_set_fun$' ).

tff('finite_domain_Nat_nat_set_fun$',axiom,
    ! [X: 'Nat_nat_set_fun$'] : ( X = 'fmb_Nat_nat_set_fun$_1' ) ).

tff('declare_A_b_fun$',type,
    'A_b_fun$': $tType ).

tff('declare_A_b_fun$1',type,
    'fmb_A_b_fun$_1': 'A_b_fun$' ).

tff('finite_domain_A_b_fun$',axiom,
    ! [X: 'A_b_fun$'] : ( X = 'fmb_A_b_fun$_1' ) ).

tff('declare_ZF_nat_prod_ZF_set_ZF_set_prod_fun$',type,
    'ZF_nat_prod_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_nat_prod_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_ZF_nat_prod_ZF_set_ZF_set_prod_fun$_1': 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_nat_prod_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_nat_prod_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_ZF_prod_set_fun_fun$',type,
    'ZF_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_ZF_prod_set_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_ZF_prod_set_fun_fun$_1': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_ZF_prod_set_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_ZF_prod_set_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_ZF_prod_set_fun_fun$_1' ) ).

tff('declare_B_set$',type,
    'B_set$': $tType ).

tff('declare_B_set$1',type,
    'fmb_B_set$_1': 'B_set$' ).

tff('finite_domain_B_set$',axiom,
    ! [X: 'B_set$'] : ( X = 'fmb_B_set$_1' ) ).

tff('declare_Nat_nat_ZF_ZF_prod_set_fun_fun$',type,
    'Nat_nat_ZF_ZF_prod_set_fun_fun$': $tType ).

tff('declare_Nat_nat_ZF_ZF_prod_set_fun_fun$1',type,
    'fmb_Nat_nat_ZF_ZF_prod_set_fun_fun$_1': 'Nat_nat_ZF_ZF_prod_set_fun_fun$' ).

tff('finite_domain_Nat_nat_ZF_ZF_prod_set_fun_fun$',axiom,
    ! [X: 'Nat_nat_ZF_ZF_prod_set_fun_fun$'] : ( X = 'fmb_Nat_nat_ZF_ZF_prod_set_fun_fun$_1' ) ).

tff('declare_A_b_fun_bool_fun$',type,
    'A_b_fun_bool_fun$': $tType ).

tff('declare_A_b_fun_bool_fun$1',type,
    'fmb_A_b_fun_bool_fun$_1': 'A_b_fun_bool_fun$' ).

tff('finite_domain_A_b_fun_bool_fun$',axiom,
    ! [X: 'A_b_fun_bool_fun$'] : ( X = 'fmb_A_b_fun_bool_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_prod_set_fun$',type,
    'Nat_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_Nat_ZF_ZF_prod_set_fun$1',type,
    'fmb_Nat_ZF_ZF_prod_set_fun$_1': 'Nat_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_Nat_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_Nat_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_A$',type,
    'A$': $tType ).

tff('declare_A$1',type,
    'fmb_A$_1': 'A$' ).

tff('finite_domain_A$',axiom,
    ! [X: 'A$'] : ( X = 'fmb_A$_1' ) ).

tff('declare_B_set_b_bool_fun_fun$',type,
    'B_set_b_bool_fun_fun$': $tType ).

tff('declare_B_set_b_bool_fun_fun$1',type,
    'fmb_B_set_b_bool_fun_fun$_1': 'B_set_b_bool_fun_fun$' ).

tff('finite_domain_B_set_b_bool_fun_fun$',axiom,
    ! [X: 'B_set_b_bool_fun_fun$'] : ( X = 'fmb_B_set_b_bool_fun_fun$_1' ) ).

tff('declare_ZF_ZF_unit_Category_ext$',type,
    'ZF_ZF_unit_Category_ext$': $tType ).

tff('declare_ZF_ZF_unit_Category_ext$1',type,
    'fmb_ZF_ZF_unit_Category_ext$_1': 'ZF_ZF_unit_Category_ext$' ).

tff('finite_domain_ZF_ZF_unit_Category_ext$',axiom,
    ! [X: 'ZF_ZF_unit_Category_ext$'] : ( X = 'fmb_ZF_ZF_unit_Category_ext$_1' ) ).

tff('declare_ZF_set_ZF_bool_fun_fun$',type,
    'ZF_set_ZF_bool_fun_fun$': $tType ).

tff('declare_ZF_set_ZF_bool_fun_fun$1',type,
    'fmb_ZF_set_ZF_bool_fun_fun$_1': 'ZF_set_ZF_bool_fun_fun$' ).

tff('finite_domain_ZF_set_ZF_bool_fun_fun$',axiom,
    ! [X: 'ZF_set_ZF_bool_fun_fun$'] : ( X = 'fmb_ZF_set_ZF_bool_fun_fun$_1' ) ).

tff('declare_ZF_ZF_fun_bool_fun$',type,
    'ZF_ZF_fun_bool_fun$': $tType ).

tff('declare_ZF_ZF_fun_bool_fun$1',type,
    'fmb_ZF_ZF_fun_bool_fun$_1': 'ZF_ZF_fun_bool_fun$' ).

tff('finite_domain_ZF_ZF_fun_bool_fun$',axiom,
    ! [X: 'ZF_ZF_fun_bool_fun$'] : ( X = 'fmb_ZF_ZF_fun_bool_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$',type,
    'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_1': 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_1' ) ).

tff('declare_Nat_nat_ZF_set_fun_fun$',type,
    'Nat_nat_ZF_set_fun_fun$': $tType ).

tff('declare_Nat_nat_ZF_set_fun_fun$1',type,
    'fmb_Nat_nat_ZF_set_fun_fun$_1': 'Nat_nat_ZF_set_fun_fun$' ).

tff('finite_domain_Nat_nat_ZF_set_fun_fun$',axiom,
    ! [X: 'Nat_nat_ZF_set_fun_fun$'] : ( X = 'fmb_Nat_nat_ZF_set_fun_fun$_1' ) ).

tff('declare_ZF_ZF_prod_set_ZF_set_fun$',type,
    'ZF_ZF_prod_set_ZF_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_set_ZF_set_fun$1',type,
    'fmb_ZF_ZF_prod_set_ZF_set_fun$_1': 'ZF_ZF_prod_set_ZF_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_set_ZF_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_set_ZF_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_set_ZF_set_fun$_1' ) ).

tff('declare_B_set_bool_fun$',type,
    'B_set_bool_fun$': $tType ).

tff('declare_B_set_bool_fun$1',type,
    'fmb_B_set_bool_fun$_1': 'B_set_bool_fun$' ).

tff('finite_domain_B_set_bool_fun$',axiom,
    ! [X: 'B_set_bool_fun$'] : ( X = 'fmb_B_set_bool_fun$_1' ) ).

tff('declare_A_b_set_fun$',type,
    'A_b_set_fun$': $tType ).

tff('declare_A_b_set_fun$1',type,
    'fmb_A_b_set_fun$_1': 'A_b_set_fun$' ).

tff('finite_domain_A_b_set_fun$',axiom,
    ! [X: 'A_b_set_fun$'] : ( X = 'fmb_A_b_set_fun$_1' ) ).

tff('declare_Nat_b_fun$',type,
    'Nat_b_fun$': $tType ).

tff('declare_Nat_b_fun$1',type,
    'fmb_Nat_b_fun$_1': 'Nat_b_fun$' ).

tff('finite_domain_Nat_b_fun$',axiom,
    ! [X: 'Nat_b_fun$'] : ( X = 'fmb_Nat_b_fun$_1' ) ).

tff('declare_ZF_set_ZF_prod_set$',type,
    'ZF_set_ZF_prod_set$': $tType ).

tff('declare_ZF_set_ZF_prod_set$1',type,
    'fmb_ZF_set_ZF_prod_set$_1': 'ZF_set_ZF_prod_set$' ).

tff('finite_domain_ZF_set_ZF_prod_set$',axiom,
    ! [X: 'ZF_set_ZF_prod_set$'] : ( X = 'fmb_ZF_set_ZF_prod_set$_1' ) ).

tff('declare_B_set_set$',type,
    'B_set_set$': $tType ).

tff('declare_B_set_set$1',type,
    'fmb_B_set_set$_1': 'B_set_set$' ).

tff('finite_domain_B_set_set$',axiom,
    ! [X: 'B_set_set$'] : ( X = 'fmb_B_set_set$_1' ) ).

tff('declare_ZF_set_ZF_set_prod$',type,
    'ZF_set_ZF_set_prod$': $tType ).

tff('declare_ZF_set_ZF_set_prod$1',type,
    'fmb_ZF_set_ZF_set_prod$_1': 'ZF_set_ZF_set_prod$' ).

tff('finite_domain_ZF_set_ZF_set_prod$',axiom,
    ! [X: 'ZF_set_ZF_set_prod$'] : ( X = 'fmb_ZF_set_ZF_set_prod$_1' ) ).

tff('declare_Nat_ZF_ZF_set_prod_fun$',type,
    'Nat_ZF_ZF_set_prod_fun$': $tType ).

tff('declare_Nat_ZF_ZF_set_prod_fun$1',type,
    'fmb_Nat_ZF_ZF_set_prod_fun$_1': 'Nat_ZF_ZF_set_prod_fun$' ).

tff('finite_domain_Nat_ZF_ZF_set_prod_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_set_prod_fun$'] : ( X = 'fmb_Nat_ZF_ZF_set_prod_fun$_1' ) ).

tff('declare_B_b_prod_b_fun$',type,
    'B_b_prod_b_fun$': $tType ).

tff('declare_B_b_prod_b_fun$1',type,
    'fmb_B_b_prod_b_fun$_1': 'B_b_prod_b_fun$' ).

tff('finite_domain_B_b_prod_b_fun$',axiom,
    ! [X: 'B_b_prod_b_fun$'] : ( X = 'fmb_B_b_prod_b_fun$_1' ) ).

tff('declare_ZF_set_ZF_fun$',type,
    'ZF_set_ZF_fun$': $tType ).

tff('declare_ZF_set_ZF_fun$1',type,
    'fmb_ZF_set_ZF_fun$_1': 'ZF_set_ZF_fun$' ).

tff('finite_domain_ZF_set_ZF_fun$',axiom,
    ! [X: 'ZF_set_ZF_fun$'] : ( X = 'fmb_ZF_set_ZF_fun$_1' ) ).

tff('declare_B_set_b_set_fun$',type,
    'B_set_b_set_fun$': $tType ).

tff('declare_B_set_b_set_fun$1',type,
    'fmb_B_set_b_set_fun$_1': 'B_set_b_set_fun$' ).

tff('finite_domain_B_set_b_set_fun$',axiom,
    ! [X: 'B_set_b_set_fun$'] : ( X = 'fmb_B_set_b_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_set_set_ZF_set_fun$',type,
    'ZF_ZF_prod_set_set_ZF_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_set_set_ZF_set_fun$1',type,
    'fmb_ZF_ZF_prod_set_set_ZF_set_fun$_1': 'ZF_ZF_prod_set_set_ZF_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_set_set_ZF_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_set_set_ZF_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_set_set_ZF_set_fun$_1' ) ).

tff('declare_B_a_fun_b_a_fun_fun$',type,
    'B_a_fun_b_a_fun_fun$': $tType ).

tff('declare_B_a_fun_b_a_fun_fun$1',type,
    'fmb_B_a_fun_b_a_fun_fun$_1': 'B_a_fun_b_a_fun_fun$' ).

tff('finite_domain_B_a_fun_b_a_fun_fun$',axiom,
    ! [X: 'B_a_fun_b_a_fun_fun$'] : ( X = 'fmb_B_a_fun_b_a_fun_fun$_1' ) ).

tff('declare_A_a_fun$',type,
    'A_a_fun$': $tType ).

tff('declare_A_a_fun$1',type,
    'fmb_A_a_fun$_1': 'A_a_fun$' ).

tff('finite_domain_A_a_fun$',axiom,
    ! [X: 'A_a_fun$'] : ( X = 'fmb_A_a_fun$_1' ) ).

tff('declare_ZF_bool_fun$',type,
    'ZF_bool_fun$': $tType ).

tff('declare_ZF_bool_fun$1',type,
    'fmb_ZF_bool_fun$_1': 'ZF_bool_fun$' ).

tff('finite_domain_ZF_bool_fun$',axiom,
    ! [X: 'ZF_bool_fun$'] : ( X = 'fmb_ZF_bool_fun$_1' ) ).

tff('declare_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$',type,
    'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$': $tType ).

tff('declare_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$1',type,
    'fmb_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$_1': 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$' ).

tff('finite_domain_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$',axiom,
    ! [X: 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$'] : ( X = 'fmb_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$_1' ) ).

tff('declare_B_b_b_fun_fun$',type,
    'B_b_b_fun_fun$': $tType ).

tff('declare_B_b_b_fun_fun$1',type,
    'fmb_B_b_b_fun_fun$_1': 'B_b_b_fun_fun$' ).

tff('finite_domain_B_b_b_fun_fun$',axiom,
    ! [X: 'B_b_b_fun_fun$'] : ( X = 'fmb_B_b_b_fun_fun$_1' ) ).

tff('declare_ZF_set_set_ZF_set_set_fun$',type,
    'ZF_set_set_ZF_set_set_fun$': $tType ).

tff('declare_ZF_set_set_ZF_set_set_fun$1',type,
    'fmb_ZF_set_set_ZF_set_set_fun$_1': 'ZF_set_set_ZF_set_set_fun$' ).

tff('finite_domain_ZF_set_set_ZF_set_set_fun$',axiom,
    ! [X: 'ZF_set_set_ZF_set_set_fun$'] : ( X = 'fmb_ZF_set_set_ZF_set_set_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$',type,
    'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$_1': 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$_1' ) ).

tff('declare_Nat_set_set_ZF_set_set_set_fun$',type,
    'Nat_set_set_ZF_set_set_set_fun$': $tType ).

tff('declare_Nat_set_set_ZF_set_set_set_fun$1',type,
    'fmb_Nat_set_set_ZF_set_set_set_fun$_1': 'Nat_set_set_ZF_set_set_set_fun$' ).

tff('finite_domain_Nat_set_set_ZF_set_set_set_fun$',axiom,
    ! [X: 'Nat_set_set_ZF_set_set_set_fun$'] : ( X = 'fmb_Nat_set_set_ZF_set_set_set_fun$_1' ) ).

tff('declare_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$',type,
    'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$': $tType ).

tff('declare_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$1',type,
    'fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' ).

tff('finite_domain_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$',axiom,
    ! [X: 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$'] : ( X = 'fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1' ) ).

tff('declare_ZF_nat_fun$',type,
    'ZF_nat_fun$': $tType ).

tff('declare_ZF_nat_fun$1',type,
    'fmb_ZF_nat_fun$_1': 'ZF_nat_fun$' ).

tff('finite_domain_ZF_nat_fun$',axiom,
    ! [X: 'ZF_nat_fun$'] : ( X = 'fmb_ZF_nat_fun$_1' ) ).

tff('declare_A_ZF_fun$',type,
    'A_ZF_fun$': $tType ).

tff('declare_A_ZF_fun$1',type,
    'fmb_A_ZF_fun$_1': 'A_ZF_fun$' ).

tff('finite_domain_A_ZF_fun$',axiom,
    ! [X: 'A_ZF_fun$'] : ( X = 'fmb_A_ZF_fun$_1' ) ).

tff('declare_A_set_a_set_fun$',type,
    'A_set_a_set_fun$': $tType ).

tff('declare_A_set_a_set_fun$1',type,
    'fmb_A_set_a_set_fun$_1': 'A_set_a_set_fun$' ).

tff('finite_domain_A_set_a_set_fun$',axiom,
    ! [X: 'A_set_a_set_fun$'] : ( X = 'fmb_A_set_a_set_fun$_1' ) ).

tff('declare_ZF_set_bool_fun$',type,
    'ZF_set_bool_fun$': $tType ).

tff('declare_ZF_set_bool_fun$1',type,
    'fmb_ZF_set_bool_fun$_1': 'ZF_set_bool_fun$' ).

tff('finite_domain_ZF_set_bool_fun$',axiom,
    ! [X: 'ZF_set_bool_fun$'] : ( X = 'fmb_ZF_set_bool_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_prod_set$',type,
    'ZF_ZF_prod_ZF_prod_set$': $tType ).

tff('declare_ZF_ZF_prod_ZF_prod_set$1',type,
    'fmb_ZF_ZF_prod_ZF_prod_set$_1': 'ZF_ZF_prod_ZF_prod_set$' ).

tff('finite_domain_ZF_ZF_prod_ZF_prod_set$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_prod_set$'] : ( X = 'fmb_ZF_ZF_prod_ZF_prod_set$_1' ) ).

tff('declare_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$',type,
    'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$1',type,
    'fmb_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$_1': 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$_1' ) ).

tff('declare_Unit$',type,
    'Unit$': $tType ).

tff('declare_Unit$1',type,
    'fmb_Unit$_1': 'Unit$' ).

tff('finite_domain_Unit$',axiom,
    ! [X: 'Unit$'] : ( X = 'fmb_Unit$_1' ) ).

tff('declare_Nat_bool_fun$',type,
    'Nat_bool_fun$': $tType ).

tff('declare_Nat_bool_fun$1',type,
    'fmb_Nat_bool_fun$_1': 'Nat_bool_fun$' ).

tff('finite_domain_Nat_bool_fun$',axiom,
    ! [X: 'Nat_bool_fun$'] : ( X = 'fmb_Nat_bool_fun$_1' ) ).

tff('declare_Bool_set$',type,
    'Bool_set$': $tType ).

tff('declare_Bool_set$1',type,
    'fmb_Bool_set$_1': 'Bool_set$' ).

tff('finite_domain_Bool_set$',axiom,
    ! [X: 'Bool_set$'] : ( X = 'fmb_Bool_set$_1' ) ).

tff('declare_ZF$',type,
    'ZF$': $tType ).

tff('declare_ZF$1',type,
    'fmb_ZF$_1': 'ZF$' ).

tff('finite_domain_ZF$',axiom,
    ! [X: 'ZF$'] : ( X = 'fmb_ZF$_1' ) ).

tff('declare_B_ZF_fun$',type,
    'B_ZF_fun$': $tType ).

tff('declare_B_ZF_fun$1',type,
    'fmb_B_ZF_fun$_1': 'B_ZF_fun$' ).

tff('finite_domain_B_ZF_fun$',axiom,
    ! [X: 'B_ZF_fun$'] : ( X = 'fmb_B_ZF_fun$_1' ) ).

tff('declare_ZF_set_set_set$',type,
    'ZF_set_set_set$': $tType ).

tff('declare_ZF_set_set_set$1',type,
    'fmb_ZF_set_set_set$_1': 'ZF_set_set_set$' ).

tff('finite_domain_ZF_set_set_set$',axiom,
    ! [X: 'ZF_set_set_set$'] : ( X = 'fmb_ZF_set_set_set$_1' ) ).

tff('declare_ZF_set_ZF_ZF_prod_set_fun$',type,
    'ZF_set_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_ZF_set_ZF_ZF_prod_set_fun$1',type,
    'fmb_ZF_set_ZF_ZF_prod_set_fun$_1': 'ZF_set_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_ZF_set_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'ZF_set_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_ZF_set_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_B_a_fun_set$',type,
    'B_a_fun_set$': $tType ).

tff('declare_B_a_fun_set$1',type,
    'fmb_B_a_fun_set$_1': 'B_a_fun_set$' ).

tff('finite_domain_B_a_fun_set$',axiom,
    ! [X: 'B_a_fun_set$'] : ( X = 'fmb_B_a_fun_set$_1' ) ).

tff('declare_Nat_ZF_fun_ZF_set_fun$',type,
    'Nat_ZF_fun_ZF_set_fun$': $tType ).

tff('declare_Nat_ZF_fun_ZF_set_fun$1',type,
    'fmb_Nat_ZF_fun_ZF_set_fun$_1': 'Nat_ZF_fun_ZF_set_fun$' ).

tff('finite_domain_Nat_ZF_fun_ZF_set_fun$',axiom,
    ! [X: 'Nat_ZF_fun_ZF_set_fun$'] : ( X = 'fmb_Nat_ZF_fun_ZF_set_fun$_1' ) ).

tff('declare_Nat_set$',type,
    'Nat_set$': $tType ).

tff('declare_Nat_set$1',type,
    'fmb_Nat_set$_1': 'Nat_set$' ).

tff('finite_domain_Nat_set$',axiom,
    ! [X: 'Nat_set$'] : ( X = 'fmb_Nat_set$_1' ) ).

tff('declare_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',type,
    'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$': $tType ).

tff('declare_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$1',type,
    'fmb_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1': 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' ).

tff('finite_domain_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$'] : ( X = 'fmb_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1' ) ).

tff('declare_ZF_bool_fun_set$',type,
    'ZF_bool_fun_set$': $tType ).

tff('declare_ZF_bool_fun_set$1',type,
    'fmb_ZF_bool_fun_set$_1': 'ZF_bool_fun_set$' ).

tff('finite_domain_ZF_bool_fun_set$',axiom,
    ! [X: 'ZF_bool_fun_set$'] : ( X = 'fmb_ZF_bool_fun_set$_1' ) ).

tff('declare_Nat_ZF_fun$',type,
    'Nat_ZF_fun$': $tType ).

tff('declare_Nat_ZF_fun$1',type,
    'fmb_Nat_ZF_fun$_1': 'Nat_ZF_fun$' ).

tff('finite_domain_Nat_ZF_fun$',axiom,
    ! [X: 'Nat_ZF_fun$'] : ( X = 'fmb_Nat_ZF_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_set_fun$',type,
    'ZF_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_ZF_prod_set_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1': 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_ZF_prod_set_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_ZF_prod_set_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1' ) ).

tff('declare_B_a_fun_bool_fun$',type,
    'B_a_fun_bool_fun$': $tType ).

tff('declare_B_a_fun_bool_fun$1',type,
    'fmb_B_a_fun_bool_fun$_1': 'B_a_fun_bool_fun$' ).

tff('finite_domain_B_a_fun_bool_fun$',axiom,
    ! [X: 'B_a_fun_bool_fun$'] : ( X = 'fmb_B_a_fun_bool_fun$_1' ) ).

tff('declare_B_bool_fun$',type,
    'B_bool_fun$': $tType ).

tff('declare_B_bool_fun$1',type,
    'fmb_B_bool_fun$_1': 'B_bool_fun$' ).

tff('finite_domain_B_bool_fun$',axiom,
    ! [X: 'B_bool_fun$'] : ( X = 'fmb_B_bool_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_ZF_prod_set_fun_fun$',type,
    'Nat_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).

tff('declare_Nat_ZF_ZF_ZF_prod_set_fun_fun$1',type,
    'fmb_Nat_ZF_ZF_ZF_prod_set_fun_fun$_1': 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff('finite_domain_Nat_ZF_ZF_ZF_prod_set_fun_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_ZF_prod_set_fun_fun$'] : ( X = 'fmb_Nat_ZF_ZF_ZF_prod_set_fun_fun$_1' ) ).

tff('declare_Nat_ZF_ZF_set_fun_fun$',type,
    'Nat_ZF_ZF_set_fun_fun$': $tType ).

tff('declare_Nat_ZF_ZF_set_fun_fun$1',type,
    'fmb_Nat_ZF_ZF_set_fun_fun$_1': 'Nat_ZF_ZF_set_fun_fun$' ).

tff('finite_domain_Nat_ZF_ZF_set_fun_fun$',axiom,
    ! [X: 'Nat_ZF_ZF_set_fun_fun$'] : ( X = 'fmb_Nat_ZF_ZF_set_fun_fun$_1' ) ).

tff('declare_B_b_set_fun$',type,
    'B_b_set_fun$': $tType ).

tff('declare_B_b_set_fun$1',type,
    'fmb_B_b_set_fun$_1': 'B_b_set_fun$' ).

tff('finite_domain_B_b_set_fun$',axiom,
    ! [X: 'B_b_set_fun$'] : ( X = 'fmb_B_b_set_fun$_1' ) ).

tff('declare_A_set_bool_fun$',type,
    'A_set_bool_fun$': $tType ).

tff('declare_A_set_bool_fun$1',type,
    'fmb_A_set_bool_fun$_1': 'A_set_bool_fun$' ).

tff('finite_domain_A_set_bool_fun$',axiom,
    ! [X: 'A_set_bool_fun$'] : ( X = 'fmb_A_set_bool_fun$_1' ) ).

tff('declare_ZF_ZF_prod_ZF_set_ZF_prod_fun$',type,
    'ZF_ZF_prod_ZF_set_ZF_prod_fun$': $tType ).

tff('declare_ZF_ZF_prod_ZF_set_ZF_prod_fun$1',type,
    'fmb_ZF_ZF_prod_ZF_set_ZF_prod_fun$_1': 'ZF_ZF_prod_ZF_set_ZF_prod_fun$' ).

tff('finite_domain_ZF_ZF_prod_ZF_set_ZF_prod_fun$',axiom,
    ! [X: 'ZF_ZF_prod_ZF_set_ZF_prod_fun$'] : ( X = 'fmb_ZF_ZF_prod_ZF_set_ZF_prod_fun$_1' ) ).

tff('declare_B_ZF_fun_bool_fun$',type,
    'B_ZF_fun_bool_fun$': $tType ).

tff('declare_B_ZF_fun_bool_fun$1',type,
    'fmb_B_ZF_fun_bool_fun$_1': 'B_ZF_fun_bool_fun$' ).

tff('finite_domain_B_ZF_fun_bool_fun$',axiom,
    ! [X: 'B_ZF_fun_bool_fun$'] : ( X = 'fmb_B_ZF_fun_bool_fun$_1' ) ).

tff('declare_ZF_ZF_bool_fun_fun$',type,
    'ZF_ZF_bool_fun_fun$': $tType ).

tff('declare_ZF_ZF_bool_fun_fun$1',type,
    'fmb_ZF_ZF_bool_fun_fun$_1': 'ZF_ZF_bool_fun_fun$' ).

tff('finite_domain_ZF_ZF_bool_fun_fun$',axiom,
    ! [X: 'ZF_ZF_bool_fun_fun$'] : ( X = 'fmb_ZF_ZF_bool_fun_fun$_1' ) ).

tff('declare_sup$',type,
    'sup$': 'ZF_set_set_ZF_set_fun$' ).

tff('sup$_definition',axiom,
    'sup$' = 'fmb_ZF_set_set_ZF_set_fun$_1' ).

tff('declare_sup$d',type,
    'sup$d': 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' ).

tff('sup$d_definition',axiom,
    'sup$d' = 'fmb_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_1' ).

tff('declare_uxj$',type,
    'uxj$': 'ZF_ZF_ZF_ZF_prod_fun_fun$' ).

tff('uxj$_definition',axiom,
    'uxj$' = 'fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1' ).

tff('declare_c$',type,
    'c$': 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('c$_definition',axiom,
    'c$' = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_uua$',type,
    'uua$': 'B_set_b_bool_fun_fun$' ).

tff('uua$_definition',axiom,
    'uua$' = 'fmb_B_set_b_bool_fun_fun$_1' ).

tff('declare_vah$',type,
    'vah$': 'ZF_ZF_ZF_fun_fun$' ).

tff('vah$_definition',axiom,
    'vah$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_top$i',type,
    'top$i': 'Nat_nat_fun_set$' ).

tff('top$i_definition',axiom,
    'top$i' = 'fmb_Nat_nat_fun_set$_1' ).

tff('declare_uuw$',type,
    'uuw$': 'ZF_ZF_ZF_fun_fun$' ).

tff('uuw$_definition',axiom,
    'uuw$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_top$b',type,
    'top$b': 'ZF_ZF_prod_set$' ).

tff('top$b_definition',axiom,
    'top$b' = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_f$',type,
    'f$': 'B$' ).

tff('f$_definition',axiom,
    'f$' = 'fmb_B$_1' ).

tff('declare_top$e',type,
    'top$e': 'Nat_nat_prod_set$' ).

tff('top$e_definition',axiom,
    'top$e' = 'fmb_Nat_nat_prod_set$_1' ).

tff('declare_top$d',type,
    'top$d': 'Nat_ZF_prod_set$' ).

tff('top$d_definition',axiom,
    'top$d' = 'fmb_Nat_ZF_prod_set$_1' ).

tff('declare_uur$',type,
    'uur$': 'ZF_ZF_fun$' ).

tff('uur$_definition',axiom,
    'uur$' = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uut$',type,
    'uut$': 'ZF_bool_fun$' ).

tff('uut$_definition',axiom,
    'uut$' = 'fmb_ZF_bool_fun$_1' ).

tff('declare_sum$',type,
    'sum$': 'ZF_ZF_fun$' ).

tff('sum$_definition',axiom,
    'sum$' = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uub$',type,
    'uub$': 'ZF_set_set_ZF_set_bool_fun_fun$' ).

tff('uub$_definition',axiom,
    'uub$' = 'fmb_ZF_set_set_ZF_set_bool_fun_fun$_1' ).

tff('declare_app$',type,
    'app$': 'ZF_ZF_ZF_fun_fun$' ).

tff('app$_definition',axiom,
    'app$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_set$',type,
    'set$': 'ZF_ZF_unit_Category_ext$' ).

tff('set$_definition',axiom,
    'set$' = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_unity$',type,
    'unity$': 'Unit$' ).

tff('unity$_definition',axiom,
    'unity$' = 'fmb_Unit$_1' ).

tff('declare_sup$f',type,
    'sup$f': 'Nat_set_set_nat_set_fun$' ).

tff('sup$f_definition',axiom,
    'sup$f' = 'fmb_Nat_set_set_nat_set_fun$_1' ).

tff('declare_top$g',type,
    'top$g': 'Nat_ZF_fun_set$' ).

tff('top$g_definition',axiom,
    'top$g' = 'fmb_Nat_ZF_fun_set$_1' ).

tff('declare_zFfunCod$',type,
    'zFfunCod$': 'ZF_ZF_fun$' ).

tff('zFfunCod$_definition',axiom,
    'zFfunCod$' = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uug$',type,
    'uug$': 'ZF_ZF_bool_fun_fun$' ).

tff('uug$_definition',axiom,
    'uug$' = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_set$a',type,
    'set$a': 'ZF_ZF_unit_Category_ext$' ).

tff('set$a_definition',axiom,
    'set$a' = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff(declare_tltrue,type,
    tltrue: tlbool ).

tff(tltrue_definition,axiom,
    tltrue = fmb_tlbool_1 ).

tff('declare_uxd$',type,
    'uxd$': 'ZF_nat_set_fun$' ).

tff('uxd$_definition',axiom,
    'uxd$' = 'fmb_ZF_nat_set_fun$_1' ).

tff('declare_zFfunComp$',type,
    'zFfunComp$': 'ZF_ZF_ZF_fun_fun$' ).

tff('zFfunComp$_definition',axiom,
    'zFfunComp$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_top$a',type,
    'top$a': 'ZF_set$' ).

tff('top$a_definition',axiom,
    'top$a' = 'fmb_ZF_set$_1' ).

tff('declare_uyn$',type,
    'uyn$': 'ZF_set_ZF_set_fun$' ).

tff('uyn$_definition',axiom,
    'uyn$' = 'fmb_ZF_set_ZF_set_fun$_1' ).

tff('declare_swap$',type,
    'swap$': 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff('swap$_definition',axiom,
    'swap$' = 'fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1' ).

tff('declare_uxe$',type,
    'uxe$': 'Nat_ZF_set_fun$' ).

tff('uxe$_definition',axiom,
    'uxe$' = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uxf$',type,
    'uxf$': 'Nat_nat_set_fun$' ).

tff('uxf$_definition',axiom,
    'uxf$' = 'fmb_Nat_nat_set_fun$_1' ).

tff('declare_opair$',type,
    'opair$': 'ZF_ZF_ZF_fun_fun$' ).

tff('opair$_definition',axiom,
    'opair$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_g$',type,
    'g$': 'B$' ).

tff('g$_definition',axiom,
    'g$' = 'fmb_B$_1' ).

tff('declare_top$f',type,
    'top$f': 'ZF_ZF_fun_set$' ).

tff('top$f_definition',axiom,
    'top$f' = 'fmb_ZF_ZF_fun_set$_1' ).

tff('declare_elem$',type,
    'elem$': 'ZF_ZF_bool_fun_fun$' ).

tff('elem$_definition',axiom,
    'elem$' = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_zFfunDom$',type,
    'zFfunDom$': 'ZF_ZF_fun$' ).

tff('zFfunDom$_definition',axiom,
    'zFfunDom$' = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uyk$',type,
    'uyk$': 'ZF_ZF_ZF_set_fun_fun$' ).

tff('uyk$_definition',axiom,
    'uyk$' = 'fmb_ZF_ZF_ZF_set_fun_fun$_1' ).

tff('declare_zFfunApp$',type,
    'zFfunApp$': 'ZF_ZF_ZF_fun_fun$' ).

tff('zFfunApp$_definition',axiom,
    'zFfunApp$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_uws$',type,
    'uws$': 'Nat_bool_fun$' ).

tff('uws$_definition',axiom,
    'uws$' = 'fmb_Nat_bool_fun$_1' ).

tff('declare_uu$',type,
    'uu$': 'A_set_a_bool_fun_fun$' ).

tff('uu$_definition',axiom,
    'uu$' = 'fmb_A_set_a_bool_fun_fun$_1' ).

tff('declare_uwy$',type,
    'uwy$': 'ZF_ZF_bool_fun_fun$' ).

tff('uwy$_definition',axiom,
    'uwy$' = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_uuv$',type,
    'uuv$': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' ).

tff('uuv$_definition',axiom,
    'uuv$' = 'fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1' ).

tff(declare_tlfalse,type,
    tlfalse: tlbool ).

tff(tlfalse_definition,axiom,
    tlfalse = fmb_tlbool_2 ).

tff('declare_uuc$',type,
    'uuc$': 'ZF_set_ZF_bool_fun_fun$' ).

tff('uuc$_definition',axiom,
    'uuc$' = 'fmb_ZF_set_ZF_bool_fun_fun$_1' ).

tff('declare_uuu$',type,
    'uuu$': 'ZF_ZF_fun$' ).

tff('uuu$_definition',axiom,
    'uuu$' = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_top$c',type,
    'top$c': 'ZF_nat_prod_set$' ).

tff('top$c_definition',axiom,
    'top$c' = 'fmb_ZF_nat_prod_set$_1' ).

tff('declare_top$h',type,
    'top$h': 'ZF_nat_fun_set$' ).

tff('top$h_definition',axiom,
    'top$h' = 'fmb_ZF_nat_fun_set$_1' ).

tff('declare_top$',type,
    'top$': 'Nat_set$' ).

tff('top$_definition',axiom,
    'top$' = 'fmb_Nat_set$_1' ).

tff('declare_uxc$',type,
    'uxc$': 'ZF_ZF_set_fun$' ).

tff('uxc$_definition',axiom,
    'uxc$' = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_explode$',type,
    'explode$': 'ZF_ZF_set_fun$' ).

tff('explode$_definition',axiom,
    'explode$' = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_isZFfun$',type,
    'isZFfun$': 'ZF_bool_fun$' ).

tff('isZFfun$_definition',axiom,
    'isZFfun$' = 'fmb_ZF_bool_fun$_1' ).

tff('declare_cartProd$',type,
    'cartProd$': 'ZF_ZF_ZF_fun_fun$' ).

tff('cartProd$_definition',axiom,
    'cartProd$' = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_sup$e',type,
    'sup$e': 'ZF_set_set_set_ZF_set_set_fun$' ).

tff('sup$e_definition',axiom,
    'sup$e' = 'fmb_ZF_set_set_set_ZF_set_set_fun$_1' ).

tff('declare_uym$',type,
    'uym$': 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).

tff('uym$_definition',axiom,
    'uym$' = 'fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1' ).

tff('declare_uuf$',type,
    'uuf$': 'ZF_ZF_bool_fun_fun$' ).

tff('uuf$_definition',axiom,
    'uuf$' = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_image$ai',type,
    'image$ai': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_image$ai',axiom,
    'image$ai'('fmb_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$_1','fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_mor_update$a',type,
    'mor_update$a': ( 'B_set_b_set_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' ) > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_mor_update$a',axiom,
    'mor_update$a'('fmb_B_set_b_set_fun$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_id$',type,
    'id$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_fun$' ).

tff('function_id$',axiom,
    'id$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_fun$_1' ).

tff('declare_fun_app$ah',type,
    'fun_app$ah': ( 'ZF_nat_bool_fun_fun$' * 'ZF$' ) > 'Nat_bool_fun$' ).

tff('function_fun_app$ah',axiom,
    'fun_app$ah'('fmb_ZF_nat_bool_fun_fun$_1','fmb_ZF$_1') = 'fmb_Nat_bool_fun$_1' ).

tff('declare_catDom$a',type,
    'catDom$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).

tff('function_catDom$a',axiom,
    'catDom$a'('fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_oppositeCategory$',type,
    'oppositeCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_oppositeCategory$',axiom,
    'oppositeCategory$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_uxn$',type,
    'uxn$': 'ZF_ZF_prod_set$' > 'ZF_ZF_ZF_prod_set_fun$' ).

tff('function_uxn$',axiom,
    'uxn$'('fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_ZF_prod_set_fun$_1' ).

tff('declare_sigma$b',type,
    'sigma$b': ( 'ZF_set$' * 'ZF_nat_set_fun$' ) > 'ZF_nat_prod_set$' ).

tff('function_sigma$b',axiom,
    'sigma$b'('fmb_ZF_set$_1','fmb_ZF_nat_set_fun$_1') = 'fmb_ZF_nat_prod_set$_1' ).

tff('declare_fun_app$bv',type,
    'fun_app$bv': ( 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' * 'ZF_ZF_prod$' ) > 'Nat_ZF_ZF_set_prod_fun$' ).

tff('function_fun_app$bv',axiom,
    'fun_app$bv'('fmb_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_Nat_ZF_ZF_set_prod_fun$_1' ).

tff('declare_relInvImage$b',type,
    'relInvImage$b': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff('function_relInvImage$b',axiom,
    'relInvImage$b'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1' ).

tff('declare_image$bg',type,
    'image$bg': ( 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$bg',axiom,
    'image$bg'('fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_rec_set_unit$',type,
    'rec_set_unit$': ( 'ZF$' * 'Unit$' ) > 'ZF_bool_fun$' ).

tff('function_rec_set_unit$',axiom,
    'rec_set_unit$'('fmb_ZF$_1','fmb_Unit$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_relcomp$',type,
    'relcomp$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_relcomp$',axiom,
    'relcomp$'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uwa$',type,
    'uwa$': ( 'B_ZF_fun$' * 'B_set$' * 'ZF_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uwa$',axiom,
    'uwa$'('fmb_B_ZF_fun$_1','fmb_B_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_mapO$a',type,
    'mapO$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_a_fun$' ).

tff('function_mapO$a',axiom,
    'mapO$a'('fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1') = 'fmb_A_a_fun$_1' ).

tff('declare_uwl$',type,
    'uwl$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_bool_fun$' ).

tff('function_uwl$',axiom,
    'uwl$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_unitFunctor$',type,
    'unitFunctor$': 'ZF_ZF_unit_Category_ext$' > 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' ).

tff('function_unitFunctor$',axiom,
    'unitFunctor$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_1' ).

tff('declare_vas$',type,
    'vas$': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat_nat_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_vas$',axiom,
    'vas$'('fmb_Nat_nat_ZF_set_fun_fun$_1','fmb_Nat_nat_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_fun_app$b',type,
    'fun_app$b': ( 'ZF_ZF_ZF_fun_fun$' * 'ZF$' ) > 'ZF_ZF_fun$' ).

tff('function_fun_app$b',axiom,
    'fun_app$b'('fmb_ZF_ZF_ZF_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uyt$',type,
    'uyt$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_fun$' ).

tff('function_uyt$',axiom,
    'uyt$'('fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_set_ZF_set_fun$_1' ).

tff('declare_constFunctor$',type,
    'constFunctor$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('function_constFunctor$',axiom,
    'constFunctor$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1' ).

tff('declare_vbb$',type,
    'vbb$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_fun_ZF_set_fun$' ).

tff('function_vbb$',axiom,
    'vbb$'('fmb_Nat_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_nat_fun_ZF_set_fun$_1' ).

tff('declare_the$a',type,
    'the$a': 'B_bool_fun$' > 'B$' ).

tff('function_the$a',axiom,
    'the$a'('fmb_B_bool_fun$_1') = 'fmb_B$_1' ).

tff('declare_mapsTo$',type,
    'mapsTo$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' * 'A$' ) > 'A_bool_fun$' ).

tff('function_mapsTo$',axiom,
    'mapsTo$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1','fmb_A$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_compDefined$',type,
    'compDefined$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_compDefined$',axiom,
    'compDefined$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_case_prod$',type,
    'case_prod$': 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_prod_ZF_fun$' ).

tff('function_case_prod$',axiom,
    'case_prod$'('fmb_ZF_ZF_ZF_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_fun$_1' ).

tff('declare_uyq$',type,
    'uyq$': ( 'Nat_ZF_set_fun$' * 'Nat_nat_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uyq$',axiom,
    'uyq$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_nat_set_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_sigma$g',type,
    'sigma$g': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_ZF_prod_ZF_prod_set$' ).

tff('function_sigma$g',axiom,
    'sigma$g'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_ZF_prod_set$_1' ).

tff('declare_uwx$',type,
    'uwx$': 'Nat_ZF_fun$' > 'ZF_bool_fun$' ).

tff('function_uwx$',axiom,
    'uwx$'('fmb_Nat_ZF_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_constFunctor$d',type,
    'constFunctor$d': ( 'ZF_ZF_unit_Category_ext$' * 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('function_constFunctor$d',axiom,
    'constFunctor$d'('fmb_ZF_ZF_unit_Category_ext$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1' ).

tff('declare_comp$f',type,
    'comp$f': ( 'ZF_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_fun$' ) > 'ZF_set_set_ZF_set_set_fun$' ).

tff('function_comp$f',axiom,
    'comp$f'('fmb_ZF_set_ZF_set_set_fun$_1','fmb_ZF_set_set_ZF_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_set_fun$_1' ).

tff('declare_sup$c',type,
    'sup$c': 'B_set_set$' > 'B_set$' ).

tff('function_sup$c',axiom,
    'sup$c'('fmb_B_set_set$_1') = 'fmb_B_set$_1' ).

tff('declare_fun_app$bk',type,
    'fun_app$bk': ( 'B_a_fun$' * 'B$' ) > 'A$' ).

tff('function_fun_app$bk',axiom,
    'fun_app$bk'('fmb_B_a_fun$_1','fmb_B$_1') = 'fmb_A$_1' ).

tff('declare_image$z',type,
    'image$z': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_image$z',axiom,
    'image$z'('fmb_ZF_ZF_ZF_prod_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_extensional$e',type,
    'extensional$e': 'B_set$' > 'B_ZF_fun_set$' ).

tff('function_extensional$e',axiom,
    'extensional$e'('fmb_B_set$_1') = 'fmb_B_ZF_fun_set$_1' ).

tff('declare_rec_unit$',type,
    'rec_unit$': ( 'ZF$' * 'Unit$' ) > 'ZF$' ).

tff('function_rec_unit$',axiom,
    'rec_unit$'('fmb_ZF$_1','fmb_Unit$_1') = 'fmb_ZF$_1' ).

tff('declare_uzv$',type,
    'uzv$': 'ZF_ZF_bool_fun_fun$' > 'ZF_bool_fun$' ).

tff('function_uzv$',axiom,
    'uzv$'('fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_member$c',type,
    'member$c': 'A$' > 'A_set_bool_fun$' ).

tff('function_member$c',axiom,
    'member$c'('fmb_A$_1') = 'fmb_A_set_bool_fun$_1' ).

tff('declare_inf$',type,
    'inf$': 'ZF_set_set$' > 'ZF_set$' ).

tff('function_inf$',axiom,
    'inf$'('fmb_ZF_set_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_sup$h',type,
    'sup$h': 'B_bool_fun_set$' > 'B_bool_fun$' ).

tff('function_sup$h',axiom,
    'sup$h'('fmb_B_bool_fun_set$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_cod_update$',type,
    'cod_update$': ( 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_cod_update$',axiom,
    'cod_update$'('fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_rec_bool$',type,
    'rec_bool$': ( 'ZF$' * 'ZF$' * tlbool ) > 'ZF$' ).

tff('function_rec_bool$',axiom,
    ( ( 'rec_bool$'('fmb_ZF$_1','fmb_ZF$_1',fmb_tlbool_1) = 'fmb_ZF$_1' )
    & ( 'rec_bool$'('fmb_ZF$_1','fmb_ZF$_1',fmb_tlbool_2) = 'fmb_ZF$_1' ) ) ).

tff('declare_member$a',type,
    'member$a': 'ZF_set$' > 'ZF_set_set_bool_fun$' ).

tff('function_member$a',axiom,
    'member$a'('fmb_ZF_set$_1') = 'fmb_ZF_set_set_bool_fun$_1' ).

tff('declare_uyh$',type,
    'uyh$': ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyh$',axiom,
    'uyh$'('fmb_ZF_ZF_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_extensional$d',type,
    'extensional$d': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_fun_set$' ).

tff('function_extensional$d',axiom,
    'extensional$d'('fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_ZF_fun_set$_1' ).

tff('declare_fun_app$av',type,
    'fun_app$av': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF$' ) > 'ZF_ZF_prod_set$' ).

tff('function_fun_app$av',axiom,
    'fun_app$av'('fmb_ZF_ZF_ZF_prod_set_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_fun_app$dd',type,
    'fun_app$dd': ( 'ZF_set_set_ZF_set_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set_set_set$' ).

tff('function_fun_app$dd',axiom,
    'fun_app$dd'('fmb_ZF_set_set_ZF_set_set_set_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_set_set_set$_1' ).

tff('declare_sigma$k',type,
    'sigma$k': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).

tff('function_sigma$k',axiom,
    'sigma$k'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1' ).

tff('declare_restrict$a',type,
    'restrict$a': ( 'B_b_prod_b_fun$' * 'B_b_prod_set$' * 'B_b_prod$' ) > 'B$' ).

tff('function_restrict$a',axiom,
    'restrict$a'('fmb_B_b_prod_b_fun$_1','fmb_B_b_prod_set$_1','fmb_B_b_prod$_1') = 'fmb_B$_1' ).

tff('declare_fun_app$ai',type,
    'fun_app$ai': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).

tff('function_fun_app$ai',axiom,
    'fun_app$ai'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF$_1' ).

tff('declare_uwk$',type,
    'uwk$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set_bool_fun$' ).

tff('function_uwk$',axiom,
    'uwk$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_fun_app$cr',type,
    'fun_app$cr': ( 'A_a_set_fun$' * 'A$' ) > 'A_set$' ).

tff('function_fun_app$cr',axiom,
    'fun_app$cr'('fmb_A_a_set_fun$_1','fmb_A$_1') = 'fmb_A_set$_1' ).

tff('declare_obj_update$',type,
    'obj_update$': ( 'A_set_a_set_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' ) > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_obj_update$',axiom,
    'obj_update$'('fmb_A_set_a_set_fun$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_uux$',type,
    'uux$': ( 'A_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uux$',axiom,
    'uux$'('fmb_A_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_image$bq',type,
    'image$bq': ( 'Nat_nat_fun_ZF_set_fun$' * 'Nat_nat_fun_set$' ) > 'ZF_set_set$' ).

tff('function_image$bq',axiom,
    'image$bq'('fmb_Nat_nat_fun_ZF_set_fun$_1','fmb_Nat_nat_fun_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_uwd$',type,
    'uwd$': ( 'ZF_set_a_fun$' * 'ZF_set_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uwd$',axiom,
    'uwd$'('fmb_ZF_set_a_fun$_1','fmb_ZF_set_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_uyb$',type,
    'uyb$': ( 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' ).

tff('function_uyb$',axiom,
    'uyb$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_nat_ZF_set_ZF_set_prod_fun_fun$_1' ).

tff('declare_id_update$',type,
    'id_update$': ( 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_id_update$',axiom,
    'id_update$'('fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_image$e',type,
    'image$e': ( 'A_set_bool_fun$' * 'A_set_set$' ) > 'Bool_set$' ).

tff('function_image$e',axiom,
    'image$e'('fmb_A_set_bool_fun$_1','fmb_A_set_set$_1') = 'fmb_Bool_set$_1' ).

tff('declare_fun_app$o',type,
    'fun_app$o': ( 'A_set_a_bool_fun_fun$' * 'A_set$' ) > 'A_bool_fun$' ).

tff('function_fun_app$o',axiom,
    'fun_app$o'('fmb_A_set_a_bool_fun_fun$_1','fmb_A_set$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_inverse_rel$',type,
    'inverse_rel$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' ) > 'B_bool_fun$' ).

tff('function_inverse_rel$',axiom,
    'inverse_rel$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_mapO$b',type,
    'mapO$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).

tff('function_mapO$b',axiom,
    'mapO$b'('fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_fun_app$co',type,
    'fun_app$co': ( 'A_ZF_set_fun$' * 'A$' ) > 'ZF_set$' ).

tff('function_fun_app$co',axiom,
    'fun_app$co'('fmb_A_ZF_set_fun$_1','fmb_A$_1') = 'fmb_ZF_set$_1' ).

tff('declare_uwp$',type,
    'uwp$': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' ) > 'ZF_bool_fun$' ).

tff('function_uwp$',axiom,
    'uwp$'('fmb_ZF_set_ZF_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_fun_app$bn',type,
    'fun_app$bn': ( 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' * 'ZF$' ) > 'ZF_ZF_ZF_prod_set_fun$' ).

tff('function_fun_app$bn',axiom,
    'fun_app$bn'('fmb_ZF_ZF_ZF_ZF_prod_set_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_prod_set_fun$_1' ).

tff('declare_uye$',type,
    'uye$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff('function_uye$',axiom,
    'uye$'('fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1' ).

tff('declare_comp$g',type,
    'comp$g': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_set_set_fun$' ) > 'ZF_ZF_prod_set_set_ZF_set_fun$' ).

tff('function_comp$g',axiom,
    'comp$g'('fmb_ZF_set_set_ZF_set_fun$_1','fmb_ZF_ZF_prod_set_set_ZF_set_set_fun$_1') = 'fmb_ZF_ZF_prod_set_set_ZF_set_fun$_1' ).

tff('declare_sup$j',type,
    'sup$j': 'ZF_bool_fun_set$' > 'ZF_bool_fun$' ).

tff('function_sup$j',axiom,
    'sup$j'('fmb_ZF_bool_fun_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_image$f',type,
    'image$f': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set_ZF_set_fun$' ).

tff('function_image$f',axiom,
    'image$f'('fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_set_ZF_set_fun$_1' ).

tff('declare_uww$',type,
    'uww$': 'Nat_ZF_set_fun$' > 'ZF_set_bool_fun$' ).

tff('function_uww$',axiom,
    'uww$'('fmb_Nat_ZF_set_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_image$',type,
    'image$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_set_fun$' ).

tff('function_image$',axiom,
    'image$'('fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_set_ZF_set_set_fun$_1' ).

tff('declare_fun_app$aa',type,
    'fun_app$aa': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat$' ) > 'Nat_ZF_set_fun$' ).

tff('function_fun_app$aa',axiom,
    'fun_app$aa'('fmb_Nat_nat_ZF_set_fun_fun$_1','fmb_Nat$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_fun_app$cg',type,
    'fun_app$cg': ( 'ZF_ZF_prod_nat_set_fun$' * 'ZF_ZF_prod$' ) > 'Nat_set$' ).

tff('function_fun_app$cg',axiom,
    'fun_app$cg'('fmb_ZF_ZF_prod_nat_set_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_Nat_set$_1' ).

tff('declare_image$ac',type,
    'image$ac': ( 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$' * 'ZF_nat_prod_set$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_image$ac',axiom,
    'image$ac'('fmb_ZF_nat_prod_ZF_set_ZF_set_prod_fun$_1','fmb_ZF_nat_prod_set$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_converse$',type,
    'converse$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$' ).

tff('function_converse$',axiom,
    'converse$'('fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uwv$',type,
    'uwv$': 'ZF_ZF_fun$' > 'ZF_bool_fun$' ).

tff('function_uwv$',axiom,
    'uwv$'('fmb_ZF_ZF_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uzb$',type,
    'uzb$': ( 'Nat_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uzb$',axiom,
    'uzb$'('fmb_Nat_ZF_ZF_set_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uxi$',type,
    'uxi$': 'ZF_set$' > 'ZF_ZF_set_fun$' ).

tff('function_uxi$',axiom,
    'uxi$'('fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_uxl$',type,
    'uxl$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_uxl$',axiom,
    'uxl$'('fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_fun_app$bf',type,
    'fun_app$bf': ( 'A_ZF_fun$' * 'A$' ) > 'ZF$' ).

tff('function_fun_app$bf',axiom,
    'fun_app$bf'('fmb_A_ZF_fun$_1','fmb_A$_1') = 'fmb_ZF$_1' ).

tff('declare_uxh$',type,
    'uxh$': 'ZF_bool_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_uxh$',axiom,
    'uxh$'('fmb_ZF_bool_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_comp$j',type,
    'comp$j': ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_fun$' ) > 'ZF_set_set_ZF_set_fun$' ).

tff('function_comp$j',axiom,
    'comp$j'('fmb_ZF_set_ZF_set_fun$_1','fmb_ZF_set_set_ZF_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_fun$_1' ).

tff('declare_gr$',type,
    'gr$': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_prod_set$' ).

tff('function_gr$',axiom,
    'gr$'('fmb_ZF_set$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_set_prod_set$_1' ).

tff('declare_comp$e',type,
    'comp$e': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_ZF_set_set_set_fun$' ) > 'ZF_set_set_ZF_set_set_fun$' ).

tff('function_comp$e',axiom,
    'comp$e'('fmb_ZF_set_set_set_ZF_set_set_fun$_1','fmb_ZF_set_set_ZF_set_set_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_set_fun$_1' ).

tff('declare_uuh$',type,
    'uuh$': ( tlbool * 'ZF$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff('function_uuh$',axiom,
    ( ( 'uuh$'(fmb_tlbool_1,'fmb_ZF$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' )
    & ( 'uuh$'(fmb_tlbool_2,'fmb_ZF$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ) ) ).

tff('declare_sigma$f',type,
    'sigma$f': ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set_ZF_prod_set$' ).

tff('function_sigma$f',axiom,
    'sigma$f'('fmb_ZF_set_set$_1','fmb_ZF_set_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_prod_set$_1' ).

tff('declare_sigma$',type,
    'sigma$': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_prod_set$' ).

tff('function_sigma$',axiom,
    'sigma$'('fmb_ZF_set$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_sup$i',type,
    'sup$i': 'ZF_set_bool_fun_set$' > 'ZF_set_bool_fun$' ).

tff('function_sup$i',axiom,
    'sup$i'('fmb_ZF_set_bool_fun_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_pair$a',type,
    'pair$a': ( 'B$' * 'B$' ) > 'B_b_prod$' ).

tff('function_pair$a',axiom,
    'pair$a'('fmb_B$_1','fmb_B$_1') = 'fmb_B_b_prod$_1' ).

tff('declare_uyp$',type,
    'uyp$': ( 'Nat_ZF_set_fun$' * 'ZF_nat_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyp$',axiom,
    'uyp$'('fmb_Nat_ZF_set_fun$_1','fmb_ZF_nat_set_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_vao$',type,
    'vao$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_vao$',axiom,
    'vao$'('fmb_Nat_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_uzn$',type,
    'uzn$': 'Nat_ZF_set_fun$' > 'Nat_ZF_ZF_set_fun_fun$' ).

tff('function_uzn$',axiom,
    'uzn$'('fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_ZF_set_fun_fun$_1' ).

tff('declare_image$m',type,
    'image$m': ( 'B_a_fun$' * 'B_set$' ) > 'A_set$' ).

tff('function_image$m',axiom,
    'image$m'('fmb_B_a_fun$_1','fmb_B_set$_1') = 'fmb_A_set$_1' ).

tff('declare_uzs$',type,
    'uzs$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uzs$',axiom,
    'uzs$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_extensional$c',type,
    'extensional$c': 'B_b_prod_set$' > 'B_b_prod_b_fun_set$' ).

tff('function_extensional$c',axiom,
    'extensional$c'('fmb_B_b_prod_set$_1') = 'fmb_B_b_prod_b_fun_set$_1' ).

tff('declare_case_prod$a',type,
    'case_prod$a': 'B_b_b_fun_fun$' > 'B_b_prod_b_fun$' ).

tff('function_case_prod$a',axiom,
    'case_prod$a'('fmb_B_b_b_fun_fun$_1') = 'fmb_B_b_prod_b_fun$_1' ).

tff('declare_uzp$',type,
    'uzp$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uzp$',axiom,
    'uzp$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_collect$i',type,
    'collect$i': 'B_bool_fun$' > 'B_set$' ).

tff('function_collect$i',axiom,
    'collect$i'('fmb_B_bool_fun$_1') = 'fmb_B_set$_1' ).

tff('declare_uve$',type,
    'uve$': ( 'ZF_set_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uve$',axiom,
    'uve$'('fmb_ZF_set_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uyc$',type,
    'uyc$': 'Nat_set$' > 'Nat_nat_set_fun$' ).

tff('function_uyc$',axiom,
    'uyc$'('fmb_Nat_set$_1') = 'fmb_Nat_nat_set_fun$_1' ).

tff('declare_image$a',type,
    'image$a': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_set_fun$' ).

tff('function_image$a',axiom,
    'image$a'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_set_set_fun$_1' ).

tff('declare_image$bc',type,
    'image$bc': ( 'Nat_ZF_set_set_fun$' * 'Nat_set$' ) > 'ZF_set_set_set$' ).

tff('function_image$bc',axiom,
    'image$bc'('fmb_Nat_ZF_set_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set_set_set$_1' ).

tff('declare_makeCat$',type,
    'makeCat$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_makeCat$',axiom,
    'makeCat$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_image$p',type,
    'image$p': 'A_a_fun$' > 'A_set_a_set_fun$' ).

tff('function_image$p',axiom,
    'image$p'('fmb_A_a_fun$_1') = 'fmb_A_set_a_set_fun$_1' ).

tff('declare_image$bh',type,
    'image$bh': ( 'A_set_a_bool_fun_fun$' * 'A_set_set$' ) > 'A_bool_fun_set$' ).

tff('function_image$bh',axiom,
    'image$bh'('fmb_A_set_a_bool_fun_fun$_1','fmb_A_set_set$_1') = 'fmb_A_bool_fun_set$_1' ).

tff('declare_fun_app$aq',type,
    'fun_app$aq': ( 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' * 'ZF_ZF_ZF_fun_fun$' ) > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_fun_app$aq',axiom,
    'fun_app$aq'('fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1','fmb_ZF_ZF_ZF_fun_fun$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_mor$a',type,
    'mor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).

tff('function_mor$a',axiom,
    'mor$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_set$_1' ).

tff('declare_uxa$',type,
    'uxa$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set_ZF_set_set_fun$' ).

tff('function_uxa$',axiom,
    'uxa$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set_ZF_set_set_fun$_1' ).

tff('declare_sigma$c',type,
    'sigma$c': ( 'Nat_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_prod_set$' ).

tff('function_sigma$c',axiom,
    'sigma$c'('fmb_Nat_set$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_prod_set$_1' ).

tff('declare_catDom$',type,
    'catDom$': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_catDom$',axiom,
    'catDom$'('fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_uui$',type,
    'uui$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_prod_bool_fun$' ).

tff('function_uui$',axiom,
    'uui$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_b_prod_bool_fun$_1' ).

tff('declare_uuz$',type,
    'uuz$': ( 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff('function_uuz$',axiom,
    'uuz$'('fmb_ZF_set_set$_1','fmb_ZF_set_bool_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_uuj$',type,
    'uuj$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_prod_bool_fun$' ).

tff('function_uuj$',axiom,
    'uuj$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_prod_bool_fun$_1' ).

tff('declare_extensional$a',type,
    'extensional$a': 'ZF_set$' > 'ZF_ZF_fun_set$' ).

tff('function_extensional$a',axiom,
    'extensional$a'('fmb_ZF_set$_1') = 'fmb_ZF_ZF_fun_set$_1' ).

tff('declare_fun_app$ay',type,
    'fun_app$ay': ( 'Nat_ZF_set_set_fun$' * 'Nat$' ) > 'ZF_set_set$' ).

tff('function_fun_app$ay',axiom,
    'fun_app$ay'('fmb_Nat_ZF_set_set_fun$_1','fmb_Nat$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_uzg$',type,
    'uzg$': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uzg$',axiom,
    'uzg$'('fmb_Nat_nat_ZF_set_fun_fun$_1','fmb_Nat_set$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_sigma$e',type,
    'sigma$e': ( 'ZF_set$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_ZF_prod_prod_set$' ).

tff('function_sigma$e',axiom,
    'sigma$e'('fmb_ZF_set$_1','fmb_ZF_ZF_ZF_prod_set_fun$_1') = 'fmb_ZF_ZF_ZF_prod_prod_set$_1' ).

tff('declare_fun_app$az',type,
    'fun_app$az': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).

tff('function_fun_app$az',axiom,
    'fun_app$az'('fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_ZF_prod$_1' ).

tff('declare_uwr$',type,
    'uwr$': ( 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_ZF_prod_fun$' ) > 'Nat_ZF_fun$' ).

tff('function_uwr$',axiom,
    'uwr$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_Nat_ZF_ZF_prod_fun$_1') = 'fmb_Nat_ZF_fun$_1' ).

tff('declare_image$ah',type,
    'image$ah': ( 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$' * 'Nat_nat_prod_set$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_image$ah',axiom,
    'image$ah'('fmb_Nat_nat_prod_ZF_set_ZF_set_prod_fun$_1','fmb_Nat_nat_prod_set$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_image$h',type,
    'image$h': ( 'ZF_b_fun$' * 'ZF_set$' ) > 'B_set$' ).

tff('function_image$h',axiom,
    'image$h'('fmb_ZF_b_fun$_1','fmb_ZF_set$_1') = 'fmb_B_set$_1' ).

tff('declare_uwt$',type,
    'uwt$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_bool_fun$' ).

tff('function_uwt$',axiom,
    'uwt$'('fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uyv$',type,
    'uyv$': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyv$',axiom,
    'uyv$'('fmb_ZF_ZF_ZF_set_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_repl$',type,
    'repl$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff('function_repl$',axiom,
    'repl$'('fmb_ZF$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF$_1' ).

tff('declare_inf$b',type,
    'inf$b': 'B_set_set$' > 'B_set$' ).

tff('function_inf$b',axiom,
    'inf$b'('fmb_B_set_set$_1') = 'fmb_B_set$_1' ).

tff('declare_fun_app$x',type,
    'fun_app$x': ( 'ZF_set_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF_set_set$' ).

tff('function_fun_app$x',axiom,
    'fun_app$x'('fmb_ZF_set_ZF_set_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_comp$d',type,
    'comp$d': ( 'Nat_set_ZF_set_set_fun$' * 'Nat_set_set_nat_set_fun$' ) > 'Nat_set_set_ZF_set_set_fun$' ).

tff('function_comp$d',axiom,
    'comp$d'('fmb_Nat_set_ZF_set_set_fun$_1','fmb_Nat_set_set_nat_set_fun$_1') = 'fmb_Nat_set_set_ZF_set_set_fun$_1' ).

tff('declare_val$',type,
    'val$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).

tff('function_val$',axiom,
    'val$'('fmb_ZF_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_obj_update$a',type,
    'obj_update$a': ( 'ZF_set_ZF_set_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_obj_update$a',axiom,
    'obj_update$a'('fmb_ZF_set_ZF_set_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_mor2ZF$',type,
    'mor2ZF$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_ZF_fun$' ).

tff('function_mor2ZF$',axiom,
    'mor2ZF$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_ZF_fun$_1' ).

tff('declare_uva$',type,
    'uva$': ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uva$',axiom,
    'uva$'('fmb_ZF_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_comp_update$',type,
    'comp_update$': ( 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_comp_update$',axiom,
    'comp_update$'('fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_uxy$',type,
    'uxy$': 'ZF_set$' > 'Nat_ZF_set_fun$' ).

tff('function_uxy$',axiom,
    'uxy$'('fmb_ZF_set$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uvg$',type,
    'uvg$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uvg$',axiom,
    'uvg$'('fmb_ZF_ZF_set_fun$_1','fmb_Nat_ZF_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uvi$',type,
    'uvi$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod_ZF_fun$' ).

tff('function_uvi$',axiom,
    'uvi$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1') = 'fmb_ZF_ZF_prod_ZF_fun$_1' ).

tff('declare_extensional$b',type,
    'extensional$b': 'A_set$' > 'A_b_fun_set$' ).

tff('function_extensional$b',axiom,
    'extensional$b'('fmb_A_set$_1') = 'fmb_A_b_fun_set$_1' ).

tff('declare_fun_app$ca',type,
    'fun_app$ca': ( 'Nat_ZF_set_ZF_set_prod_fun$' * 'Nat$' ) > 'ZF_set_ZF_set_prod$' ).

tff('function_fun_app$ca',axiom,
    'fun_app$ca'('fmb_Nat_ZF_set_ZF_set_prod_fun$_1','fmb_Nat$_1') = 'fmb_ZF_set_ZF_set_prod$_1' ).

tff('declare_uvb$',type,
    'uvb$': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uvb$',axiom,
    'uvb$'('fmb_ZF_bool_fun$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_image$bj',type,
    'image$bj': ( 'ZF_set_set_ZF_set_bool_fun_fun$' * 'ZF_set_set_set$' ) > 'ZF_set_bool_fun_set$' ).

tff('function_image$bj',axiom,
    'image$bj'('fmb_ZF_set_set_ZF_set_bool_fun_fun$_1','fmb_ZF_set_set_set$_1') = 'fmb_ZF_set_bool_fun_set$_1' ).

tff('declare_fun_app$bw',type,
    'fun_app$bw': ( 'ZF_ZF_prod_ZF_set_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set_ZF_prod$' ).

tff('function_fun_app$bw',axiom,
    'fun_app$bw'('fmb_ZF_ZF_prod_ZF_set_ZF_prod_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_set_ZF_prod$_1' ).

tff('declare_uuk$',type,
    'uuk$': 'ZF_ZF_fun$' > 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' ).

tff('function_uuk$',axiom,
    'uuk$'('fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_1' ).

tff('declare_gr$a',type,
    'gr$a': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_prod_set$' ).

tff('function_gr$a',axiom,
    'gr$a'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_ZF_prod_set$_1' ).

tff('declare_uxb$',type,
    'uxb$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uxb$',axiom,
    'uxb$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_dom_update$',type,
    'dom_update$': ( 'B_a_fun_b_a_fun_fun$' * 'A_b_b_c_LSCategory_ext_Category_ext$' ) > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_dom_update$',axiom,
    'dom_update$'('fmb_B_a_fun_b_a_fun_fun$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_vaw$',type,
    'vaw$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).

tff('function_vaw$',axiom,
    'vaw$'('fmb_ZF_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_zFfun$',type,
    'zFfun$': ( 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff('function_zFfun$',axiom,
    'zFfun$'('fmb_ZF$_1','fmb_ZF$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF$_1' ).

tff('declare_fun_app$cx',type,
    'fun_app$cx': ( 'B_ZF_set_fun$' * 'B$' ) > 'ZF_set$' ).

tff('function_fun_app$cx',axiom,
    'fun_app$cx'('fmb_B_ZF_set_fun$_1','fmb_B$_1') = 'fmb_ZF_set$_1' ).

tff('declare_image$az',type,
    'image$az': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$az',axiom,
    'image$az'('fmb_ZF_ZF_ZF_prod_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_vba$',type,
    'vba$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).

tff('function_vba$',axiom,
    'vba$'('fmb_Nat_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uvo$',type,
    'uvo$': ( 'B_a_fun$' * 'B_set$' * 'A_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uvo$',axiom,
    'uvo$'('fmb_B_a_fun$_1','fmb_B_set$_1','fmb_A_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_image$as',type,
    'image$as': ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$as',axiom,
    'image$as'('fmb_ZF_set_ZF_ZF_prod_set_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_comp$h',type,
    'comp$h': ( 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_prod_set_set_ZF_set_fun$' ).

tff('function_comp$h',axiom,
    'comp$h'('fmb_ZF_ZF_prod_set_ZF_set_fun$_1','fmb_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_1') = 'fmb_ZF_ZF_prod_set_set_ZF_set_fun$_1' ).

tff('declare_identityFunctor$b',type,
    'identityFunctor$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).

tff('function_identityFunctor$b',axiom,
    'identityFunctor$b'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1' ).

tff('declare_pair$',type,
    'pair$': 'ZF$' > 'ZF_ZF_ZF_prod_fun$' ).

tff('function_pair$',axiom,
    'pair$'('fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_prod_fun$_1' ).

tff('declare_case_prod$n',type,
    'case_prod$n': 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' > 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff('function_case_prod$n',axiom,
    'case_prod$n'('fmb_Nat_ZF_ZF_ZF_prod_set_fun_fun$_1') = 'fmb_Nat_ZF_prod_ZF_ZF_prod_set_fun$_1' ).

tff('declare_uvh$',type,
    'uvh$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_set_fun$' ).

tff('function_uvh$',axiom,
    'uvh$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_ZF_set_fun$_1' ).

tff('declare_vac$',type,
    'vac$': 'Nat_ZF_set_fun$' > 'Nat_ZF_bool_fun_fun$' ).

tff('function_vac$',axiom,
    'vac$'('fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_bool_fun_fun$_1' ).

tff('declare_fun_app$w',type,
    'fun_app$w': ( 'ZF_nat_fun_ZF_set_fun$' * 'ZF_nat_fun$' ) > 'ZF_set$' ).

tff('function_fun_app$w',axiom,
    'fun_app$w'('fmb_ZF_nat_fun_ZF_set_fun$_1','fmb_ZF_nat_fun$_1') = 'fmb_ZF_set$_1' ).

tff('declare_vax$',type,
    'vax$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_fun_ZF_set_fun$' ).

tff('function_vax$',axiom,
    'vax$'('fmb_ZF_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_fun_ZF_set_fun$_1' ).

tff('declare_image$an',type,
    'image$an': ( 'B_b_set_fun$' * 'B_set$' ) > 'B_set_set$' ).

tff('function_image$an',axiom,
    'image$an'('fmb_B_b_set_fun$_1','fmb_B_set$_1') = 'fmb_B_set_set$_1' ).

tff('declare_obj$a',type,
    'obj$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).

tff('function_obj$a',axiom,
    'obj$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_set$_1' ).

tff('declare_uwf$',type,
    'uwf$': ( 'Nat_ZF_set_fun$' * 'Nat_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff('function_uwf$',axiom,
    'uwf$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_bool_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_uvr$',type,
    'uvr$': ( 'B_b_fun$' * 'B_set$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uvr$',axiom,
    'uvr$'('fmb_B_b_fun$_1','fmb_B_set$_1','fmb_B_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_uwu$',type,
    'uwu$': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$' ).

tff('function_uwu$',axiom,
    'uwu$'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_fun_app$aj',type,
    'fun_app$aj': ( 'Nat_ZF_fun$' * 'Nat$' ) > 'ZF$' ).

tff('function_fun_app$aj',axiom,
    'fun_app$aj'('fmb_Nat_ZF_fun$_1','fmb_Nat$_1') = 'fmb_ZF$_1' ).

tff('declare_uzm$',type,
    'uzm$': ( 'ZF_ZF_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uzm$',axiom,
    'uzm$'('fmb_ZF_ZF_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_fun_app$ct',type,
    'fun_app$ct': ( 'B_a_set_fun$' * 'B$' ) > 'A_set$' ).

tff('function_fun_app$ct',axiom,
    'fun_app$ct'('fmb_B_a_set_fun$_1','fmb_B$_1') = 'fmb_A_set$_1' ).

tff('declare_uvu$',type,
    'uvu$': ( 'ZF_a_fun$' * 'ZF_set$' * 'A_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uvu$',axiom,
    'uvu$'('fmb_ZF_a_fun$_1','fmb_ZF_set$_1','fmb_A_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uze$',type,
    'uze$': ( 'Nat_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uze$',axiom,
    'uze$'('fmb_Nat_nat_ZF_set_fun_fun$_1','fmb_Nat_set$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_image$ax',type,
    'image$ax': ( 'Nat_nat_set_fun$' * 'Nat_set$' ) > 'Nat_set_set$' ).

tff('function_image$ax',axiom,
    'image$ax'('fmb_Nat_nat_set_fun$_1','fmb_Nat_set$_1') = 'fmb_Nat_set_set$_1' ).

tff('declare_uyl$',type,
    'uyl$': 'ZF$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_uyl$',axiom,
    'uyl$'('fmb_ZF$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_case_prod$l',type,
    'case_prod$l': 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$' ).

tff('function_case_prod$l',axiom,
    'case_prod$l'('fmb_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_uun$',type,
    'uun$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_uun$',axiom,
    'uun$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_fun_app$cn',type,
    'fun_app$cn': ( 'ZF_set_set_ZF_set_set_fun$' * 'ZF_set_set$' ) > 'ZF_set_set$' ).

tff('function_fun_app$cn',axiom,
    'fun_app$cn'('fmb_ZF_set_set_ZF_set_set_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_image$bb',type,
    'image$bb': ( 'ZF_ZF_set_set_fun$' * 'ZF_set$' ) > 'ZF_set_set_set$' ).

tff('function_image$bb',axiom,
    'image$bb'('fmb_ZF_ZF_set_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_set_set_set$_1' ).

tff('declare_uyg$',type,
    'uyg$': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_ZF_ZF_prod_fun_fun$' ).

tff('function_uyg$',axiom,
    'uyg$'('fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1' ).

tff('declare_uzd$',type,
    'uzd$': ( 'Nat_ZF_ZF_set_fun_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uzd$',axiom,
    'uzd$'('fmb_Nat_ZF_ZF_set_fun_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_var$',type,
    'var$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).

tff('function_var$',axiom,
    'var$'('fmb_Nat_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_homFtor$',type,
    'homFtor$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('function_homFtor$',axiom,
    'homFtor$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ).

tff('declare_category_ext$',type,
    'category_ext$': ( 'A_set$' * 'B_set$' * 'B_a_fun$' * 'B_a_fun$' * 'A_b_fun$' * 'B_b_b_fun_fun$' * 'B_c_LSCategory_ext$' ) > 'A_b_b_c_LSCategory_ext_Category_ext$' ).

tff('function_category_ext$',axiom,
    'category_ext$'('fmb_A_set$_1','fmb_B_set$_1','fmb_B_a_fun$_1','fmb_B_a_fun$_1','fmb_A_b_fun$_1','fmb_B_b_b_fun_fun$_1','fmb_B_c_LSCategory_ext$_1') = 'fmb_A_b_b_c_LSCategory_ext_Category_ext$_1' ).

tff('declare_uxk$',type,
    'uxk$': ( 'ZF_bool_fun$' * 'ZF_ZF_bool_fun_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff('function_uxk$',axiom,
    'uxk$'('fmb_ZF_bool_fun$_1','fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_vau$',type,
    'vau$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_vau$',axiom,
    'vau$'('fmb_ZF_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_fun_app$bm',type,
    'fun_app$bm': ( 'A_a_fun$' * 'A$' ) > 'A$' ).

tff('function_fun_app$bm',axiom,
    'fun_app$bm'('fmb_A_a_fun$_1','fmb_A$_1') = 'fmb_A$_1' ).

tff('declare_uxm$',type,
    'uxm$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' ).

tff('function_uxm$',axiom,
    'uxm$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1' ).

tff('declare_vaf$',type,
    'vaf$': 'ZF_set_set_set$' > 'ZF_set_bool_fun$' ).

tff('function_vaf$',axiom,
    'vaf$'('fmb_ZF_set_set_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_collect$b',type,
    'collect$b': 'B_b_prod_bool_fun$' > 'B_b_prod_set$' ).

tff('function_collect$b',axiom,
    'collect$b'('fmb_B_b_prod_bool_fun$_1') = 'fmb_B_b_prod_set$_1' ).

tff('declare_uvz$',type,
    'uvz$': ( 'B_ZF_fun$' * 'B_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uvz$',axiom,
    'uvz$'('fmb_B_ZF_fun$_1','fmb_B_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_cod$',type,
    'cod$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).

tff('function_cod$',axiom,
    'cod$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_a_fun$_1' ).

tff('declare_collect$d',type,
    'collect$d': 'B_ZF_fun_bool_fun$' > 'B_ZF_fun_set$' ).

tff('function_collect$d',axiom,
    'collect$d'('fmb_B_ZF_fun_bool_fun$_1') = 'fmb_B_ZF_fun_set$_1' ).

tff('declare_fun_app$cy',type,
    'fun_app$cy': ( 'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_fun_app$cy',axiom,
    'fun_app$cy'('fmb_ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_1','fmb_ZF_ZF_prod_set_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_case_prod$e',type,
    'case_prod$e': 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' > 'ZF_nat_prod_ZF_set_ZF_set_prod_fun$' ).

tff('function_case_prod$e',axiom,
    'case_prod$e'('fmb_ZF_nat_ZF_set_ZF_set_prod_fun_fun$_1') = 'fmb_ZF_nat_prod_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_sigma$a',type,
    'sigma$a': ( 'ZF_set_set$' * 'ZF_set_ZF_set_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_sigma$a',axiom,
    'sigma$a'('fmb_ZF_set_set$_1','fmb_ZF_set_ZF_set_set_fun$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_uxg$',type,
    'uxg$': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff('function_uxg$',axiom,
    'uxg$'('fmb_ZF_bool_fun$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_collect$c',type,
    'collect$c': 'ZF_ZF_fun_bool_fun$' > 'ZF_ZF_fun_set$' ).

tff('function_collect$c',axiom,
    'collect$c'('fmb_ZF_ZF_fun_bool_fun$_1') = 'fmb_ZF_ZF_fun_set$_1' ).

tff('declare_uxp$',type,
    'uxp$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' ).

tff('function_uxp$',axiom,
    'uxp$'('fmb_ZF_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_ZF_nat_ZF_set_ZF_set_prod_fun_fun$_1' ).

tff('declare_relImage$a',type,
    'relImage$a': ( 'Nat_nat_prod_set$' * 'Nat_ZF_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_relImage$a',axiom,
    'relImage$a'('fmb_Nat_nat_prod_set$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_sigma$h',type,
    'sigma$h': ( 'ZF_set$' * 'ZF_ZF_set_set_fun$' ) > 'ZF_ZF_set_prod_set$' ).

tff('function_sigma$h',axiom,
    'sigma$h'('fmb_ZF_set$_1','fmb_ZF_ZF_set_set_fun$_1') = 'fmb_ZF_ZF_set_prod_set$_1' ).

tff('declare_mapM$',type,
    'mapM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'B_ZF_fun$' ).

tff('function_mapM$',axiom,
    'mapM$'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1') = 'fmb_B_ZF_fun$_1' ).

tff('declare_obj$',type,
    'obj$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_set$' ).

tff('function_obj$',axiom,
    'obj$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_set$_1' ).

tff('declare_inverse$',type,
    'inverse$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_fun$' ).

tff('function_inverse$',axiom,
    'inverse$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_b_fun$_1' ).

tff('declare_uxq$',type,
    'uxq$': 'Nat_set$' > 'ZF_nat_set_fun$' ).

tff('function_uxq$',axiom,
    'uxq$'('fmb_Nat_set$_1') = 'fmb_ZF_nat_set_fun$_1' ).

tff('declare_uxo$',type,
    'uxo$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_ZF_set_fun$' ).

tff('function_uxo$',axiom,
    'uxo$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_set_ZF_set_fun$_1' ).

tff('declare_uvv$',type,
    'uvv$': ( 'ZF_b_fun$' * 'ZF_set$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uvv$',axiom,
    'uvv$'('fmb_ZF_b_fun$_1','fmb_ZF_set$_1','fmb_B_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_fun_app$bc',type,
    'fun_app$bc': ( 'ZF_nat_set_fun$' * 'ZF$' ) > 'Nat_set$' ).

tff('function_fun_app$bc',axiom,
    'fun_app$bc'('fmb_ZF_nat_set_fun$_1','fmb_ZF$_1') = 'fmb_Nat_set$_1' ).

tff('declare_collect$j',type,
    'collect$j': 'ZF_set_bool_fun$' > 'ZF_set_set$' ).

tff('function_collect$j',axiom,
    'collect$j'('fmb_ZF_set_bool_fun$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_uud$',type,
    'uud$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).

tff('function_uud$',axiom,
    'uud$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_b_b_fun_fun$_1' ).

tff('declare_fun_app$cd',type,
    'fun_app$cd': ( 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' * 'Nat$' ) > 'ZF_ZF_set_ZF_set_prod_fun$' ).

tff('function_fun_app$cd',axiom,
    'fun_app$cd'('fmb_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_fun_app$cc',type,
    'fun_app$cc': ( 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' * 'Nat$' ) > 'ZF_ZF_prod_ZF_set_ZF_prod_fun$' ).

tff('function_fun_app$cc',axiom,
    'fun_app$cc'('fmb_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_prod_ZF_set_ZF_prod_fun$_1' ).

tff('declare_uzu$',type,
    'uzu$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff('function_uzu$',axiom,
    'uzu$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_ZF_ZF_prod_set_fun_fun$_1' ).

tff('declare_vam$',type,
    'vam$': ( 'ZF_nat_ZF_set_fun_fun$' * 'Nat_ZF_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_vam$',axiom,
    'vam$'('fmb_ZF_nat_ZF_set_fun_fun$_1','fmb_Nat_ZF_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uvc$',type,
    'uvc$': ( 'ZF_set_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uvc$',axiom,
    'uvc$'('fmb_ZF_set_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_fun_app$ad',type,
    'fun_app$ad': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF$' ) > 'ZF_ZF_set_fun$' ).

tff('function_fun_app$ad',axiom,
    'fun_app$ad'('fmb_ZF_ZF_ZF_set_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_constFunctor$e',type,
    'constFunctor$e': ( 'ZF_ZF_unit_Category_ext$' * 'ZF_ZF_unit_Category_ext$' * 'ZF$' ) > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).

tff('function_constFunctor$e',axiom,
    'constFunctor$e'('fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1' ).

tff('declare_fun_app$be',type,
    'fun_app$be': ( 'ZF_set_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).

tff('function_fun_app$be',axiom,
    'fun_app$be'('fmb_ZF_set_ZF_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF$_1' ).

tff('declare_uza$',type,
    'uza$': ( 'ZF_nat_ZF_set_fun_fun$' * 'ZF_set$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uza$',axiom,
    'uza$'('fmb_ZF_nat_ZF_set_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_mapsTo$a',type,
    'mapsTo$a': ( 'ZF_ZF_unit_Category_ext$' * 'ZF$' ) > 'ZF_ZF_bool_fun_fun$' ).

tff('function_mapsTo$a',axiom,
    'mapsTo$a'('fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_image$aq',type,
    'image$aq': ( 'A_ZF_set_fun$' * 'A_set$' ) > 'ZF_set_set$' ).

tff('function_image$aq',axiom,
    'image$aq'('fmb_A_ZF_set_fun$_1','fmb_A_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_fun_app$bd',type,
    'fun_app$bd': ( 'Nat_nat_set_fun$' * 'Nat$' ) > 'Nat_set$' ).

tff('function_fun_app$bd',axiom,
    'fun_app$bd'('fmb_Nat_nat_set_fun$_1','fmb_Nat$_1') = 'fmb_Nat_set$_1' ).

tff('declare_fun_app$bp',type,
    'fun_app$bp': ( 'ZF_nat_ZF_ZF_prod_set_fun_fun$' * 'ZF$' ) > 'Nat_ZF_ZF_prod_set_fun$' ).

tff('function_fun_app$bp',axiom,
    'fun_app$bp'('fmb_ZF_nat_ZF_ZF_prod_set_fun_fun$_1','fmb_ZF$_1') = 'fmb_Nat_ZF_ZF_prod_set_fun$_1' ).

tff('declare_uvp$',type,
    'uvp$': ( 'A_b_fun$' * 'A_set$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uvp$',axiom,
    'uvp$'('fmb_A_b_fun$_1','fmb_A_set$_1','fmb_B_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_fun_app$bi',type,
    'fun_app$bi': ( 'ZF_a_fun$' * 'ZF$' ) > 'A$' ).

tff('function_fun_app$bi',axiom,
    'fun_app$bi'('fmb_ZF_a_fun$_1','fmb_ZF$_1') = 'fmb_A$_1' ).

tff('declare_image$al',type,
    'image$al': ( 'A_b_set_fun$' * 'A_set$' ) > 'B_set_set$' ).

tff('function_image$al',axiom,
    'image$al'('fmb_A_b_set_fun$_1','fmb_A_set$_1') = 'fmb_B_set_set$_1' ).

tff('declare_case_prod$f',type,
    'case_prod$f': 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$' ).

tff('function_case_prod$f',axiom,
    'case_prod$f'('fmb_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$_1' ).

tff('declare_sup$g',type,
    'sup$g': 'A_bool_fun_set$' > 'A_bool_fun$' ).

tff('function_sup$g',axiom,
    'sup$g'('fmb_A_bool_fun_set$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_homFtorContra$a',type,
    'homFtorContra$a': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('function_homFtorContra$a',axiom,
    'homFtorContra$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ).

tff('declare_homFtorContra$',type,
    'homFtorContra$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('function_homFtorContra$',axiom,
    'homFtorContra$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ).

tff('declare_uyz$',type,
    'uyz$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_ZF_set_fun_fun$' ).

tff('function_uyz$',axiom,
    'uyz$'('fmb_ZF_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_ZF_set_fun_fun$_1' ).

tff('declare_image$w',type,
    'image$w': ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff('function_image$w',axiom,
    'image$w'('fmb_ZF_set_ZF_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_fun_app$u',type,
    'fun_app$u': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).

tff('function_fun_app$u',axiom,
    'fun_app$u'('fmb_ZF_set_set_ZF_set_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_inf$a',type,
    'inf$a': 'A_set_set$' > 'A_set$' ).

tff('function_inf$a',axiom,
    'inf$a'('fmb_A_set_set$_1') = 'fmb_A_set$_1' ).

tff('declare_fun_app$db',type,
    'fun_app$db': ( 'Nat_set_set_ZF_set_set_set_fun$' * 'Nat_set_set$' ) > 'ZF_set_set_set$' ).

tff('function_fun_app$db',axiom,
    'fun_app$db'('fmb_Nat_set_set_ZF_set_set_set_fun$_1','fmb_Nat_set_set$_1') = 'fmb_ZF_set_set_set$_1' ).

tff('declare_uzw$',type,
    'uzw$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_uzw$',axiom,
    'uzw$'('fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_image$n',type,
    'image$n': ( 'A_ZF_fun$' * 'A_set$' ) > 'ZF_set$' ).

tff('function_image$n',axiom,
    'image$n'('fmb_A_ZF_fun$_1','fmb_A_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_image$r',type,
    'image$r': ( 'Nat_ZF_fun$' * 'Nat_set$' ) > 'ZF_set$' ).

tff('function_image$r',axiom,
    'image$r'('fmb_Nat_ZF_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_image$ak',type,
    'image$ak': ( 'A_a_set_fun$' * 'A_set$' ) > 'A_set_set$' ).

tff('function_image$ak',axiom,
    'image$ak'('fmb_A_a_set_fun$_1','fmb_A_set$_1') = 'fmb_A_set_set$_1' ).

tff('declare_compDefined$a',type,
    'compDefined$a': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' ) > 'B_bool_fun$' ).

tff('function_compDefined$a',axiom,
    'compDefined$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_oppositeCategory$a',type,
    'oppositeCategory$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).

tff('function_oppositeCategory$a',axiom,
    'oppositeCategory$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_the$',type,
    'the$': 'ZF_bool_fun$' > 'ZF$' ).

tff('function_the$',axiom,
    'the$'('fmb_ZF_bool_fun$_1') = 'fmb_ZF$_1' ).

tff('declare_constFunctor$a',type,
    'constFunctor$a': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'ZF_ZF_unit_Category_ext$' * 'ZF$' ) > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('function_constFunctor$a',axiom,
    'constFunctor$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF$_1') = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ).

tff('declare_image$ag',type,
    'image$ag': ( 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' * 'Nat_ZF_ZF_prod_prod_set$' ) > 'ZF_set_ZF_prod_set$' ).

tff('function_image$ag',axiom,
    'image$ag'('fmb_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1','fmb_Nat_ZF_ZF_prod_prod_set$_1') = 'fmb_ZF_set_ZF_prod_set$_1' ).

tff('declare_uwb$',type,
    'uwb$': ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uwb$',axiom,
    'uwb$'('fmb_ZF_ZF_fun$_1','fmb_ZF_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_fun_app$a',type,
    'fun_app$a': ( 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).

tff('function_fun_app$a',axiom,
    'fun_app$a'('fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uvw$',type,
    'uvw$': ( 'ZF_b_fun$' * 'ZF_set$' * 'B_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uvw$',axiom,
    'uvw$'('fmb_ZF_b_fun$_1','fmb_ZF_set$_1','fmb_B_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_vap$',type,
    'vap$': ( 'Nat_ZF_ZF_set_fun_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_vap$',axiom,
    'vap$'('fmb_Nat_ZF_ZF_set_fun_fun$_1','fmb_ZF_nat_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_fun_app$as',type,
    'fun_app$as': ( 'ZF_b_fun$' * 'ZF$' ) > 'B$' ).

tff('function_fun_app$as',axiom,
    'fun_app$as'('fmb_ZF_b_fun$_1','fmb_ZF$_1') = 'fmb_B$_1' ).

tff('declare_uzf$',type,
    'uzf$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_ZF_set_fun_fun$' ).

tff('function_uzf$',axiom,
    'uzf$'('fmb_Nat_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_nat_ZF_set_fun_fun$_1' ).

tff('declare_image$ad',type,
    'image$ad': ( 'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$' * 'ZF_ZF_prod_ZF_prod_set$' ) > 'ZF_ZF_set_prod_set$' ).

tff('function_image$ad',axiom,
    'image$ad'('fmb_ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$_1','fmb_ZF_ZF_prod_ZF_prod_set$_1') = 'fmb_ZF_ZF_set_prod_set$_1' ).

tff('declare_uxv$',type,
    'uxv$': 'Nat_set$' > 'ZF_ZF_prod_nat_set_fun$' ).

tff('function_uxv$',axiom,
    'uxv$'('fmb_Nat_set$_1') = 'fmb_ZF_ZF_prod_nat_set_fun$_1' ).

tff('declare_fun_app$af',type,
    'fun_app$af': ( 'Nat_set_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set$' ).

tff('function_fun_app$af',axiom,
    'fun_app$af'('fmb_Nat_set_ZF_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_image$g',type,
    'image$g': 'ZF_ZF_fun$' > 'ZF_set_ZF_set_fun$' ).

tff('function_image$g',axiom,
    'image$g'('fmb_ZF_ZF_fun$_1') = 'fmb_ZF_set_ZF_set_fun$_1' ).

tff('declare_rec_set_bool$',type,
    'rec_set_bool$': ( 'ZF$' * 'ZF$' * tlbool ) > 'ZF_bool_fun$' ).

tff('function_rec_set_bool$',axiom,
    ( ( 'rec_set_bool$'('fmb_ZF$_1','fmb_ZF$_1',fmb_tlbool_1) = 'fmb_ZF_bool_fun$_1' )
    & ( 'rec_set_bool$'('fmb_ZF$_1','fmb_ZF$_1',fmb_tlbool_2) = 'fmb_ZF_bool_fun$_1' ) ) ).

tff('declare_fun_app$bh',type,
    'fun_app$bh': ( 'A_set_a_set_fun$' * 'A_set$' ) > 'A_set$' ).

tff('function_fun_app$bh',axiom,
    'fun_app$bh'('fmb_A_set_a_set_fun$_1','fmb_A_set$_1') = 'fmb_A_set$_1' ).

tff('declare_vag$',type,
    'vag$': 'ZF_set_set$' > 'ZF_bool_fun$' ).

tff('function_vag$',axiom,
    'vag$'('fmb_ZF_set_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uxr$',type,
    'uxr$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' ).

tff('function_uxr$',axiom,
    'uxr$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_1' ).

tff('declare_fun_app$br',type,
    'fun_app$br': ( 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff('function_fun_app$br',axiom,
    'fun_app$br'('fmb_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1' ).

tff('declare_fun_app$bx',type,
    'fun_app$bx': ( 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' * 'ZF$' ) > 'ZF_ZF_prod_ZF_set_ZF_prod_fun$' ).

tff('function_fun_app$bx',axiom,
    'fun_app$bx'('fmb_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_prod_ZF_set_ZF_prod_fun$_1' ).

tff('declare_case_prod$m',type,
    'case_prod$m': 'ZF_nat_ZF_ZF_prod_set_fun_fun$' > 'ZF_nat_prod_ZF_ZF_prod_set_fun$' ).

tff('function_case_prod$m',axiom,
    'case_prod$m'('fmb_ZF_nat_ZF_ZF_prod_set_fun_fun$_1') = 'fmb_ZF_nat_prod_ZF_ZF_prod_set_fun$_1' ).

tff('declare_case_prod$c',type,
    'case_prod$c': 'ZF_ZF_ZF_ZF_prod_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).

tff('function_case_prod$c',axiom,
    'case_prod$c'('fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1' ).

tff('declare_gr$c',type,
    'gr$c': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff('function_gr$c',axiom,
    'gr$c'('fmb_ZF_set$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uvm$',type,
    'uvm$': ( 'A_a_fun$' * 'A_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvm$',axiom,
    'uvm$'('fmb_A_a_fun$_1','fmb_A_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_uvf$',type,
    'uvf$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uvf$',axiom,
    'uvf$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_vaq$',type,
    'vaq$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$' ).

tff('function_vaq$',axiom,
    'vaq$'('fmb_Nat_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_nat_fun_ZF_set_fun$_1' ).

tff('declare_uwn$',type,
    'uwn$': ( 'B_ZF_fun$' * 'B_set$' ) > 'ZF_bool_fun$' ).

tff('function_uwn$',axiom,
    'uwn$'('fmb_B_ZF_fun$_1','fmb_B_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_identityFunctor$',type,
    'identityFunctor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('function_identityFunctor$',axiom,
    'identityFunctor$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1' ).

tff('declare_image$i',type,
    'image$i': ( 'ZF_a_fun$' * 'ZF_set$' ) > 'A_set$' ).

tff('function_image$i',axiom,
    'image$i'('fmb_ZF_a_fun$_1','fmb_ZF_set$_1') = 'fmb_A_set$_1' ).

tff('declare_lSCategory_ext$',type,
    'lSCategory_ext$': ( 'B_ZF_fun$' * 'C$' ) > 'B_c_LSCategory_ext$' ).

tff('function_lSCategory_ext$',axiom,
    'lSCategory_ext$'('fmb_B_ZF_fun$_1','fmb_C$_1') = 'fmb_B_c_LSCategory_ext$_1' ).

tff('declare_identityFunctor$a',type,
    'identityFunctor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).

tff('function_identityFunctor$a',axiom,
    'identityFunctor$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1' ).

tff('declare_fun_app$ar',type,
    'fun_app$ar': ( 'B_ZF_fun$' * 'B$' ) > 'ZF$' ).

tff('function_fun_app$ar',axiom,
    'fun_app$ar'('fmb_B_ZF_fun$_1','fmb_B$_1') = 'fmb_ZF$_1' ).

tff('declare_restrict$b',type,
    'restrict$b': ( 'B_a_fun$' * 'B_set$' ) > 'B_a_fun$' ).

tff('function_restrict$b',axiom,
    'restrict$b'('fmb_B_a_fun$_1','fmb_B_set$_1') = 'fmb_B_a_fun$_1' ).

tff('declare_fun_app$d',type,
    'fun_app$d': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF$' ) > 'ZF_ZF_prod$' ).

tff('function_fun_app$d',axiom,
    'fun_app$d'('fmb_ZF_ZF_ZF_prod_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_prod$_1' ).

tff('declare_fun_app$cp',type,
    'fun_app$cp': ( 'Nat_a_fun$' * 'Nat$' ) > 'A$' ).

tff('function_fun_app$cp',axiom,
    'fun_app$cp'('fmb_Nat_a_fun$_1','fmb_Nat$_1') = 'fmb_A$_1' ).

tff('declare_uyw$',type,
    'uyw$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_ZF_set_fun_fun$' ).

tff('function_uyw$',axiom,
    'uyw$'('fmb_ZF_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_ZF_set_fun_fun$_1' ).

tff('declare_image$c',type,
    'image$c': ( 'ZF_set_set_bool_fun$' * 'ZF_set_set_set$' ) > 'Bool_set$' ).

tff('function_image$c',axiom,
    'image$c'('fmb_ZF_set_set_bool_fun$_1','fmb_ZF_set_set_set$_1') = 'fmb_Bool_set$_1' ).

tff('declare_inverse_rel$a',type,
    'inverse_rel$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_inverse_rel$a',axiom,
    'inverse_rel$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_image$x',type,
    'image$x': ( 'Nat_a_fun$' * 'Nat_set$' ) > 'A_set$' ).

tff('function_image$x',axiom,
    'image$x'('fmb_Nat_a_fun$_1','fmb_Nat_set$_1') = 'fmb_A_set$_1' ).

tff('declare_case_prod$d',type,
    'case_prod$d': 'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' > 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' ).

tff('function_case_prod$d',axiom,
    'case_prod$d'('fmb_ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1') = 'fmb_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1' ).

tff('declare_case_prod$g',type,
    'case_prod$g': 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' > 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$' ).

tff('function_case_prod$g',axiom,
    'case_prod$g'('fmb_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_1') = 'fmb_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$_1' ).

tff('declare_uvy$',type,
    'uvy$': ( 'A_ZF_fun$' * 'A_set$' * 'ZF_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvy$',axiom,
    'uvy$'('fmb_A_ZF_fun$_1','fmb_A_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_fun_app$ab',type,
    'fun_app$ab': ( 'ZF_nat_ZF_set_fun_fun$' * 'ZF$' ) > 'Nat_ZF_set_fun$' ).

tff('function_fun_app$ab',axiom,
    'fun_app$ab'('fmb_ZF_nat_ZF_set_fun_fun$_1','fmb_ZF$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_vai$',type,
    'vai$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_vai$',axiom,
    'vai$'('fmb_ZF_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_van$',type,
    'van$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_fun_ZF_set_fun$' ).

tff('function_van$',axiom,
    'van$'('fmb_ZF_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_ZF_fun_ZF_set_fun$_1' ).

tff('declare_uvq$',type,
    'uvq$': ( 'A_b_fun$' * 'A_set$' * 'B_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvq$',axiom,
    'uvq$'('fmb_A_b_fun$_1','fmb_A_set$_1','fmb_B_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_uxu$',type,
    'uxu$': ( 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$' ).

tff('function_uxu$',axiom,
    'uxu$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_1' ).

tff('declare_member$',type,
    'member$': 'ZF$' > 'ZF_set_bool_fun$' ).

tff('function_member$',axiom,
    'member$'('fmb_ZF$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_vat$',type,
    'vat$': 'Nat_nat_ZF_set_fun_fun$' > 'Nat_nat_fun_ZF_set_fun$' ).

tff('function_vat$',axiom,
    'vat$'('fmb_Nat_nat_ZF_set_fun_fun$_1') = 'fmb_Nat_nat_fun_ZF_set_fun$_1' ).

tff('declare_fun_app$cu',type,
    'fun_app$cu': ( 'B_b_set_fun$' * 'B$' ) > 'B_set$' ).

tff('function_fun_app$cu',axiom,
    'fun_app$cu'('fmb_B_b_set_fun$_1','fmb_B$_1') = 'fmb_B_set$_1' ).

tff('declare_uwe$',type,
    'uwe$': ( 'ZF_set_a_fun$' * 'ZF_set_set$' * 'A_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff('function_uwe$',axiom,
    'uwe$'('fmb_ZF_set_a_fun$_1','fmb_ZF_set_set$_1','fmb_A_bool_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_uum$',type,
    'uum$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).

tff('function_uum$',axiom,
    'uum$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_b_b_fun_fun$_1' ).

tff('declare_uyx$',type,
    'uyx$': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyx$',axiom,
    'uyx$'('fmb_ZF_ZF_ZF_set_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_image$b',type,
    'image$b': ( 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'Bool_set$' ).

tff('function_image$b',axiom,
    'image$b'('fmb_ZF_set_bool_fun$_1','fmb_ZF_set_set$_1') = 'fmb_Bool_set$_1' ).

tff('declare_uwo$',type,
    'uwo$': ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_bool_fun$' ).

tff('function_uwo$',axiom,
    'uwo$'('fmb_ZF_ZF_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uya$',type,
    'uya$': 'ZF_ZF_prod_set$' > 'Nat_ZF_ZF_prod_set_fun$' ).

tff('function_uya$',axiom,
    'uya$'('fmb_ZF_ZF_prod_set$_1') = 'fmb_Nat_ZF_ZF_prod_set_fun$_1' ).

tff('declare_collect$f',type,
    'collect$f': 'A_b_fun_bool_fun$' > 'A_b_fun_set$' ).

tff('function_collect$f',axiom,
    'collect$f'('fmb_A_b_fun_bool_fun$_1') = 'fmb_A_b_fun_set$_1' ).

tff('declare_relInvImage$a',type,
    'relInvImage$a': ( 'Nat_set$' * 'ZF_set_ZF_set_prod_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_nat_prod_set$' ).

tff('function_relInvImage$a',axiom,
    'relInvImage$a'('fmb_Nat_set$_1','fmb_ZF_set_ZF_set_prod_set$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_nat_prod_set$_1' ).

tff('declare_uxs$',type,
    'uxs$': 'ZF_set$' > 'ZF_ZF_prod_ZF_set_fun$' ).

tff('function_uxs$',axiom,
    'uxs$'('fmb_ZF_set$_1') = 'fmb_ZF_ZF_prod_ZF_set_fun$_1' ).

tff('declare_hOMCollection$',type,
    'hOMCollection$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_set_fun$' ).

tff('function_hOMCollection$',axiom,
    'hOMCollection$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_set_fun$_1' ).

tff('declare_image$y',type,
    'image$y': ( 'Nat_b_fun$' * 'Nat_set$' ) > 'B_set$' ).

tff('function_image$y',axiom,
    'image$y'('fmb_Nat_b_fun$_1','fmb_Nat_set$_1') = 'fmb_B_set$_1' ).

tff('declare_case_prod$h',type,
    'case_prod$h': 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' > 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$' ).

tff('function_case_prod$h',axiom,
    'case_prod$h'('fmb_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_1') = 'fmb_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_image$ab',type,
    'image$ab': ( 'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' * 'ZF_ZF_ZF_prod_prod_set$' ) > 'ZF_set_ZF_prod_set$' ).

tff('function_image$ab',axiom,
    'image$ab'('fmb_ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1','fmb_ZF_ZF_ZF_prod_prod_set$_1') = 'fmb_ZF_set_ZF_prod_set$_1' ).

tff('declare_fun_app$s',type,
    'fun_app$s': ( 'ZF_ZF_set_fun$' * 'ZF$' ) > 'ZF_set$' ).

tff('function_fun_app$s',axiom,
    'fun_app$s'('fmb_ZF_ZF_set_fun$_1','fmb_ZF$_1') = 'fmb_ZF_set$_1' ).

tff('declare_vaa$',type,
    'vaa$': 'ZF_nat_bool_fun_fun$' > 'Nat_ZF_set_fun$' ).

tff('function_vaa$',axiom,
    'vaa$'('fmb_ZF_nat_bool_fun_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_uyi$',type,
    'uyi$': 'ZF_set_set$' > 'ZF_ZF_set_set_fun$' ).

tff('function_uyi$',axiom,
    'uyi$'('fmb_ZF_set_set$_1') = 'fmb_ZF_ZF_set_set_fun$_1' ).

tff('declare_fun_app$cq',type,
    'fun_app$cq': ( 'Nat_b_fun$' * 'Nat$' ) > 'B$' ).

tff('function_fun_app$cq',axiom,
    'fun_app$cq'('fmb_Nat_b_fun$_1','fmb_Nat$_1') = 'fmb_B$_1' ).

tff('declare_fun_app$ae',type,
    'fun_app$ae': ( 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).

tff('function_fun_app$ae',axiom,
    'fun_app$ae'('fmb_ZF_set_ZF_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_inverse$a',type,
    'inverse$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).

tff('function_inverse$a',axiom,
    'inverse$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_mapO$',type,
    'mapO$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$' ).

tff('function_mapO$',axiom,
    'mapO$'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1') = 'fmb_A_ZF_fun$_1' ).

tff('declare_fun_app$y',type,
    'fun_app$y': ( 'Nat_ZF_fun_ZF_set_fun$' * 'Nat_ZF_fun$' ) > 'ZF_set$' ).

tff('function_fun_app$y',axiom,
    'fun_app$y'('fmb_Nat_ZF_fun_ZF_set_fun$_1','fmb_Nat_ZF_fun$_1') = 'fmb_ZF_set$_1' ).

tff('declare_image$ap',type,
    'image$ap': ( 'ZF_b_set_fun$' * 'ZF_set$' ) > 'B_set_set$' ).

tff('function_image$ap',axiom,
    'image$ap'('fmb_ZF_b_set_fun$_1','fmb_ZF_set$_1') = 'fmb_B_set_set$_1' ).

tff('declare_fun_app$bu',type,
    'fun_app$bu': ( 'Nat_ZF_ZF_set_prod_fun$' * 'Nat$' ) > 'ZF_ZF_set_prod$' ).

tff('function_fun_app$bu',axiom,
    'fun_app$bu'('fmb_Nat_ZF_ZF_set_prod_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_set_prod$_1' ).

tff('declare_fun_app$bg',type,
    'fun_app$bg': ( 'B_set_b_set_fun$' * 'B_set$' ) > 'B_set$' ).

tff('function_fun_app$bg',axiom,
    'fun_app$bg'('fmb_B_set_b_set_fun$_1','fmb_B_set$_1') = 'fmb_B_set$_1' ).

tff('declare_fun_app$bo',type,
    'fun_app$bo': ( 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' * 'Nat$' ) > 'ZF_ZF_ZF_prod_set_fun$' ).

tff('function_fun_app$bo',axiom,
    'fun_app$bo'('fmb_Nat_ZF_ZF_ZF_prod_set_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_ZF_prod_set_fun$_1' ).

tff('declare_category_ext$a',type,
    'category_ext$a': ( 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_ZF_fun_fun$' * 'Unit$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_category_ext$a',axiom,
    'category_ext$a'('fmb_ZF_set$_1','fmb_ZF_set$_1','fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_ZF_fun_fun$_1','fmb_Unit$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_uyo$',type,
    'uyo$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_ZF_prod_set_fun$' ).

tff('function_uyo$',axiom,
    'uyo$'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_ZF_prod_set_fun$_1' ).

tff('declare_homFtorMap$',type,
    'homFtorMap$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'B_ZF_fun$' ).

tff('function_homFtorMap$',axiom,
    'homFtorMap$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_B_ZF_fun$_1' ).

tff('declare_uzt$',type,
    'uzt$': ( 'Nat_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_nat_ZF_ZF_prod_set_fun_fun$' ).

tff('function_uzt$',axiom,
    'uzt$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_nat_ZF_ZF_prod_set_fun_fun$_1' ).

tff('declare_uuq$',type,
    'uuq$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' ) > 'ZF_ZF_fun$' ).

tff('function_uuq$',axiom,
    'uuq$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_fun_app$bt',type,
    'fun_app$bt': ( 'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_ZF_set_prod_fun$' ).

tff('function_fun_app$bt',axiom,
    'fun_app$bt'('fmb_ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_ZF_ZF_set_prod_fun$_1' ).

tff('declare_extensional$',type,
    'extensional$': 'B_set$' > 'B_a_fun_set$' ).

tff('function_extensional$',axiom,
    'extensional$'('fmb_B_set$_1') = 'fmb_B_a_fun_set$_1' ).

tff('declare_image$aj',type,
    'image$aj': ( 'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_image$aj',axiom,
    'image$aj'('fmb_ZF_ZF_prod_ZF_set_ZF_set_prod_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_image$d',type,
    'image$d': ( 'B_set_bool_fun$' * 'B_set_set$' ) > 'Bool_set$' ).

tff('function_image$d',axiom,
    'image$d'('fmb_B_set_bool_fun$_1','fmb_B_set_set$_1') = 'fmb_Bool_set$_1' ).

tff('declare_fun_app$cw',type,
    'fun_app$cw': ( 'ZF_b_set_fun$' * 'ZF$' ) > 'B_set$' ).

tff('function_fun_app$cw',axiom,
    'fun_app$cw'('fmb_ZF_b_set_fun$_1','fmb_ZF$_1') = 'fmb_B_set$_1' ).

tff('declare_uuo$',type,
    'uuo$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'ZF$' ) > 'B_bool_fun$' ).

tff('function_uuo$',axiom,
    'uuo$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_ZF$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_uuy$',type,
    'uuy$': ( 'B_set$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uuy$',axiom,
    'uuy$'('fmb_B_set$_1','fmb_B_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_uyy$',type,
    'uyy$': ( 'ZF_nat_ZF_set_fun_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyy$',axiom,
    'uyy$'('fmb_ZF_nat_ZF_set_fun_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_collect$',type,
    'collect$': 'ZF_bool_fun$' > 'ZF_set$' ).

tff('function_collect$',axiom,
    'collect$'('fmb_ZF_bool_fun$_1') = 'fmb_ZF_set$_1' ).

tff('declare_fun_app$ao',type,
    'fun_app$ao': ( 'ZF_nat_fun$' * 'ZF$' ) > 'Nat$' ).

tff('function_fun_app$ao',axiom,
    'fun_app$ao'('fmb_ZF_nat_fun$_1','fmb_ZF$_1') = 'fmb_Nat$_1' ).

tff('declare_vae$',type,
    'vae$': 'B_set_set$' > 'B_bool_fun$' ).

tff('function_vae$',axiom,
    'vae$'('fmb_B_set_set$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_member$b',type,
    'member$b': 'B$' > 'B_set_bool_fun$' ).

tff('function_member$b',axiom,
    'member$b'('fmb_B$_1') = 'fmb_B_set_bool_fun$_1' ).

tff('declare_fun_app$ac',type,
    'fun_app$ac': ( 'Nat_ZF_ZF_set_fun_fun$' * 'Nat$' ) > 'ZF_ZF_set_fun$' ).

tff('function_fun_app$ac',axiom,
    'fun_app$ac'('fmb_Nat_ZF_ZF_set_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_more_update$',type,
    'more_update$': ( 'Unit_unit_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_more_update$',axiom,
    'more_update$'('fmb_Unit_unit_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_image$aa',type,
    'image$aa': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_image$aa',axiom,
    'image$aa'('fmb_Nat_ZF_ZF_prod_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uzy$',type,
    'uzy$': 'ZF_nat_bool_fun_fun$' > 'ZF_bool_fun$' ).

tff('function_uzy$',axiom,
    'uzy$'('fmb_ZF_nat_bool_fun_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uxw$',type,
    'uxw$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_ZF_set_set_fun$' ).

tff('function_uxw$',axiom,
    'uxw$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_set_set_fun$_1' ).

tff('declare_comp$b',type,
    'comp$b': 'ZF_ZF_fun$' > 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).

tff('function_comp$b',axiom,
    'comp$b'('fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1' ).

tff('declare_more$',type,
    'more$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_c_LSCategory_ext$' ).

tff('function_more$',axiom,
    'more$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_c_LSCategory_ext$_1' ).

tff('declare_uwh$',type,
    'uwh$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uwh$',axiom,
    'uwh$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uyr$',type,
    'uyr$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uyr$',axiom,
    'uyr$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_restrict$',type,
    'restrict$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_ZF_fun$' ).

tff('function_restrict$',axiom,
    'restrict$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_ZF_fun$_1' ).

tff('declare_image$bi',type,
    'image$bi': ( 'B_set_b_bool_fun_fun$' * 'B_set_set$' ) > 'B_bool_fun_set$' ).

tff('function_image$bi',axiom,
    'image$bi'('fmb_B_set_b_bool_fun_fun$_1','fmb_B_set_set$_1') = 'fmb_B_bool_fun_set$_1' ).

tff('declare_more$a',type,
    'more$a': 'ZF_ZF_unit_Category_ext$' > 'Unit$' ).

tff('function_more$a',axiom,
    'more$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_Unit$_1' ).

tff('declare_uvs$',type,
    'uvs$': ( 'B_b_fun$' * 'B_set$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).

tff('function_uvs$',axiom,
    'uvs$'('fmb_B_b_fun$_1','fmb_B_set$_1','fmb_B_bool_fun$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_comp$i',type,
    'comp$i': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set_ZF_set_set_fun$' ) > 'ZF_set_set_ZF_set_fun$' ).

tff('function_comp$i',axiom,
    'comp$i'('fmb_ZF_set_set_ZF_set_fun$_1','fmb_ZF_set_set_ZF_set_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_fun$_1' ).

tff('declare_image$bn',type,
    'image$bn': ( 'ZF_ZF_fun_ZF_set_fun$' * 'ZF_ZF_fun_set$' ) > 'ZF_set_set$' ).

tff('function_image$bn',axiom,
    'image$bn'('fmb_ZF_ZF_fun_ZF_set_fun$_1','fmb_ZF_ZF_fun_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_fun_app$cb',type,
    'fun_app$cb': ( 'ZF_nat_ZF_set_ZF_set_prod_fun_fun$' * 'ZF$' ) > 'Nat_ZF_set_ZF_set_prod_fun$' ).

tff('function_fun_app$cb',axiom,
    'fun_app$cb'('fmb_ZF_nat_ZF_set_ZF_set_prod_fun_fun$_1','fmb_ZF$_1') = 'fmb_Nat_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_fun_app$bs',type,
    'fun_app$bs': ( 'ZF_ZF_ZF_set_prod_fun$' * 'ZF$' ) > 'ZF_ZF_set_prod$' ).

tff('function_fun_app$bs',axiom,
    'fun_app$bs'('fmb_ZF_ZF_ZF_set_prod_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_set_prod$_1' ).

tff('declare_vaj$',type,
    'vaj$': ( 'ZF_ZF_ZF_set_fun_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_vaj$',axiom,
    'vaj$'('fmb_ZF_ZF_ZF_set_fun_fun$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_restrict$c',type,
    'restrict$c': ( 'A_b_fun$' * 'A_set$' ) > 'A_b_fun$' ).

tff('function_restrict$c',axiom,
    'restrict$c'('fmb_A_b_fun$_1','fmb_A_set$_1') = 'fmb_A_b_fun$_1' ).

tff('declare_dom$',type,
    'dom$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).

tff('function_dom$',axiom,
    'dom$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_a_fun$_1' ).

tff('declare_uzk$',type,
    'uzk$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_set_fun$' ).

tff('function_uzk$',axiom,
    'uzk$'('fmb_ZF_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_set_set_fun$_1' ).

tff('declare_vak$',type,
    'vak$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$' ).

tff('function_vak$',axiom,
    'vak$'('fmb_ZF_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_fun_ZF_set_fun$_1' ).

tff('declare_image$o',type,
    'image$o': ( 'A_b_fun$' * 'A_set$' ) > 'B_set$' ).

tff('function_image$o',axiom,
    'image$o'('fmb_A_b_fun$_1','fmb_A_set$_1') = 'fmb_B_set$_1' ).

tff('declare_fun_app$bb',type,
    'fun_app$bb': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set$' ).

tff('function_fun_app$bb',axiom,
    'fun_app$bb'('fmb_ZF_ZF_prod_ZF_set_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_set$_1' ).

tff('declare_uzr$',type,
    'uzr$': ( 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'Nat_ZF_ZF_ZF_prod_set_fun_fun$' ).

tff('function_uzr$',axiom,
    'uzr$'('fmb_Nat_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_Nat_ZF_ZF_ZF_prod_set_fun_fun$_1' ).

tff('declare_case_prod$p',type,
    'case_prod$p': 'ZF_ZF_ZF_ZF_prod_set_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' ).

tff('function_case_prod$p',axiom,
    'case_prod$p'('fmb_ZF_ZF_ZF_ZF_prod_set_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1' ).

tff('declare_uwg$',type,
    'uwg$': ( 'ZF_ZF_set_fun$' * 'ZF_bool_fun$' ) > 'ZF_set_bool_fun$' ).

tff('function_uwg$',axiom,
    'uwg$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_case_prod$b',type,
    'case_prod$b': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_prod_bool_fun$' ).

tff('function_case_prod$b',axiom,
    'case_prod$b'('fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_ZF_prod_bool_fun$_1' ).

tff('declare_lambda$',type,
    'lambda$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).

tff('function_lambda$',axiom,
    'lambda$'('fmb_ZF$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF$_1' ).

tff('declare_uzo$',type,
    'uzo$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'ZF_nat_ZF_ZF_prod_set_fun_fun$' ).

tff('function_uzo$',axiom,
    'uzo$'('fmb_ZF_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_ZF_nat_ZF_ZF_prod_set_fun_fun$_1' ).

tff('declare_cod$a',type,
    'cod$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).

tff('function_cod$a',axiom,
    'cod$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uvn$',type,
    'uvn$': ( 'B_a_fun$' * 'B_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvn$',axiom,
    'uvn$'('fmb_B_a_fun$_1','fmb_B_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_more$b',type,
    'more$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'C$' ).

tff('function_more$b',axiom,
    'more$b'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_C$_1' ).

tff('declare_fun_app$v',type,
    'fun_app$v': ( 'Nat_set_ZF_set_set_fun$' * 'Nat_set$' ) > 'ZF_set_set$' ).

tff('function_fun_app$v',axiom,
    'fun_app$v'('fmb_Nat_set_ZF_set_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_vad$',type,
    'vad$': 'A_set_set$' > 'A_bool_fun$' ).

tff('function_vad$',axiom,
    'vad$'('fmb_A_set_set$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_fun_app$cf',type,
    'fun_app$cf': ( 'ZF_ZF_prod_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_set$' ).

tff('function_fun_app$cf',axiom,
    'fun_app$cf'('fmb_ZF_ZF_prod_ZF_ZF_prod_set_fun$_1','fmb_ZF_ZF_prod$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_comp$',type,
    'comp$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_comp$',axiom,
    'comp$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_image$ar',type,
    'image$ar': ( 'B_ZF_set_fun$' * 'B_set$' ) > 'ZF_set_set$' ).

tff('function_image$ar',axiom,
    'image$ar'('fmb_B_ZF_set_fun$_1','fmb_B_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_zF2mor$',type,
    'zF2mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_b_fun$' ).

tff('function_zF2mor$',axiom,
    'zF2mor$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_ZF_b_fun$_1' ).

tff('declare_uus$',type,
    'uus$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_uus$',axiom,
    'uus$'('fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_image$t',type,
    'image$t': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_image$t',axiom,
    'image$t'('fmb_ZF_ZF_prod_ZF_ZF_prod_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uxz$',type,
    'uxz$': ( 'Nat_ZF_set_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' ).

tff('function_uxz$',axiom,
    'uxz$'('fmb_Nat_ZF_set_fun$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1' ).

tff('declare_dom_update$a',type,
    'dom_update$a': ( 'ZF_ZF_fun_ZF_ZF_fun_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_dom_update$a',axiom,
    'dom_update$a'('fmb_ZF_ZF_fun_ZF_ZF_fun_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_uwm$',type,
    'uwm$': ( 'A_ZF_fun$' * 'A_set$' ) > 'ZF_bool_fun$' ).

tff('function_uwm$',axiom,
    'uwm$'('fmb_A_ZF_fun$_1','fmb_A_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_fun_app$ce',type,
    'fun_app$ce': ( 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' * 'Nat$' ) > 'Nat_ZF_set_ZF_set_prod_fun$' ).

tff('function_fun_app$ce',axiom,
    'fun_app$ce'('fmb_Nat_nat_ZF_set_ZF_set_prod_fun_fun$_1','fmb_Nat$_1') = 'fmb_Nat_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_fun_app$cm',type,
    'fun_app$cm': ( 'Unit_unit_fun$' * 'Unit$' ) > 'Unit$' ).

tff('function_fun_app$cm',axiom,
    'fun_app$cm'('fmb_Unit_unit_fun$_1','fmb_Unit$_1') = 'fmb_Unit$_1' ).

tff('declare_fun_app$at',type,
    'fun_app$at': ( 'Nat_ZF_bool_fun_fun$' * 'Nat$' ) > 'ZF_bool_fun$' ).

tff('function_fun_app$at',axiom,
    'fun_app$at'('fmb_Nat_ZF_bool_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_homFtorMapContra$',type,
    'homFtorMapContra$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' ) > 'A_ZF_fun$' ).

tff('function_homFtorMapContra$',axiom,
    'homFtorMapContra$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1') = 'fmb_A_ZF_fun$_1' ).

tff('declare_uue$',type,
    'uue$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_uue$',axiom,
    'uue$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_uzj$',type,
    'uzj$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_set_fun$' ).

tff('function_uzj$',axiom,
    'uzj$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_set_set_fun$_1' ).

tff('declare_uzq$',type,
    'uzq$': 'ZF_ZF_set_fun$' > 'ZF_ZF_ZF_set_fun_fun$' ).

tff('function_uzq$',axiom,
    'uzq$'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_ZF_set_fun_fun$_1' ).

tff('declare_collect$g',type,
    'collect$g': 'Nat_bool_fun$' > 'Nat_set$' ).

tff('function_collect$g',axiom,
    'collect$g'('fmb_Nat_bool_fun$_1') = 'fmb_Nat_set$_1' ).

tff('declare_constFunctor$c',type,
    'constFunctor$c': ( 'ZF_ZF_unit_Category_ext$' * 'ZF_ZF_unit_Category_ext$' * 'ZF$' ) > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).

tff('function_constFunctor$c',axiom,
    'constFunctor$c'('fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF_ZF_unit_Category_ext$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1' ).

tff('declare_fun_app$by',type,
    'fun_app$by': ( 'ZF_ZF_set_ZF_set_prod_fun$' * 'ZF$' ) > 'ZF_set_ZF_set_prod$' ).

tff('function_fun_app$by',axiom,
    'fun_app$by'('fmb_ZF_ZF_set_ZF_set_prod_fun$_1','fmb_ZF$_1') = 'fmb_ZF_set_ZF_set_prod$_1' ).

tff('declare_fun_app$am',type,
    'fun_app$am': ( 'B_b_fun$' * 'B$' ) > 'B$' ).

tff('function_fun_app$am',axiom,
    'fun_app$am'('fmb_B_b_fun$_1','fmb_B$_1') = 'fmb_B$_1' ).

tff('declare_collect$h',type,
    'collect$h': 'A_bool_fun$' > 'A_set$' ).

tff('function_collect$h',axiom,
    'collect$h'('fmb_A_bool_fun$_1') = 'fmb_A_set$_1' ).

tff('declare_uzh$',type,
    'uzh$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uzh$',axiom,
    'uzh$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_ZF_prod_set_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_comp$a',type,
    'comp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).

tff('function_comp$a',axiom,
    'comp$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_b_b_fun_fun$_1' ).

tff('declare_fun_app$au',type,
    'fun_app$au': ( 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).

tff('function_fun_app$au',axiom,
    'fun_app$au'('fmb_ZF_ZF_prod_set_ZF_set_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_uyu$',type,
    'uyu$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_fun$' ).

tff('function_uyu$',axiom,
    'uyu$'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_set_fun$_1' ).

tff('declare_relImage$b',type,
    'relImage$b': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).

tff('function_relImage$b',axiom,
    'relImage$b'('fmb_ZF_ZF_prod_ZF_ZF_prod_prod_set$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uxx$',type,
    'uxx$': ( 'Nat_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$' ).

tff('function_uxx$',axiom,
    'uxx$'('fmb_Nat_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_1' ).

tff('declare_fun_app$bq',type,
    'fun_app$bq': ( 'Nat_nat_ZF_ZF_prod_set_fun_fun$' * 'Nat$' ) > 'Nat_ZF_ZF_prod_set_fun$' ).

tff('function_fun_app$bq',axiom,
    'fun_app$bq'('fmb_Nat_nat_ZF_ZF_prod_set_fun_fun$_1','fmb_Nat$_1') = 'fmb_Nat_ZF_ZF_prod_set_fun$_1' ).

tff('declare_product$',type,
    'product$': ( 'ZF_set$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_product$',axiom,
    'product$'('fmb_ZF_set$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uyd$',type,
    'uyd$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' ).

tff('function_uyd$',axiom,
    'uyd$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_1' ).

tff('declare_uvj$',type,
    'uvj$': ( 'Nat_ZF_set_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uvj$',axiom,
    'uvj$'('fmb_Nat_ZF_set_fun$_1','fmb_ZF_nat_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_uwq$',type,
    'uwq$': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF_ZF_fun$' ).

tff('function_uwq$',axiom,
    'uwq$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_ZF_prod_fun$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_pair$d',type,
    'pair$d': ( 'ZF_set$' * 'ZF_set$' ) > 'ZF_set_ZF_set_prod$' ).

tff('function_pair$d',axiom,
    'pair$d'('fmb_ZF_set$_1','fmb_ZF_set$_1') = 'fmb_ZF_set_ZF_set_prod$_1' ).

tff('declare_image$j',type,
    'image$j': ( 'ZF_set_a_fun$' * 'ZF_set_set$' ) > 'A_set$' ).

tff('function_image$j',axiom,
    'image$j'('fmb_ZF_set_a_fun$_1','fmb_ZF_set_set$_1') = 'fmb_A_set$_1' ).

tff('declare_fun_app$',type,
    'fun_app$': ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).

tff('function_fun_app$',axiom,
    'fun_app$'('fmb_ZF_ZF_fun$_1','fmb_ZF$_1') = 'fmb_ZF$_1' ).

tff('declare_fun_app$l',type,
    'fun_app$l': ( 'B_set_b_bool_fun_fun$' * 'B_set$' ) > 'B_bool_fun$' ).

tff('function_fun_app$l',axiom,
    'fun_app$l'('fmb_B_set_b_bool_fun_fun$_1','fmb_B_set$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_objIso$',type,
    'objIso$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_objIso$',axiom,
    'objIso$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_fun_app$ax',type,
    'fun_app$ax': ( 'ZF_ZF_set_set_fun$' * 'ZF$' ) > 'ZF_set_set$' ).

tff('function_fun_app$ax',axiom,
    'fun_app$ax'('fmb_ZF_ZF_set_set_fun$_1','fmb_ZF$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_fun_app$cs',type,
    'fun_app$cs': ( 'A_b_set_fun$' * 'A$' ) > 'B_set$' ).

tff('function_fun_app$cs',axiom,
    'fun_app$cs'('fmb_A_b_set_fun$_1','fmb_A$_1') = 'fmb_B_set$_1' ).

tff('declare_uzz$',type,
    'uzz$': ( 'ZF_nat_bool_fun_fun$' * 'Nat$' ) > 'ZF_bool_fun$' ).

tff('function_uzz$',axiom,
    'uzz$'('fmb_ZF_nat_bool_fun_fun$_1','fmb_Nat$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_fun_app$aw',type,
    'fun_app$aw': ( 'Nat_ZF_ZF_prod_set_fun$' * 'Nat$' ) > 'ZF_ZF_prod_set$' ).

tff('function_fun_app$aw',axiom,
    'fun_app$aw'('fmb_Nat_ZF_ZF_prod_set_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_collect$e',type,
    'collect$e': 'B_a_fun_bool_fun$' > 'B_a_fun_set$' ).

tff('function_collect$e',axiom,
    'collect$e'('fmb_B_a_fun_bool_fun$_1') = 'fmb_B_a_fun_set$_1' ).

tff('declare_fun_app$g',type,
    'fun_app$g': ( 'ZF_set_ZF_bool_fun_fun$' * 'ZF_set$' ) > 'ZF_bool_fun$' ).

tff('function_fun_app$g',axiom,
    'fun_app$g'('fmb_ZF_set_ZF_bool_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_restrict$d',type,
    'restrict$d': ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_ZF_fun$' ).

tff('function_restrict$d',axiom,
    'restrict$d'('fmb_ZF_ZF_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_image$af',type,
    'image$af': ( 'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$' * 'Nat_ZF_prod_set$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_image$af',axiom,
    'image$af'('fmb_Nat_ZF_prod_ZF_set_ZF_set_prod_fun$_1','fmb_Nat_ZF_prod_set$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_uvl$',type,
    'uvl$': ( 'A_a_fun$' * 'A_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvl$',axiom,
    'uvl$'('fmb_A_a_fun$_1','fmb_A_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_isomorphism$a',type,
    'isomorphism$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_bool_fun$' ).

tff('function_isomorphism$a',axiom,
    'isomorphism$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_bool_fun$_1' ).

tff('declare_image$bd',type,
    'image$bd': ( 'ZF_nat_prod_ZF_ZF_prod_set_fun$' * 'ZF_nat_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$bd',axiom,
    'image$bd'('fmb_ZF_nat_prod_ZF_ZF_prod_set_fun$_1','fmb_ZF_nat_prod_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_image$q',type,
    'image$q': 'ZF_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$' ).

tff('function_image$q',axiom,
    'image$q'('fmb_ZF_set_ZF_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_set_fun$_1' ).

tff('declare_fun_app$an',type,
    'fun_app$an': ( 'B_b_b_fun_fun$' * 'B$' ) > 'B_b_fun$' ).

tff('function_fun_app$an',axiom,
    'fun_app$an'('fmb_B_b_b_fun_fun$_1','fmb_B$_1') = 'fmb_B_b_fun$_1' ).

tff('declare_uwz$',type,
    'uwz$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set_ZF_set_set_fun$' ).

tff('function_uwz$',axiom,
    'uwz$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_set_ZF_set_set_fun$_1' ).

tff('declare_image$av',type,
    'image$av': 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set_set_ZF_set_set_fun$' ).

tff('function_image$av',axiom,
    'image$av'('fmb_ZF_ZF_prod_set_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_set_set_ZF_set_set_fun$_1' ).

tff('declare_image$aw',type,
    'image$aw': ( 'ZF_nat_set_fun$' * 'ZF_set$' ) > 'Nat_set_set$' ).

tff('function_image$aw',axiom,
    'image$aw'('fmb_ZF_nat_set_fun$_1','fmb_ZF_set$_1') = 'fmb_Nat_set_set$_1' ).

tff('declare_image$bp',type,
    'image$bp': ( 'ZF_nat_fun_ZF_set_fun$' * 'ZF_nat_fun_set$' ) > 'ZF_set_set$' ).

tff('function_image$bp',axiom,
    'image$bp'('fmb_ZF_nat_fun_ZF_set_fun$_1','fmb_ZF_nat_fun_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_fun_app$ap',type,
    'fun_app$ap': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).

tff('function_fun_app$ap',axiom,
    'fun_app$ap'('fmb_Nat_nat_fun$_1','fmb_Nat$_1') = 'fmb_Nat$_1' ).

tff('declare_image$am',type,
    'image$am': ( 'B_a_set_fun$' * 'B_set$' ) > 'A_set_set$' ).

tff('function_image$am',axiom,
    'image$am'('fmb_B_a_set_fun$_1','fmb_B_set$_1') = 'fmb_A_set_set$_1' ).

tff('declare_vab$',type,
    'vab$': 'ZF_ZF_set_fun$' > 'ZF_ZF_bool_fun_fun$' ).

tff('function_vab$',axiom,
    'vab$'('fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_bool_fun_fun$_1' ).

tff('declare_sup$b',type,
    'sup$b': 'A_set_set$' > 'A_set$' ).

tff('function_sup$b',axiom,
    'sup$b'('fmb_A_set_set$_1') = 'fmb_A_set$_1' ).

tff('declare_fun_app$z',type,
    'fun_app$z': ( 'ZF_ZF_fun_ZF_set_fun$' * 'ZF_ZF_fun$' ) > 'ZF_set$' ).

tff('function_fun_app$z',axiom,
    'fun_app$z'('fmb_ZF_ZF_fun_ZF_set_fun$_1','fmb_ZF_ZF_fun$_1') = 'fmb_ZF_set$_1' ).

tff('declare_isomorphism$',type,
    'isomorphism$': 'ZF_ZF_unit_Category_ext$' > 'ZF_bool_fun$' ).

tff('function_isomorphism$',axiom,
    'isomorphism$'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_image$ae',type,
    'image$ae': ( 'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$' * 'ZF_ZF_prod_nat_prod_set$' ) > 'ZF_ZF_set_prod_set$' ).

tff('function_image$ae',axiom,
    'image$ae'('fmb_ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$_1','fmb_ZF_ZF_prod_nat_prod_set$_1') = 'fmb_ZF_ZF_set_prod_set$_1' ).

tff('declare_uzi$',type,
    'uzi$': ( 'ZF_ZF_prod_ZF_fun$' * 'Nat_ZF_ZF_prod_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uzi$',axiom,
    'uzi$'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_Nat_ZF_ZF_prod_set_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_id$a',type,
    'id$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).

tff('function_id$a',axiom,
    'id$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_case_prod$k',type,
    'case_prod$k': 'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$' ).

tff('function_case_prod$k',axiom,
    'case_prod$k'('fmb_ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_1') = 'fmb_ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$_1' ).

tff('declare_sigma$j',type,
    'sigma$j': ( 'Nat_set$' * 'Nat_ZF_ZF_prod_set_fun$' ) > 'Nat_ZF_ZF_prod_prod_set$' ).

tff('function_sigma$j',axiom,
    'sigma$j'('fmb_Nat_set$_1','fmb_Nat_ZF_ZF_prod_set_fun$_1') = 'fmb_Nat_ZF_ZF_prod_prod_set$_1' ).

tff('declare_uzc$',type,
    'uzc$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_ZF_set_fun_fun$' ).

tff('function_uzc$',axiom,
    'uzc$'('fmb_Nat_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_nat_ZF_set_fun_fun$_1' ).

tff('declare_comp$c',type,
    'comp$c': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'Nat_set_set_ZF_set_set_set_fun$' ) > 'Nat_set_set_ZF_set_set_fun$' ).

tff('function_comp$c',axiom,
    'comp$c'('fmb_ZF_set_set_set_ZF_set_set_fun$_1','fmb_Nat_set_set_ZF_set_set_set_fun$_1') = 'fmb_Nat_set_set_ZF_set_set_fun$_1' ).

tff('declare_uvd$',type,
    'uvd$': ( 'ZF_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_fun$' ).

tff('function_uvd$',axiom,
    'uvd$'('fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_prod_ZF_fun$_1' ).

tff('declare_uvt$',type,
    'uvt$': ( 'ZF_a_fun$' * 'ZF_set$' * 'A_bool_fun$' ) > 'A_bool_fun$' ).

tff('function_uvt$',axiom,
    'uvt$'('fmb_ZF_a_fun$_1','fmb_ZF_set$_1','fmb_A_bool_fun$_1') = 'fmb_A_bool_fun$_1' ).

tff('declare_fun_app$dc',type,
    'fun_app$dc': ( 'ZF_ZF_prod_set_set_ZF_set_set_fun$' * 'ZF_ZF_prod_set_set$' ) > 'ZF_set_set$' ).

tff('function_fun_app$dc',axiom,
    'fun_app$dc'('fmb_ZF_ZF_prod_set_set_ZF_set_set_fun$_1','fmb_ZF_ZF_prod_set_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_constFunctor$b',type,
    'constFunctor$b': ( 'ZF_ZF_unit_Category_ext$' * 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' ).

tff('function_constFunctor$b',axiom,
    'constFunctor$b'('fmb_ZF_ZF_unit_Category_ext$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1' ).

tff('declare_fun_app$cz',type,
    'fun_app$cz': ( 'Nat_set_set_nat_set_fun$' * 'Nat_set_set$' ) > 'Nat_set$' ).

tff('function_fun_app$cz',axiom,
    'fun_app$cz'('fmb_Nat_set_set_nat_set_fun$_1','fmb_Nat_set_set$_1') = 'fmb_Nat_set$_1' ).

tff('declare_uwi$',type,
    'uwi$': ( 'ZF_ZF_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uwi$',axiom,
    'uwi$'('fmb_ZF_ZF_fun$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uyf$',type,
    'uyf$': ( 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' ).

tff('function_uyf$',axiom,
    'uyf$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_1' ).

tff('declare_image$k',type,
    'image$k': ( 'B_ZF_fun$' * 'B_set$' ) > 'ZF_set$' ).

tff('function_image$k',axiom,
    'image$k'('fmb_B_ZF_fun$_1','fmb_B_set$_1') = 'fmb_ZF_set$_1' ).

tff('declare_case_prod$j',type,
    'case_prod$j': 'Nat_nat_ZF_set_ZF_set_prod_fun_fun$' > 'Nat_nat_prod_ZF_set_ZF_set_prod_fun$' ).

tff('function_case_prod$j',axiom,
    'case_prod$j'('fmb_Nat_nat_ZF_set_ZF_set_prod_fun_fun$_1') = 'fmb_Nat_nat_prod_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_fun_app$ba',type,
    'fun_app$ba': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat$' ) > 'ZF_ZF_prod$' ).

tff('function_fun_app$ba',axiom,
    'fun_app$ba'('fmb_Nat_ZF_ZF_prod_fun$_1','fmb_Nat$_1') = 'fmb_ZF_ZF_prod$_1' ).

tff('declare_relImage$',type,
    'relImage$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set_ZF_set_prod_set$' ).

tff('function_relImage$',axiom,
    'relImage$'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_set_ZF_set_prod_set$_1' ).

tff('declare_image$be',type,
    'image$be': ( 'Nat_ZF_prod_ZF_ZF_prod_set_fun$' * 'Nat_ZF_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$be',axiom,
    'image$be'('fmb_Nat_ZF_prod_ZF_ZF_prod_set_fun$_1','fmb_Nat_ZF_prod_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_homFtor$a',type,
    'homFtor$a': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).

tff('function_homFtor$a',axiom,
    'homFtor$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1' ).

tff('declare_sigma$l',type,
    'sigma$l': ( 'Nat_set$' * 'Nat_ZF_set_set_fun$' ) > 'Nat_ZF_set_prod_set$' ).

tff('function_sigma$l',axiom,
    'sigma$l'('fmb_Nat_set$_1','fmb_Nat_ZF_set_set_fun$_1') = 'fmb_Nat_ZF_set_prod_set$_1' ).

tff('declare_fun_app$bj',type,
    'fun_app$bj': ( 'ZF_set_a_fun$' * 'ZF_set$' ) > 'A$' ).

tff('function_fun_app$bj',axiom,
    'fun_app$bj'('fmb_ZF_set_a_fun$_1','fmb_ZF_set$_1') = 'fmb_A$_1' ).

tff('declare_uzx$',type,
    'uzx$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_uzx$',axiom,
    'uzx$'('fmb_ZF_ZF_bool_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_relInvImage$',type,
    'relInvImage$': ( 'ZF_set$' * 'ZF_set_ZF_set_prod_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_prod_set$' ).

tff('function_relInvImage$',axiom,
    'relInvImage$'('fmb_ZF_set$_1','fmb_ZF_set_ZF_set_prod_set$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_case_prod$i',type,
    'case_prod$i': 'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$' > 'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$' ).

tff('function_case_prod$i',axiom,
    'case_prod$i'('fmb_Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_1') = 'fmb_Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_1' ).

tff('declare_vav$',type,
    'vav$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$' ).

tff('function_vav$',axiom,
    'vav$'('fmb_ZF_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_fun_ZF_set_fun$_1' ).

tff('declare_fun_app$ch',type,
    'fun_app$ch': ( 'B_a_fun_b_a_fun_fun$' * 'B_a_fun$' ) > 'B_a_fun$' ).

tff('function_fun_app$ch',axiom,
    'fun_app$ch'('fmb_B_a_fun_b_a_fun_fun$_1','fmb_B_a_fun$_1') = 'fmb_B_a_fun$_1' ).

tff('declare_image$bl',type,
    'image$bl': ( 'ZF_ZF_bool_fun_fun$' * 'ZF_set$' ) > 'ZF_bool_fun_set$' ).

tff('function_image$bl',axiom,
    'image$bl'('fmb_ZF_ZF_bool_fun_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_bool_fun_set$_1' ).

tff('declare_case_prod$o',type,
    'case_prod$o': 'Nat_nat_ZF_ZF_prod_set_fun_fun$' > 'Nat_nat_prod_ZF_ZF_prod_set_fun$' ).

tff('function_case_prod$o',axiom,
    'case_prod$o'('fmb_Nat_nat_ZF_ZF_prod_set_fun_fun$_1') = 'fmb_Nat_nat_prod_ZF_ZF_prod_set_fun$_1' ).

tff('declare_fun_app$da',type,
    'fun_app$da': ( 'ZF_set_set_set_ZF_set_set_fun$' * 'ZF_set_set_set$' ) > 'ZF_set_set$' ).

tff('function_fun_app$da',axiom,
    'fun_app$da'('fmb_ZF_set_set_set_ZF_set_set_fun$_1','fmb_ZF_set_set_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_uul$',type,
    'uul$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_ZF_fun_fun$' ).

tff('function_uul$',axiom,
    'uul$'('fmb_ZF_ZF_prod_ZF_fun$_1') = 'fmb_ZF_ZF_ZF_fun_fun$_1' ).

tff('declare_sigma$d',type,
    'sigma$d': ( 'Nat_set$' * 'Nat_nat_set_fun$' ) > 'Nat_nat_prod_set$' ).

tff('function_sigma$d',axiom,
    'sigma$d'('fmb_Nat_set$_1','fmb_Nat_nat_set_fun$_1') = 'fmb_Nat_nat_prod_set$_1' ).

tff('declare_image$s',type,
    'image$s': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_set$' ).

tff('function_image$s',axiom,
    'image$s'('fmb_ZF_ZF_prod_ZF_set_fun$_1','fmb_ZF_ZF_prod_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_image$v',type,
    'image$v': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).

tff('function_image$v',axiom,
    'image$v'('fmb_Nat_nat_fun$_1','fmb_Nat_set$_1') = 'fmb_Nat_set$_1' ).

tff('declare_uvx$',type,
    'uvx$': ( 'A_ZF_fun$' * 'A_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uvx$',axiom,
    'uvx$'('fmb_A_ZF_fun$_1','fmb_A_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_homSet$',type,
    'homSet$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'A$' ) > 'A_ZF_fun$' ).

tff('function_homSet$',axiom,
    'homSet$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_A$_1') = 'fmb_A_ZF_fun$_1' ).

tff('declare_image$bm',type,
    'image$bm': ( 'Nat_ZF_bool_fun_fun$' * 'Nat_set$' ) > 'ZF_bool_fun_set$' ).

tff('function_image$bm',axiom,
    'image$bm'('fmb_Nat_ZF_bool_fun_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_bool_fun_set$_1' ).

tff('declare_fun_app$cv',type,
    'fun_app$cv': ( 'ZF_a_set_fun$' * 'ZF$' ) > 'A_set$' ).

tff('function_fun_app$cv',axiom,
    'fun_app$cv'('fmb_ZF_a_set_fun$_1','fmb_ZF$_1') = 'fmb_A_set$_1' ).

tff('declare_uzl$',type,
    'uzl$': ( 'ZF_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_ZF_set_fun$' ).

tff('function_uzl$',axiom,
    'uzl$'('fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_set_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_pair$b',type,
    'pair$b': ( 'ZF$' * 'ZF_set$' ) > 'ZF_ZF_set_prod$' ).

tff('function_pair$b',axiom,
    'pair$b'('fmb_ZF$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_prod$_1' ).

tff('declare_mor_update$',type,
    'mor_update$': ( 'ZF_set_ZF_set_fun$' * 'ZF_ZF_unit_Category_ext$' ) > 'ZF_ZF_unit_Category_ext$' ).

tff('function_mor_update$',axiom,
    'mor_update$'('fmb_ZF_set_ZF_set_fun$_1','fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_image$bo',type,
    'image$bo': ( 'Nat_ZF_fun_ZF_set_fun$' * 'Nat_ZF_fun_set$' ) > 'ZF_set_set$' ).

tff('function_image$bo',axiom,
    'image$bo'('fmb_Nat_ZF_fun_ZF_set_fun$_1','fmb_Nat_ZF_fun_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_image$ay',type,
    'image$ay': ( 'Nat_set_ZF_set_fun$' * 'Nat_set_set$' ) > 'ZF_set_set$' ).

tff('function_image$ay',axiom,
    'image$ay'('fmb_Nat_set_ZF_set_fun$_1','fmb_Nat_set_set$_1') = 'fmb_ZF_set_set$_1' ).

tff('declare_image$bf',type,
    'image$bf': ( 'Nat_nat_prod_ZF_ZF_prod_set_fun$' * 'Nat_nat_prod_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$bf',axiom,
    'image$bf'('fmb_Nat_nat_prod_ZF_ZF_prod_set_fun$_1','fmb_Nat_nat_prod_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_sigma$i',type,
    'sigma$i': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_nat_set_fun$' ) > 'ZF_ZF_prod_nat_prod_set$' ).

tff('function_sigma$i',axiom,
    'sigma$i'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_nat_set_fun$_1') = 'fmb_ZF_ZF_prod_nat_prod_set$_1' ).

tff('declare_image$l',type,
    'image$l': 'B_b_fun$' > 'B_set_b_set_fun$' ).

tff('function_image$l',axiom,
    'image$l'('fmb_B_b_fun$_1') = 'fmb_B_set_b_set_fun$_1' ).

tff('declare_uxt$',type,
    'uxt$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_set_set_fun$' ).

tff('function_uxt$',axiom,
    'uxt$'('fmb_ZF_ZF_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_set_set_fun$_1' ).

tff('declare_image$at',type,
    'image$at': 'Nat_set_ZF_set_set_fun$' > 'Nat_set_set_ZF_set_set_set_fun$' ).

tff('function_image$at',axiom,
    'image$at'('fmb_Nat_set_ZF_set_set_fun$_1') = 'fmb_Nat_set_set_ZF_set_set_set_fun$_1' ).

tff('declare_vaz$',type,
    'vaz$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$' ).

tff('function_vaz$',axiom,
    'vaz$'('fmb_Nat_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_nat_fun_ZF_set_fun$_1' ).

tff('declare_uvk$',type,
    'uvk$': ( 'Nat_ZF_set_fun$' * 'Nat_nat_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uvk$',axiom,
    'uvk$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_nat_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_fun_app$q',type,
    'fun_app$q': ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' ) > 'ZF_bool_fun$' ).

tff('function_fun_app$q',axiom,
    'fun_app$q'('fmb_ZF_ZF_bool_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_uwc$',type,
    'uwc$': ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).

tff('function_uwc$',axiom,
    'uwc$'('fmb_ZF_ZF_fun$_1','fmb_ZF_set$_1','fmb_ZF_bool_fun$_1') = 'fmb_ZF_bool_fun$_1' ).

tff('declare_fun_app$bl',type,
    'fun_app$bl': ( 'A_b_fun$' * 'A$' ) > 'B$' ).

tff('function_fun_app$bl',axiom,
    'fun_app$bl'('fmb_A_b_fun$_1','fmb_A$_1') = 'fmb_B$_1' ).

tff('declare_uys$',type,
    'uys$': ( 'ZF_ZF_set_fun$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_fun$' ).

tff('function_uys$',axiom,
    'uys$'('fmb_ZF_ZF_set_fun$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_set_fun$_1' ).

tff('declare_gr$b',type,
    'gr$b': ( 'Nat_set$' * 'Nat_ZF_set_fun$' ) > 'Nat_ZF_set_prod_set$' ).

tff('function_gr$b',axiom,
    'gr$b'('fmb_Nat_set$_1','fmb_Nat_ZF_set_fun$_1') = 'fmb_Nat_ZF_set_prod_set$_1' ).

tff('declare_less_eq$c',type,
    'less_eq$c': 'ZF_set$' > 'ZF_set_bool_fun$' ).

tff('function_less_eq$c',axiom,
    'less_eq$c'('fmb_ZF_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_fun_app$c',type,
    'fun_app$c': ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).

tff('function_fun_app$c',axiom,
    'fun_app$c'('fmb_ZF_set_ZF_ZF_prod_set_fun$_1','fmb_ZF_set$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_uyj$',type,
    'uyj$': 'ZF_set_set$' > 'Nat_ZF_set_set_fun$' ).

tff('function_uyj$',axiom,
    'uyj$'('fmb_ZF_set_set$_1') = 'fmb_Nat_ZF_set_set_fun$_1' ).

tff('declare_vay$',type,
    'vay$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).

tff('function_vay$',axiom,
    'vay$'('fmb_Nat_ZF_ZF_set_fun_fun$_1') = 'fmb_ZF_ZF_set_fun$_1' ).

tff('declare_image$au',type,
    'image$au': 'ZF_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_set_set_fun$' ).

tff('function_image$au',axiom,
    'image$au'('fmb_ZF_set_ZF_set_set_fun$_1') = 'fmb_ZF_set_set_ZF_set_set_set_fun$_1' ).

tff('declare_pair$c',type,
    'pair$c': ( 'ZF_set$' * 'ZF$' ) > 'ZF_set_ZF_prod$' ).

tff('function_pair$c',axiom,
    'pair$c'('fmb_ZF_set$_1','fmb_ZF$_1') = 'fmb_ZF_set_ZF_prod$_1' ).

tff('declare_fun_app$e',type,
    'fun_app$e': ( 'ZF_ZF_ZF_ZF_prod_fun_fun$' * 'ZF$' ) > 'ZF_ZF_ZF_prod_fun$' ).

tff('function_fun_app$e',axiom,
    'fun_app$e'('fmb_ZF_ZF_ZF_ZF_prod_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_ZF_prod_fun$_1' ).

tff('declare_makeCat$a',type,
    'makeCat$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).

tff('function_makeCat$a',axiom,
    'makeCat$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_unit_Category_ext$_1' ).

tff('declare_image$u',type,
    'image$u': ( 'ZF_nat_fun$' * 'ZF_set$' ) > 'Nat_set$' ).

tff('function_image$u',axiom,
    'image$u'('fmb_ZF_nat_fun$_1','fmb_ZF_set$_1') = 'fmb_Nat_set$_1' ).

tff('declare_fun_app$bz',type,
    'fun_app$bz': ( 'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$' * 'ZF$' ) > 'ZF_ZF_set_ZF_set_prod_fun$' ).

tff('function_fun_app$bz',axiom,
    'fun_app$bz'('fmb_ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_1','fmb_ZF$_1') = 'fmb_ZF_ZF_set_ZF_set_prod_fun$_1' ).

tff('declare_dom$a',type,
    'dom$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).

tff('function_dom$a',axiom,
    'dom$a'('fmb_ZF_ZF_unit_Category_ext$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_fun_app$r',type,
    'fun_app$r': ( 'Nat_ZF_set_fun$' * 'Nat$' ) > 'ZF_set$' ).

tff('function_fun_app$r',axiom,
    'fun_app$r'('fmb_Nat_ZF_set_fun$_1','fmb_Nat$_1') = 'fmb_ZF_set$_1' ).

tff('declare_fun_app$t',type,
    'fun_app$t': ( 'Nat_nat_fun_ZF_set_fun$' * 'Nat_nat_fun$' ) > 'ZF_set$' ).

tff('function_fun_app$t',axiom,
    'fun_app$t'('fmb_Nat_nat_fun_ZF_set_fun$_1','fmb_Nat_nat_fun$_1') = 'fmb_ZF_set$_1' ).

tff('declare_fun_app$i',type,
    'fun_app$i': ( 'ZF_set_set_ZF_set_bool_fun_fun$' * 'ZF_set_set$' ) > 'ZF_set_bool_fun$' ).

tff('function_fun_app$i',axiom,
    'fun_app$i'('fmb_ZF_set_set_ZF_set_bool_fun_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_uup$',type,
    'uup$': ( 'A_b_b_c_LSCategory_ext_Category_ext$' * 'B$' ) > 'ZF_ZF_fun$' ).

tff('function_uup$',axiom,
    'uup$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_B$_1') = 'fmb_ZF_ZF_fun$_1' ).

tff('declare_uwj$',type,
    'uwj$': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set_bool_fun$' ).

tff('function_uwj$',axiom,
    'uwj$'('fmb_Nat_ZF_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_set_bool_fun$_1' ).

tff('declare_image$ba',type,
    'image$ba': ( 'Nat_ZF_ZF_prod_set_fun$' * 'Nat_set$' ) > 'ZF_ZF_prod_set_set$' ).

tff('function_image$ba',axiom,
    'image$ba'('fmb_Nat_ZF_ZF_prod_set_fun$_1','fmb_Nat_set$_1') = 'fmb_ZF_ZF_prod_set_set$_1' ).

tff('declare_image$bk',type,
    'image$bk': ( 'ZF_set_ZF_bool_fun_fun$' * 'ZF_set_set$' ) > 'ZF_bool_fun_set$' ).

tff('function_image$bk',axiom,
    'image$bk'('fmb_ZF_set_ZF_bool_fun_fun$_1','fmb_ZF_set_set$_1') = 'fmb_ZF_bool_fun_set$_1' ).

tff('declare_image$ao',type,
    'image$ao': ( 'ZF_a_set_fun$' * 'ZF_set$' ) > 'A_set_set$' ).

tff('function_image$ao',axiom,
    'image$ao'('fmb_ZF_a_set_fun$_1','fmb_ZF_set$_1') = 'fmb_A_set_set$_1' ).

tff('declare_collect$a',type,
    'collect$a': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_set$' ).

tff('function_collect$a',axiom,
    'collect$a'('fmb_ZF_ZF_prod_bool_fun$_1') = 'fmb_ZF_ZF_prod_set$_1' ).

tff('declare_mor$',type,
    'mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_set$' ).

tff('function_mor$',axiom,
    'mor$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') = 'fmb_B_set$_1' ).

tff('declare_less_eq$e',type,
    'less_eq$e': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > $o ).

tff('predicate_less_eq$e',axiom,
    'less_eq$e'('fmb_ZF_ZF_prod_set$_1','fmb_ZF_ZF_prod_set$_1') ).

tff('declare_functorM$',type,
    'functorM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).

tff('predicate_functorM$',axiom,
    'functorM$'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1') ).

tff('declare_fun_app$ak',type,
    'fun_app$ak': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' ) > $o ).

tff('predicate_fun_app$ak',axiom,
    'fun_app$ak'('fmb_ZF_ZF_prod_bool_fun$_1','fmb_ZF_ZF_prod$_1') ).

tff('declare_less_eq$f',type,
    'less_eq$f': ( 'ZF_ZF_set_prod_set$' * 'ZF_ZF_set_prod_set$' ) > $o ).

tff('predicate_less_eq$f',axiom,
    'less_eq$f'('fmb_ZF_ZF_set_prod_set$_1','fmb_ZF_ZF_set_prod_set$_1') ).

tff('declare_lSCategory$',type,
    'lSCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).

tff('predicate_lSCategory$',axiom,
    'lSCategory$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') ).

tff('declare_less_eq$k',type,
    'less_eq$k': ( 'B_bool_fun$' * 'B_bool_fun$' ) > $o ).

tff('predicate_less_eq$k',axiom,
    'less_eq$k'('fmb_B_bool_fun$_1','fmb_B_bool_fun$_1') ).

tff('declare_member$l',type,
    'member$l': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun_set$' ) > $o ).

tff('predicate_member$l',axiom,
    'member$l'('fmb_ZF_ZF_prod_ZF_fun$_1','fmb_ZF_ZF_prod_ZF_fun_set$_1') ).

tff('declare_category$a',type,
    'category$a': 'ZF_ZF_unit_Category_ext$' > $o ).

tff('predicate_category$a',axiom,
    'category$a'('fmb_ZF_ZF_unit_Category_ext$_1') ).

tff('declare_functorM$b',type,
    'functorM$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).

tff('predicate_functorM$b',axiom,
    'functorM$b'('fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1') ).

tff('declare_category$',type,
    'category$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).

tff('predicate_category$',axiom,
    'category$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') ).

tff('declare_functorM$a',type,
    'functorM$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).

tff('predicate_functorM$a',axiom,
    'functorM$a'('fmb_A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_1') ).

tff('declare_fun_app$ck',type,
    'fun_app$ck': ( 'B_a_fun_bool_fun$' * 'B_a_fun$' ) > $o ).

tff('predicate_fun_app$ck',axiom,
    'fun_app$ck'('fmb_B_a_fun_bool_fun$_1','fmb_B_a_fun$_1') ).

tff('declare_less_eq$m',type,
    'less_eq$m': ( 'ZF_set_bool_fun$' * 'ZF_set_bool_fun$' ) > $o ).

tff('predicate_less_eq$m',axiom,
    'less_eq$m'('fmb_ZF_set_bool_fun$_1','fmb_ZF_set_bool_fun$_1') ).

tff('declare_fun_app$h',type,
    'fun_app$h': ( 'ZF_set_bool_fun$' * 'ZF_set$' ) > $o ).

tff('predicate_fun_app$h',axiom,
    'fun_app$h'('fmb_ZF_set_bool_fun$_1','fmb_ZF_set$_1') ).

tff('declare_functor$b',type,
    'functor$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).

tff('predicate_functor$b',axiom,
    'functor$b'('fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1') ).

tff('declare_functor$a',type,
    'functor$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).

tff('predicate_functor$a',axiom,
    'functor$a'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1') ).

tff('declare_fun_app$f',type,
    'fun_app$f': ( 'ZF_bool_fun$' * 'ZF$' ) > $o ).

tff('predicate_fun_app$f',axiom,
    'fun_app$f'('fmb_ZF_bool_fun$_1','fmb_ZF$_1') ).

tff('declare_member$j',type,
    'member$j': ( 'B_b_prod$' * 'B_b_prod_set$' ) > $o ).

tff('predicate_member$j',axiom,
    'member$j'('fmb_B_b_prod$_1','fmb_B_b_prod_set$_1') ).

tff('declare_preFunctor$b',type,
    'preFunctor$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).

tff('predicate_preFunctor$b',axiom,
    ~ 'preFunctor$b'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1') ).

tff('declare_member$k',type,
    'member$k': ( 'B_b_prod_b_fun$' * 'B_b_prod_b_fun_set$' ) > $o ).

tff('predicate_member$k',axiom,
    ~ 'member$k'('fmb_B_b_prod_b_fun$_1','fmb_B_b_prod_b_fun_set$_1') ).

tff('declare_lSCategory_axioms$',type,
    'lSCategory_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).

tff('predicate_lSCategory_axioms$',axiom,
    'lSCategory_axioms$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') ).

tff('declare_extCategory$a',type,
    'extCategory$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).

tff('predicate_extCategory$a',axiom,
    ~ 'extCategory$a'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') ).

tff('declare_fun_app$ag',type,
    'fun_app$ag': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff('predicate_fun_app$ag',axiom,
    'fun_app$ag'('fmb_Nat_bool_fun$_1','fmb_Nat$_1') ).

tff('declare_member$g',type,
    'member$g': ( 'B_ZF_fun$' * 'B_ZF_fun_set$' ) > $o ).

tff('predicate_member$g',axiom,
    'member$g'('fmb_B_ZF_fun$_1','fmb_B_ZF_fun_set$_1') ).

tff('declare_extCategory$',type,
    'extCategory$': 'ZF_ZF_unit_Category_ext$' > $o ).

tff('predicate_extCategory$',axiom,
    'extCategory$'('fmb_ZF_ZF_unit_Category_ext$_1') ).

tff('declare_less_eq$i',type,
    'less_eq$i': ( 'Nat_set$' * 'Nat_set$' ) > $o ).

tff('predicate_less_eq$i',axiom,
    ~ 'less_eq$i'('fmb_Nat_set$_1','fmb_Nat_set$_1') ).

tff('declare_category_axioms$',type,
    'category_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).

tff('predicate_category_axioms$',axiom,
    'category_axioms$'('fmb_A_b_b_c_LSCategory_ext_Category_ext$_1') ).

tff('declare_functor_abbrev$',type,
    'functor_abbrev$': ( 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' * 'A_b_b_c_LSCategory_ext_Category_ext$' * 'ZF_ZF_unit_Category_ext$' ) > $o ).

tff('predicate_functor_abbrev$',axiom,
    'functor_abbrev$'('fmb_A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_1','fmb_A_b_b_c_LSCategory_ext_Category_ext$_1','fmb_ZF_ZF_unit_Category_ext$_1') ).

tff('declare_functorM$c',type,
    'functorM$c': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).

tff('predicate_functorM$c',axiom,
    'functorM$c'('fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1') ).

tff('declare_member$f',type,
    'member$f': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun_set$' ) > $o ).

tff('predicate_member$f',axiom,
    'member$f'('fmb_ZF_ZF_fun$_1','fmb_ZF_ZF_fun_set$_1') ).

tff('declare_less_eq$',type,
    'less_eq$': ( 'A_set$' * 'A_set$' ) > $o ).

tff('predicate_less_eq$',axiom,
    'less_eq$'('fmb_A_set$_1','fmb_A_set$_1') ).

tff('declare_less_eq$j',type,
    'less_eq$j': ( 'A_bool_fun$' * 'A_bool_fun$' ) > $o ).

tff('predicate_less_eq$j',axiom,
    'less_eq$j'('fmb_A_bool_fun$_1','fmb_A_bool_fun$_1') ).

tff('declare_less_eq$a',type,
    'less_eq$a': ( 'B_set$' * 'B_set$' ) > $o ).

tff('predicate_less_eq$a',axiom,
    'less_eq$a'('fmb_B_set$_1','fmb_B_set$_1') ).

tff('declare_fun_app$cl',type,
    'fun_app$cl': ( 'A_b_fun_bool_fun$' * 'A_b_fun$' ) > $o ).

tff('predicate_fun_app$cl',axiom,
    ~ 'fun_app$cl'('fmb_A_b_fun_bool_fun$_1','fmb_A_b_fun$_1') ).

tff('declare_sup$a',type,
    'sup$a': 'Bool_set$' > $o ).

tff('predicate_sup$a',axiom,
    'sup$a'('fmb_Bool_set$_1') ).

tff('declare_less_eq$l',type,
    'less_eq$l': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > $o ).

tff('predicate_less_eq$l',axiom,
    'less_eq$l'('fmb_ZF_bool_fun$_1','fmb_ZF_bool_fun$_1') ).

tff('declare_fun_app$k',type,
    'fun_app$k': ( 'B_bool_fun$' * 'B$' ) > $o ).

tff('predicate_fun_app$k',axiom,
    'fun_app$k'('fmb_B_bool_fun$_1','fmb_B$_1') ).

tff('declare_member$i',type,
    'member$i': ( 'A_b_fun$' * 'A_b_fun_set$' ) > $o ).

tff('predicate_member$i',axiom,
    ~ 'member$i'('fmb_A_b_fun$_1','fmb_A_b_fun_set$_1') ).

tff('declare_less_eq$h',type,
    'less_eq$h': ( 'Nat_ZF_set_prod_set$' * 'Nat_ZF_set_prod_set$' ) > $o ).

tff('predicate_less_eq$h',axiom,
    'less_eq$h'('fmb_Nat_ZF_set_prod_set$_1','fmb_Nat_ZF_set_prod_set$_1') ).

tff('declare_fun_app$al',type,
    'fun_app$al': ( 'B_b_prod_bool_fun$' * 'B_b_prod$' ) > $o ).

tff('predicate_fun_app$al',axiom,
    'fun_app$al'('fmb_B_b_prod_bool_fun$_1','fmb_B_b_prod$_1') ).

tff('declare_member$d',type,
    'member$d': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' ) > $o ).

tff('predicate_member$d',axiom,
    'member$d'('fmb_ZF_ZF_prod$_1','fmb_ZF_ZF_prod_set$_1') ).

tff('declare_less_eq$d',type,
    'less_eq$d': ( 'ZF_set_ZF_set_prod_set$' * 'ZF_set_ZF_set_prod_set$' ) > $o ).

tff('predicate_less_eq$d',axiom,
    ~ 'less_eq$d'('fmb_ZF_set_ZF_set_prod_set$_1','fmb_ZF_set_ZF_set_prod_set$_1') ).

tff('declare_less_eq$g',type,
    'less_eq$g': ( 'ZF_ZF_prod_ZF_prod_set$' * 'ZF_ZF_prod_ZF_prod_set$' ) > $o ).

tff('predicate_less_eq$g',axiom,
    'less_eq$g'('fmb_ZF_ZF_prod_ZF_prod_set$_1','fmb_ZF_ZF_prod_ZF_prod_set$_1') ).

tff('declare_category_axioms$a',type,
    'category_axioms$a': 'ZF_ZF_unit_Category_ext$' > $o ).

tff('predicate_category_axioms$a',axiom,
    'category_axioms$a'('fmb_ZF_ZF_unit_Category_ext$_1') ).

tff('declare_preFunctor$a',type,
    'preFunctor$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).

tff('predicate_preFunctor$a',axiom,
    'preFunctor$a'('fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1') ).

tff('declare_functor$',type,
    'functor$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).

tff('predicate_functor$',axiom,
    'functor$'('fmb_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_1') ).

tff('declare_less_eq$b',type,
    'less_eq$b': ( 'ZF_set_set$' * 'ZF_set_set$' ) > $o ).

tff('predicate_less_eq$b',axiom,
    'less_eq$b'('fmb_ZF_set_set$_1','fmb_ZF_set_set$_1') ).

tff('declare_fun_app$n',type,
    'fun_app$n': ( 'A_bool_fun$' * 'A$' ) > $o ).

tff('predicate_fun_app$n',axiom,
    'fun_app$n'('fmb_A_bool_fun$_1','fmb_A$_1') ).

tff('declare_functor$c',type,
    'functor$c': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).

tff('predicate_functor$c',axiom,
    'functor$c'('fmb_ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_1') ).

tff('declare_member$e',type,
    'member$e': ( 'Nat$' * 'Nat_set$' ) > $o ).

tff('predicate_member$e',axiom,
    'member$e'('fmb_Nat$_1','fmb_Nat_set$_1') ).

tff('declare_fun_app$j',type,
    'fun_app$j': ( 'ZF_set_set_bool_fun$' * 'ZF_set_set$' ) > $o ).

tff('predicate_fun_app$j',axiom,
    'fun_app$j'('fmb_ZF_set_set_bool_fun$_1','fmb_ZF_set_set$_1') ).

tff('declare_fun_app$m',type,
    'fun_app$m': ( 'B_set_bool_fun$' * 'B_set$' ) > $o ).

tff('predicate_fun_app$m',axiom,
    'fun_app$m'('fmb_B_set_bool_fun$_1','fmb_B_set$_1') ).

tff('declare_preFunctor$',type,
    'preFunctor$': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).

tff('predicate_preFunctor$',axiom,
    'preFunctor$'('fmb_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_1') ).

tff('declare_member$h',type,
    'member$h': ( 'B_a_fun$' * 'B_a_fun_set$' ) > $o ).

tff('predicate_member$h',axiom,
    'member$h'('fmb_B_a_fun$_1','fmb_B_a_fun_set$_1') ).

tff('declare_fun_app$cj',type,
    'fun_app$cj': ( 'B_ZF_fun_bool_fun$' * 'B_ZF_fun$' ) > $o ).

tff('predicate_fun_app$cj',axiom,
    'fun_app$cj'('fmb_B_ZF_fun_bool_fun$_1','fmb_B_ZF_fun$_1') ).

tff('declare_fun_app$p',type,
    'fun_app$p': ( 'A_set_bool_fun$' * 'A_set$' ) > $o ).

tff('predicate_fun_app$p',axiom,
    'fun_app$p'('fmb_A_set_bool_fun$_1','fmb_A_set$_1') ).

tff('declare_fun_app$ci',type,
    'fun_app$ci': ( 'ZF_ZF_fun_bool_fun$' * 'ZF_ZF_fun$' ) > $o ).

tff('predicate_fun_app$ci',axiom,
    'fun_app$ci'('fmb_ZF_ZF_fun_bool_fun$_1','fmb_ZF_ZF_fun$_1') ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : ITP302_10 : TPTP v9.3.1. Released v8.2.0.
% 0.00/0.07  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43  % Computer : n018.cluster.edu
% 0.16/0.43  % Model    : x86_64 x86_64
% 0.16/0.43  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43  % Memory   : 8046.5625MB
% 0.16/0.43  % OS       : Linux 6.8.0-71-generic
% 0.16/0.43  % CPULimit : 300
% 0.16/0.43  % WCLimit  : 300
% 0.16/0.43  % DateTime : Sun Sep 27 12:55:53 UTC 2026
% 0.16/0.43  % CPUTime  : 
% 0.16/0.43  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.20/0.49  Running first-order model finding
% 0.20/0.49  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.75/4.07  % (2321633)Will run a generic schedule for satisfiability detection.
% 24.75/4.07  % (2321641)dis+10_1_sil=32000:sp=arity:random_seed=1480320317:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 24.75/4.07  % (2321639)% WARNING: option uhcvi not known.
% 24.75/4.07  % (2321642)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=578863376:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 24.75/4.07  % (2321638)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3626440488_2999 on theBenchmark for (2999ds/0Mi)
% 24.75/4.07  % (2321640)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3679825437:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 24.75/4.07  % (2321639)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=93107372:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 24.75/4.07  % (2321643)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3045047592:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 24.75/4.07  % (2321644)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=151252360:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 24.75/4.07  % (2321641)Instruction limit reached! 
% 24.75/4.07  % (2321641)------------------------------
% 24.75/4.07  % (2321641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.75/4.07  % (2321641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.75/4.07  % (2321641)CaDiCaL version: 2.1.3
% 24.75/4.07  % (2321641)Termination reason: Instruction limit
% 24.75/4.07  % (2321641)Termination phase: Saturation
% 24.75/4.07  % (2321641)Time elapsed: 0.053 s
% 24.75/4.07  % (2321641)Peak memory usage: 14 MB
% 24.75/4.07  % (2321641)Instructions burned: 104 (million)
% 24.75/4.07  % (2321652)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=33980223:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 24.75/4.07  % (2321642)Instruction limit reached! 
% 24.75/4.07  % (2321642)------------------------------
% 24.75/4.07  % (2321642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.75/4.07  % (2321642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.75/4.07  % (2321642)CaDiCaL version: 2.1.3
% 24.75/4.07  % (2321642)Termination reason: Instruction limit
% 24.75/4.07  % (2321642)Termination phase: Saturation
% 24.75/4.07  % (2321642)Time elapsed: 0.106 s
% 24.75/4.07  % (2321642)Peak memory usage: 14 MB
% 24.75/4.07  % (2321642)Instructions burned: 116 (million)
% 24.75/4.07  % (2321643)Instruction limit reached! 
% 24.75/4.07  % (2321643)------------------------------
% 24.75/4.07  % (2321643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.75/4.07  % (2321643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.75/4.07  % (2321643)CaDiCaL version: 2.1.3
% 24.75/4.07  % (2321643)Termination reason: Instruction limit
% 24.75/4.07  % (2321643)Termination phase: Saturation
% 24.75/4.07  % (2321643)Time elapsed: 0.123 s
% 24.75/4.07  % (2321643)Peak memory usage: 15 MB
% 24.75/4.07  % (2321643)Instructions burned: 131 (million)
% 24.75/4.07  % (2321654)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2089747865:i=131:bd=preordered:fsd=on_2997 on theBenchmark for (2997ds/131Mi)
% 24.75/4.07  % (2321655)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=547308985:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2997 on theBenchmark for (2997ds/684Mi)
% 24.75/4.07  % (2321644)Instruction limit reached! 
% 24.75/4.07  % (2321644)------------------------------
% 24.75/4.07  % (2321644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.75/4.07  % (2321644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.75/4.07  % (2321644)CaDiCaL version: 2.1.3
% 24.75/4.07  % (2321644)Termination reason: Instruction limit
% 24.75/4.07  % (2321644)Termination phase: Saturation
% 24.75/4.07  % (2321644)Time elapsed: 0.159 s
% 24.75/4.07  % (2321644)Peak memory usage: 16 MB
% 24.75/4.07  % (2321644)Instructions burned: 159 (million)
% 24.75/4.07  % (2321658)ott-21_1_sil=16000:fs=off:random_seed=2144237855:i=180:av=off:fsr=off_2997 on theBenchmark for (2997ds/180Mi)
% 24.75/4.07  % (2321654)Instruction limit reached! 
% 24.75/4.07  % (2321654)------------------------------
% 24.75/4.07  % (2321654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 24.75/4.07  % (2321654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.75/4.07  % (2321654)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321654)Termination reason: Instruction limit
% 34.11/5.47  % (2321654)Termination phase: Saturation
% 34.11/5.47  % (2321654)Time elapsed: 0.108 s
% 34.11/5.47  % (2321654)Peak memory usage: 15 MB
% 34.11/5.47  % (2321654)Instructions burned: 131 (million)
% 34.11/5.47  % (2321660)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3274691265:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 34.11/5.47  % (2321658)Instruction limit reached! 
% 34.11/5.47  % (2321658)------------------------------
% 34.11/5.47  % (2321658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321658)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321658)Termination reason: Instruction limit
% 34.11/5.47  % (2321658)Termination phase: Saturation
% 34.11/5.47  % (2321658)Time elapsed: 0.179 s
% 34.11/5.47  % (2321658)Peak memory usage: 15 MB
% 34.11/5.47  % (2321658)Instructions burned: 180 (million)
% 34.11/5.47  % (2321652)Instruction limit reached! 
% 34.11/5.47  % (2321652)------------------------------
% 34.11/5.47  % (2321652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321652)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321652)Termination reason: Instruction limit
% 34.11/5.47  % (2321652)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321652)Time elapsed: 0.319 s
% 34.11/5.47  % (2321652)Peak memory usage: 18 MB
% 34.11/5.47  % (2321652)Instructions burned: 715 (million)
% 34.11/5.47  % (2321663)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3373705664:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 34.11/5.47  % (2321662)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=169885573:fmbsr=1.3:i=865:ins=25_2995 on theBenchmark for (2995ds/865Mi)
% 34.11/5.47  % (2321660)Instruction limit reached! 
% 34.11/5.47  % (2321660)------------------------------
% 34.11/5.47  % (2321660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321660)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321660)Termination reason: Instruction limit
% 34.11/5.47  % (2321660)Termination phase: Saturation
% 34.11/5.47  % (2321660)Time elapsed: 0.504 s
% 34.11/5.47  % (2321660)Peak memory usage: 16 MB
% 34.11/5.47  % (2321660)Instructions burned: 477 (million)
% 34.11/5.47  % (2321668)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2880354293:i=889:ins=1_2991 on theBenchmark for (2991ds/889Mi)
% 34.11/5.47  % (2321655)Instruction limit reached! 
% 34.11/5.47  % (2321655)------------------------------
% 34.11/5.47  % (2321655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321655)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321655)Termination reason: Instruction limit
% 34.11/5.47  % (2321655)Termination phase: Saturation
% 34.11/5.47  % (2321655)Time elapsed: 0.708 s
% 34.11/5.47  % (2321655)Peak memory usage: 21 MB
% 34.11/5.47  % (2321655)Instructions burned: 684 (million)
% 34.11/5.47  % (2321670)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3745010002:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2990 on theBenchmark for (2990ds/692Mi)
% 34.11/5.47  % (2321663)Instruction limit reached! 
% 34.11/5.47  % (2321663)------------------------------
% 34.11/5.47  % (2321663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321663)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321663)Termination reason: Instruction limit
% 34.11/5.47  % (2321663)Termination phase: Saturation
% 34.11/5.47  % (2321663)Time elapsed: 0.595 s
% 34.11/5.47  % (2321663)Peak memory usage: 30 MB
% 34.11/5.47  % (2321663)Instructions burned: 1182 (million)
% 34.11/5.47  % (2321674)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3203576514:i=879:kws=inv_precedence:fsr=off_2989 on theBenchmark for (2989ds/879Mi)
% 34.11/5.47  % (2321662)Instruction limit reached! 
% 34.11/5.47  % (2321662)------------------------------
% 34.11/5.47  % (2321662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321662)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321662)Termination reason: Instruction limit
% 34.11/5.47  % (2321662)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321662)Time elapsed: 0.654 s
% 34.11/5.47  % (2321662)Peak memory usage: 26 MB
% 34.11/5.47  % (2321662)Instructions burned: 867 (million)
% 34.11/5.47  % (2321676)fmb+10_1_sil=64000:random_seed=597343872:i=22061:nm=2:gsp=on_2988 on theBenchmark for (2988ds/22061Mi)
% 34.11/5.47  % (2321674)Instruction limit reached! 
% 34.11/5.47  % (2321674)------------------------------
% 34.11/5.47  % (2321674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321674)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321674)Termination reason: Instruction limit
% 34.11/5.47  % (2321674)Termination phase: Saturation
% 34.11/5.47  % (2321674)Time elapsed: 0.239 s
% 34.11/5.47  % (2321674)Peak memory usage: 20 MB
% 34.11/5.47  % (2321674)Instructions burned: 880 (million)
% 34.11/5.47  % (2321721)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3339120812:i=9515:nm=5_2986 on theBenchmark for (2986ds/9515Mi)
% 34.11/5.47  % (2321668)Instruction limit reached! 
% 34.11/5.47  % (2321668)------------------------------
% 34.11/5.47  % (2321668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321668)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321668)Termination reason: Instruction limit
% 34.11/5.47  % (2321668)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321668)Time elapsed: 0.476 s
% 34.11/5.47  % (2321668)Peak memory usage: 26 MB
% 34.11/5.47  % (2321668)Instructions burned: 891 (million)
% 34.11/5.47  % (2321736)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1374734666:fmbsr=1.7:i=920_2986 on theBenchmark for (2986ds/920Mi)
% 34.11/5.47  % (2321670)Instruction limit reached! 
% 34.11/5.47  % (2321670)------------------------------
% 34.11/5.47  % (2321670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321670)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321670)Termination reason: Instruction limit
% 34.11/5.47  % (2321670)Termination phase: Saturation
% 34.11/5.47  % (2321670)Time elapsed: 0.423 s
% 34.11/5.47  % (2321670)Peak memory usage: 23 MB
% 34.11/5.47  % (2321670)Instructions burned: 692 (million)
% 34.11/5.47  % (2321748)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4194987537:i=5131_2985 on theBenchmark for (2985ds/5131Mi)
% 34.11/5.47  % (2321736)Instruction limit reached! 
% 34.11/5.47  % (2321736)------------------------------
% 34.11/5.47  % (2321736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321736)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321736)Termination reason: Instruction limit
% 34.11/5.47  % (2321736)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321736)Time elapsed: 0.438 s
% 34.11/5.47  % (2321736)Peak memory usage: 27 MB
% 34.11/5.47  % (2321736)Instructions burned: 920 (million)
% 34.11/5.47  % (2321831)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1697258311:i=1472:ins=7:fdi=8:gsp=on_2981 on theBenchmark for (2981ds/1472Mi)
% 34.11/5.47  % (2321831)Instruction limit reached! 
% 34.11/5.47  % (2321831)------------------------------
% 34.11/5.47  % (2321831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321831)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321831)Termination reason: Instruction limit
% 34.11/5.47  % (2321831)Termination phase: Saturation
% 34.11/5.47  % (2321831)Time elapsed: 0.680 s
% 34.11/5.47  % (2321831)Peak memory usage: 26 MB
% 34.11/5.47  % (2321831)Instructions burned: 1473 (million)
% 34.11/5.47  % (2321839)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3318347471:i=6324_2974 on theBenchmark for (2974ds/6324Mi)
% 34.11/5.47  % (2321721)Instruction limit reached! 
% 34.11/5.47  % (2321721)------------------------------
% 34.11/5.47  % (2321721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321721)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321721)Termination reason: Instruction limit
% 34.11/5.47  % (2321721)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321721)Time elapsed: 2.211 s
% 34.11/5.47  % (2321721)Peak memory usage: 66 MB
% 34.11/5.47  % (2321721)Instructions burned: 9519 (million)
% 34.11/5.47  % (2321841)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3454678755:fmbsr=2.30978:i=2174_2964 on theBenchmark for (2964ds/2174Mi)
% 34.11/5.47  % (2321841)Instruction limit reached! 
% 34.11/5.47  % (2321841)------------------------------
% 34.11/5.47  % (2321841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321841)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321841)Termination reason: Instruction limit
% 34.11/5.47  % (2321841)Termination phase: Finite model building preprocessing
% 34.11/5.47  % (2321841)Time elapsed: 0.565 s
% 34.11/5.47  % (2321841)Peak memory usage: 35 MB
% 34.11/5.47  % (2321841)Instructions burned: 2175 (million)
% 34.11/5.47  % (2321843)ott-2_1_sil=16000:newcnf=on:random_seed=618512360:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2958 on theBenchmark for (2958ds/869Mi)
% 34.11/5.47  % (2321843)Instruction limit reached! 
% 34.11/5.47  % (2321843)------------------------------
% 34.11/5.47  % (2321843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321843)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321843)Termination reason: Instruction limit
% 34.11/5.47  % (2321843)Termination phase: Saturation
% 34.11/5.47  % (2321843)Time elapsed: 0.301 s
% 34.11/5.47  % (2321843)Peak memory usage: 24 MB
% 34.11/5.47  % (2321843)Instructions burned: 870 (million)
% 34.11/5.47  % (2321845)ott+10_1_sil=32000:tgt=ground:random_seed=2340120458:i=5114:av=off_2955 on theBenchmark for (2955ds/5114Mi)
% 34.11/5.47  % (2321748)Instruction limit reached! 
% 34.11/5.47  % (2321748)------------------------------
% 34.11/5.47  % (2321748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.47  % (2321748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.47  % (2321748)CaDiCaL version: 2.1.3
% 34.11/5.47  % (2321748)Termination reason: Instruction limit
% 34.11/5.47  % (2321748)Termination phase: Saturation
% 34.11/5.47  % (2321748)Time elapsed: 3.113 s
% 34.11/5.47  % (2321748)Peak memory usage: 68 MB
% 34.11/5.47  % (2321748)Instructions burned: 5131 (million)
% 34.11/5.47  % (2321847)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1431025993:i=54282_2954 on theBenchmark for (2954ds/54282Mi)
% 34.11/5.47  % Detected minimum model sizes of [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 34.11/5.47  % Detected maximum model sizes of [max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,max,2,max,max,max]
% 34.11/5.47  % TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 34.11/5.47  % TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1]
% 34.11/5.47  % Finite Model Found!
% 34.11/5.47  % SZS status Satisfiable for theBenchmark
% 34.11/5.47  % (2321638) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2321633-2321638"...
% 34.11/5.47  % (2321638)...printing done.
% 34.11/5.47  % SZS output start FiniteModel for theBenchmark
% See solution above
% 34.11/5.50  % (2321638)------------------------------
% 34.11/5.50  % (2321638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 34.11/5.50  % (2321638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 34.11/5.50  % (2321638)CaDiCaL version: 2.1.3
% 34.11/5.50  % (2321638)Termination reason: Satisfiable
% 34.11/5.50  % (2321638)Time elapsed: 4.850 s
% 34.11/5.50  % (2321638)Peak memory usage: 73 MB
% 34.11/5.50  % (2321638)Instructions burned: 10429 (million)
% 34.11/5.50  % (2321633)Success in time 4.976 s
% 34.11/5.50  % Vampire exiting
%------------------------------------------------------------------------------