%------------------------------------------------------------------------------
% File     : ITP109_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : int_bitwise.ax [Gau19]
%          : HL4109_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  244 (  84 unt; 126 typ;   0 def)
%            Number of atoms       :  195 ( 120 equ)
%            Maximal formula atoms :    8 (   0 avg)
%            Number of connectives :   87 (  10   ~;   4   |;  17   &)
%                                         (  26 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :   12 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  101 (  61   >;  40   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  122 ( 122 usr;  35 con; 0-6 aty)
%            Number of variables   :  416 ( 336   !;   1   ?; 416   :)
%                                         (  79  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Einteger_2Eint,type,
    tyop_2Einteger_2Eint: $tType ).

tff(tyop_2Elist_2Elist,type,
    tyop_2Elist_2Elist: $tType > $tType ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: $tType ).

tff(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: $tType ).

tff(tyop_2Epair_2Eprod,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

tff(app_2E2,type,
    app_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(p,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(combin_i_2E0,type,
    combin_i_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(combin_k_2E0,type,
    combin_k_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(combin_s_2E0,type,
    combin_s_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_21_2E1,type,
    c_2Ebool_2E_21_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Earithmetic_2E_2A_2E0,type,
    c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2A_2E2,type,
    c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2E_2B_2E0,type,
    c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2B_2E2,type,
    c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).

tff(c_2Epair_2E_2C_2E2,type,
    c_2Epair_2E_2C_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2E_2D_2E2,type,
    c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).

tff(c_2Eprim__rec_2E_3C_2E0,type,
    c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Eprim__rec_2E_3C_2E2,type,
    c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2E_3C_3D_2E0,type,
    c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Earithmetic_2E_3C_3D_2E2,type,
    c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_3F_2E1,type,
    c_2Ebool_2E_3F_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).

tff(c_2Emin_2E_40_2E1,type,
    c_2Emin_2E_40_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EAPPEND_2E2,type,
    c_2Elist_2EAPPEND_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ebit_2EBIT_2E0,type,
    c_2Ebit_2EBIT_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).

tff(c_2Ebit_2EBIT_2E2,type,
    c_2Ebit_2EBIT_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).

tff(c_2Earithmetic_2EBIT1_2E0,type,
    c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT1_2E1,type,
    c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2EBIT2_2E1,type,
    c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).

tff(c_2Ebool_2ECOND_2E3,type,
    c_2Ebool_2ECOND_2E3: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2ECONS_2E2,type,
    c_2Elist_2ECONS_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Earithmetic_2EDIV_2E0,type,
    c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Earithmetic_2EDIV_2E2,type,
    c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).

tff(c_2Elist_2EDROP_2E0,type,
    c_2Elist_2EDROP_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EDROP_2E2,type,
    c_2Elist_2EDROP_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Elist_2EEL_2E0,type,
    c_2Elist_2EEL_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).

tff(c_2Elist_2EEL_2E2,type,
    c_2Elist_2EEL_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).

tff(c_2Epair_2EFST_2E1,type,
    c_2Epair_2EFST_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(A_27a))) ).

tff(c_2Elist_2EGENLIST_2E2,type,
    c_2Elist_2EGENLIST_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) * tyop_2Enum_2Enum ) > tyop_2Elist_2Elist(A_27a) ) ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: 
      !>[A_27a: $tType] : ( A_27a > A_27a ) ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).

tff(c_2Ecombin_2EK_2E1,type,
    c_2Ecombin_2EK_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).

tff(c_2Elist_2ELENGTH_2E0,type,
    c_2Elist_2ELENGTH_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).

tff(c_2Elist_2ELENGTH_2E1,type,
    c_2Elist_2ELENGTH_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).

tff(c_2Elist_2EMAP_2E0,type,
    c_2Elist_2EMAP_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).

tff(c_2Elist_2EMAP_2E2,type,
    c_2Elist_2EMAP_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: 
      !>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).

tff(c_2Earithmetic_2ENUMERAL_2E1,type,
    c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).

tff(c_2Einteger_2ENum_2E0,type,
    c_2Einteger_2ENum_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Enum_2Enum) ).

tff(c_2Einteger_2ENum_2E1,type,
    c_2Einteger_2ENum_2E1: tyop_2Einteger_2Eint > tyop_2Enum_2Enum ).

tff(c_2Earithmetic_2EODD_2E0,type,
    c_2Earithmetic_2EODD_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).

tff(c_2Earithmetic_2EODD_2E1,type,
    c_2Earithmetic_2EODD_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).

tff(c_2Epair_2ESND_2E1,type,
    c_2Epair_2ESND_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).

tff(c_2Epair_2EUNCURRY_2E1,type,
    c_2Epair_2EUNCURRY_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).

tff(c_2Erelation_2EWF_2E0,type,
    c_2Erelation_2EWF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).

tff(c_2Erelation_2EWF_2E1,type,
    c_2Erelation_2EWF_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).

tff(c_2Erelation_2EWFREC_2E0,type,
    c_2Erelation_2EWFREC_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).

tff(c_2Erelation_2EWFREC_2E2,type,
    c_2Erelation_2EWFREC_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(c_2Eint__bitwise_2Ebits__bitwise_2E0,type,
    c_2Eint__bitwise_2Ebits__bitwise_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))) ).

tff(c_2Eint__bitwise_2Ebits__bitwise_2E3,type,
    c_2Eint__bitwise_2Ebits__bitwise_2E3: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) * tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b) * tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c) ) > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a) ) ).

tff(c_2Eint__bitwise_2Ebits__of__int_2E0,type,
    c_2Eint__bitwise_2Ebits__of__int_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Eint__bitwise_2Ebits__of__int_2E1,type,
    c_2Eint__bitwise_2Ebits__of__int_2E1: tyop_2Einteger_2Eint > tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Eint__bitwise_2Ebits__of__num_2E0,type,
    c_2Eint__bitwise_2Ebits__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)) ).

tff(c_2Eint__bitwise_2Ebits__of__num_2E1,type,
    c_2Eint__bitwise_2Ebits__of__num_2E1: tyop_2Enum_2Enum > tyop_2Elist_2Elist(tyop_2Emin_2Ebool) ).

tff(c_2Eint__bitwise_2Eint__and_2E0,type,
    c_2Eint__bitwise_2Eint__and_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__and_2E2,type,
    c_2Eint__bitwise_2Eint__and_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__bit_2E0,type,
    c_2Eint__bitwise_2Eint__bit_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).

tff(c_2Eint__bitwise_2Eint__bit_2E2,type,
    c_2Eint__bitwise_2Eint__bit_2E2: ( tyop_2Enum_2Enum * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).

tff(c_2Eint__bitwise_2Eint__bitwise_2E0,type,
    c_2Eint__bitwise_2Eint__bitwise_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint))) ).

tff(c_2Eint__bitwise_2Eint__bitwise_2E1,type,
    c_2Eint__bitwise_2Eint__bitwise_2E1: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) > tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__bitwise_2E2,type,
    c_2Eint__bitwise_2Eint__bitwise_2E2: ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) * tyop_2Einteger_2Eint ) > tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).

tff(c_2Eint__bitwise_2Eint__bitwise_2E3,type,
    c_2Eint__bitwise_2Eint__bitwise_2E3: ( tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) * tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Einteger_2Eint__lt_2E0,type,
    c_2Einteger_2Eint__lt_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool)) ).

tff(c_2Einteger_2Eint__lt_2E2,type,
    c_2Einteger_2Eint__lt_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Emin_2Ebool ).

tff(c_2Eint__bitwise_2Eint__not_2E0,type,
    c_2Eint__bitwise_2Eint__not_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint) ).

tff(c_2Eint__bitwise_2Eint__not_2E1,type,
    c_2Eint__bitwise_2Eint__not_2E1: tyop_2Einteger_2Eint > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__of__bits_2E0,type,
    c_2Eint__bitwise_2Eint__of__bits_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint) ).

tff(c_2Eint__bitwise_2Eint__of__bits_2E1,type,
    c_2Eint__bitwise_2Eint__of__bits_2E1: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) > tyop_2Einteger_2Eint ).

tff(c_2Einteger_2Eint__of__num_2E0,type,
    c_2Einteger_2Eint__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Einteger_2Eint) ).

tff(c_2Einteger_2Eint__of__num_2E1,type,
    c_2Einteger_2Eint__of__num_2E1: tyop_2Enum_2Enum > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__or_2E0,type,
    c_2Eint__bitwise_2Eint__or_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__or_2E2,type,
    c_2Eint__bitwise_2Eint__or_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__shift__left_2E0,type,
    c_2Eint__bitwise_2Eint__shift__left_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__shift__left_2E2,type,
    c_2Eint__bitwise_2Eint__shift__left_2E2: ( tyop_2Enum_2Enum * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__shift__right_2E0,type,
    c_2Eint__bitwise_2Eint__shift__right_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__shift__right_2E2,type,
    c_2Eint__bitwise_2Eint__shift__right_2E2: ( tyop_2Enum_2Enum * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Einteger_2Eint__sub_2E0,type,
    c_2Einteger_2Eint__sub_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Einteger_2Eint__sub_2E2,type,
    c_2Einteger_2Eint__sub_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Eint__bitwise_2Eint__xor_2E0,type,
    c_2Eint__bitwise_2Eint__xor_2E0: tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)) ).

tff(c_2Eint__bitwise_2Eint__xor_2E2,type,
    c_2Eint__bitwise_2Eint__xor_2E2: ( tyop_2Einteger_2Eint * tyop_2Einteger_2Eint ) > tyop_2Einteger_2Eint ).

tff(c_2Elist_2Elist__CASE_2E0,type,
    c_2Elist_2Elist__CASE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).

tff(c_2Elist_2Elist__CASE_2E3,type,
    c_2Elist_2Elist__CASE_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).

tff(c_2Eint__bitwise_2Enum__of__bits_2E0,type,
    c_2Eint__bitwise_2Enum__of__bits_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).

tff(c_2Eint__bitwise_2Enum__of__bits_2E1,type,
    c_2Eint__bitwise_2Enum__of__bits_2E1: tyop_2Elist_2Elist(tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(c_2Ebool_2E_7E_2E1,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
      ( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
     => ( V0f_2E0 = V1g_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Eboolext,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(V0_2E0)
      <=> p(V1_2E0) )
     => ( V0_2E0 = V1_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Etruth,axiom,
    p(c_2Ebool_2ET_2E0) ).

tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
    ~ p(c_2Ebool_2EF_2E0) ).

tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0: tyop_2Emin_2Ebool] :
      ( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
      | ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).

tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
    ! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).

tff(thm_2Eextra_2Dho_2Es__thm,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).

tff(logicdef_2E_2F_5C,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        & p(V1_2E0) ) ) ).

tff(logicdef_2E_5C_2F,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
        | p(V1_2E0) ) ) ).

tff(logicdef_2E_7E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Ebool_2E_7E_2E1(V0_2E0))
    <=> ~ p(V0_2E0) ) ).

tff(logicdef_2E_3D_3D_3E,axiom,
    ! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
      ( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
    <=> ( p(V0_2E0)
       => p(V1_2E0) ) ) ).

tff(logicdef_2E_3D,axiom,
    ! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
      ( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
    <=> ( V0_2E0 = V1_2E0 ) ) ).

tff(quantdef_2E_21,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
    <=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(quantdef_2E_3F,axiom,
    ! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
    <=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(A_27b),X1_2E0: A_27b] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,X0_2E0,X1_2E0) = app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27b),A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: tyop_2Elist_2Elist(A_27c),X1_2E0: A_27c] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,X0_2E0,X1_2E0) = app_2E2(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Emin_2Efun(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27c),A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Ebool] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        & p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
      ( ( X0_2E0 = X1_2E0 )
    <=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).

tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
       => p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EAPPEND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebit_2EBIT_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebit_2EBIT_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ebit_2EBIT_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Einteger_2Eint,X2_2E0: tyop_2Einteger_2Eint] : ( c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Ebool_2ECOND_2E0(tyop_2Einteger_2Eint),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X2_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Ebool_2ECOND_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Elist_2Elist(A_27c)] : ( c_2Elist_2ECONS_2E2(A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E0(A_27c),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2ECONS_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EDROP_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EDROP_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Elist_2EEL_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Epair_2EFST_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EGENLIST_2E2_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Elist_2EGENLIST_2E2(tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EGENLIST_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Ecombin_2EI_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Ecombin_2EK_2E0(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint,X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint),c_2Ebool_2ELET_2E0(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X1_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Elist_2EMAP_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),c_2Elist_2EMAP_2E0(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Einteger_2ENum_2E1,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2ENum_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Enum_2Enum,c_2Einteger_2ENum_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Earithmetic_2EODD_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EODD_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epair_2ESND_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),c_2Epair_2EUNCURRY_2E0(tyop_2Elist_2Elist(A_27a),A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Einteger_2Eint,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint),c_2Epair_2EUNCURRY_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,tyop_2Einteger_2Eint),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0) ) ).

tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Erelation_2EWFREC_2E0(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),c_2Erelation_2EWFREC_2E0(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
      ( ( p(X0_2E0)
        | p(X1_2E0) )
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).

tff(arityeq3_2Ec_2Eint__bitwise_2Ebits__bitwise_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c)] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),c_2Eint__bitwise_2Ebits__bitwise_2E0(A_27a,A_27b,A_27c),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Eint__bitwise_2Ebits__bitwise_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),X2_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eint__bitwise_2Ebits__bitwise_2E0(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Ebits__of__int_2E1,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Ebits__of__int_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Eint__bitwise_2Ebits__of__int_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Ebits__of__num_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Eint__bitwise_2Ebits__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Eint__bitwise_2Ebits__of__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__and_2E2,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__and_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Eint__bitwise_2Eint__and_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__bit_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bit_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Eint__bitwise_2Eint__bit_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Eint__bitwise_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] : ( c_2Eint__bitwise_2Eint__bitwise_2E1(X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Eint__bitwise_2Eint__bitwise_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__bitwise_2E2,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bitwise_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Eint__bitwise_2Eint__bitwise_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Eint__bitwise_2Eint__bitwise_2E3,axiom,
    ! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Einteger_2Eint,X2_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bitwise_2E3(X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint)),c_2Eint__bitwise_2Eint__bitwise_2E0,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Einteger_2Eint__lt_2E2,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__lt_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Eint__not_2E1,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__not_2E1(X0_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,c_2Eint__bitwise_2Eint__not_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Eint__of__bits_2E1,axiom,
    ! [X0_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Eint__of__bits_2E1(X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint,c_2Eint__bitwise_2Eint__of__bits_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Einteger_2Eint__of__num_2E1,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Einteger_2Eint__of__num_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Einteger_2Eint,c_2Einteger_2Eint__of__num_2E0,X0_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__or_2E2,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__or_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Eint__bitwise_2Eint__or_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__shift__left_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__shift__left_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Eint__bitwise_2Eint__shift__left_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__shift__right_2E2,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__shift__right_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Eint__bitwise_2Eint__shift__right_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Einteger_2Eint__sub_2E2,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Einteger_2Eint__sub_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Einteger_2Eint__sub_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eint__bitwise_2Eint__xor_2E2,axiom,
    ! [X0_2E0: tyop_2Einteger_2Eint,X1_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__xor_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint,app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Einteger_2Eint),c_2Eint__bitwise_2Eint__xor_2E0,X0_2E0),X1_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),tyop_2Enum_2Enum)),c_2Elist_2Elist__CASE_2E0(tyop_2Emin_2Ebool,tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq1_2Ec_2Eint__bitwise_2Enum__of__bits_2E1,axiom,
    ! [X0_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Enum__of__bits_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Eint__bitwise_2Enum__of__bits_2E0,X0_2E0) ) ).

tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0: tyop_2Emin_2Ebool] :
      ( ~ p(X0_2E0)
    <=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).

tff(thm_2Eint__bitwise_2Eint__not__def,axiom,
    ! [V0i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__not_2E1(V0i_2E0) = c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__sub_2E2(c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0),V0i_2E0),c_2Einteger_2Eint__of__num_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool))] :
      ( ! [V0b_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] :
          ( p(app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V1i_2E0))
        <=> ~ p(c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Einteger_2ENum_2E1(c_2Eint__bitwise_2Eint__not_2E1(V1i_2E0)))) )
     => ! [V0b_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bit_2E2(V0b_2E0,V1i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Einteger_2Eint__lt_2E2(V1i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),app_2E2(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Einteger_2Eint,tyop_2Emin_2Ebool),F0_2E0,V0b_2E0),V1i_2E0),c_2Ebit_2EBIT_2E2(V0b_2E0,c_2Einteger_2ENum_2E1(V1i_2E0))) ) ) ).

tff(thm_2Eint__bitwise_2Ebits__of__num__primitive__def,axiom,
    ! [F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V3a_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3a_2E0))
        <=> ( V3a_2E0 = c_2Enum_2E0_2E0 ) )
     => ( ! [V2bits__of__num_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),V3a_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool)),F1_2E0,V2bits__of__num_2E0),V3a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3a_2E0),c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(V3a_2E0),app_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V2bits__of__num_2E0,c_2Earithmetic_2EDIV_2E2(V3a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
            <=> ( p(c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,V0R_2E0))
                & ! [V1n_2E0: tyop_2Enum_2Enum] :
                    ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
                   => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V1n_2E0)) ) ) )
         => ( c_2Eint__bitwise_2Ebits__of__num_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Elist_2Elist(tyop_2Emin_2Ebool),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).

tff(thm_2Eint__bitwise_2Ebits__of__int__def,axiom,
    ! [V0i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Ebits__of__int_2E1(V0i_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Einteger_2Eint__lt_2E2(V0i_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Elist_2EMAP_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,c_2Eint__bitwise_2Ebits__of__num_2E1(c_2Einteger_2ENum_2E1(c_2Eint__bitwise_2Eint__not_2E1(V0i_2E0)))),c_2Ebool_2ET_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Eint__bitwise_2Ebits__of__num_2E1(c_2Einteger_2ENum_2E1(V0i_2E0)),c_2Ebool_2EF_2E0)) ) ).

tff(thm_2Eint__bitwise_2Enum__of__bits__primitive__def,axiom,
    ! [F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
      ( ! [V3num__of__bits_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V5v_2E0: tyop_2Emin_2Ebool,V6bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),F2_2E0,V3num__of__bits_2E0),V5v_2E0),V6bs_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,V5v_2E0,c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,V3num__of__bits_2E0,V6bs_2E0)))),c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,V3num__of__bits_2E0,V6bs_2E0)))) )
     => ( ! [V3num__of__bits_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V4a_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),F1_2E0,V3num__of__bits_2E0),V4a_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,V4a_2E0,c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Enum_2E0_2E0),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),F2_2E0,V3num__of__bits_2E0)) )
       => ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))] :
              ( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
            <=> ( p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V0R_2E0))
                & ! [V1bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0R_2E0,V1bs_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,V1bs_2E0)))
                & ! [V2bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),V0R_2E0,V2bs_2E0),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,V2bs_2E0))) ) )
         => ( c_2Eint__bitwise_2Enum__of__bits_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).

tff(thm_2Eint__bitwise_2Eint__of__bits__def,axiom,
    ! [V0bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V1rest_2E0: tyop_2Emin_2Ebool] : ( c_2Eint__bitwise_2Eint__of__bits_2E1(c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0bs_2E0,V1rest_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Einteger_2Eint,V1rest_2E0,c_2Eint__bitwise_2Eint__not_2E1(c_2Einteger_2Eint__of__num_2E1(c_2Eint__bitwise_2Enum__of__bits_2E1(c_2Elist_2EMAP_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,V0bs_2E0)))),c_2Einteger_2Eint__of__num_2E1(c_2Eint__bitwise_2Enum__of__bits_2E1(V0bs_2E0))) ) ).

tff(thm_2Eint__bitwise_2Eint__bitwise__def,axiom,
    ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V1i_2E0: tyop_2Einteger_2Eint,V2j_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bitwise_2E3(V0f_2E0,V1i_2E0,V2j_2E0) = c_2Eint__bitwise_2Eint__of__bits_2E1(c_2Eint__bitwise_2Ebits__bitwise_2E3(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,V0f_2E0,c_2Eint__bitwise_2Ebits__of__int_2E1(V1i_2E0),c_2Eint__bitwise_2Ebits__of__int_2E1(V2j_2E0))) ) ).

tff(thm_2Eint__bitwise_2Eint__and__def,axiom,
    c_2Eint__bitwise_2Eint__and_2E0 = c_2Eint__bitwise_2Eint__bitwise_2E1(c_2Ebool_2E_2F_5C_2E0) ).

tff(thm_2Eint__bitwise_2Eint__or__def,axiom,
    c_2Eint__bitwise_2Eint__or_2E0 = c_2Eint__bitwise_2Eint__bitwise_2E1(c_2Ebool_2E_5C_2F_2E0) ).

tff(thm_2Eint__bitwise_2Eint__xor__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
      ( ! [V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool] :
          ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
        <=> ( V0x_2E0 != V1y_2E0 ) )
     => ( c_2Eint__bitwise_2Eint__xor_2E0 = c_2Eint__bitwise_2Eint__bitwise_2E1(F0_2E0) ) ) ).

tff(thm_2Eint__bitwise_2Eint__shift__left__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V2bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3r_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)),F0_2E0,V0n_2E0),V2bs_2E0),V3r_2E0) = c_2Eint__bitwise_2Eint__of__bits_2E1(c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Elist_2EAPPEND_2E2(tyop_2Emin_2Ebool,c_2Elist_2EGENLIST_2E2(tyop_2Emin_2Ebool,c_2Ecombin_2EK_2E1(tyop_2Emin_2Ebool,tyop_2Enum_2Enum,c_2Ebool_2EF_2E0),V0n_2E0),V2bs_2E0),V3r_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__shift__left_2E2(V0n_2E0,V1i_2E0) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint,c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)),F0_2E0,V0n_2E0)),c_2Eint__bitwise_2Ebits__of__int_2E1(V1i_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__shift__right__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)))] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum,V2bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool),V3r_2E0: tyop_2Emin_2Ebool] : ( app_2E2(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)),F0_2E0,V0n_2E0),V2bs_2E0),V3r_2E0) = c_2Eint__bitwise_2Eint__of__bits_2E1(c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Elist_2EDROP_2E2(tyop_2Emin_2Ebool,V0n_2E0,V2bs_2E0),V3r_2E0)) )
     => ! [V0n_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__shift__right_2E2(V0n_2E0,V1i_2E0) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),tyop_2Einteger_2Eint,c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,tyop_2Einteger_2Eint,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Einteger_2Eint)),F0_2E0,V0n_2E0)),c_2Eint__bitwise_2Ebits__of__int_2E1(V1i_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__not__not,axiom,
    ! [V0i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__not_2E1(c_2Eint__bitwise_2Eint__not_2E1(V0i_2E0)) = V0i_2E0 ) ).

tff(thm_2Eint__bitwise_2Eint__bit__not,axiom,
    ! [V0b_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Einteger_2Eint] :
      ( p(c_2Eint__bitwise_2Eint__bit_2E2(V0b_2E0,c_2Eint__bitwise_2Eint__not_2E1(V1i_2E0)))
    <=> ~ p(c_2Eint__bitwise_2Eint__bit_2E2(V0b_2E0,V1i_2E0)) ) ).

tff(thm_2Eint__bitwise_2Ebits__of__num__ind,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V1n_2E0: tyop_2Enum_2Enum] :
          ( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
           => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EDIV_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) )
         => p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0)) )
     => ! [V2v_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).

tff(thm_2Eint__bitwise_2Ebits__of__num__def,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
      ( ! [V0n_2E0: tyop_2Enum_2Enum] :
          ( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
        <=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
     => ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Eint__bitwise_2Ebits__of__num_2E1(V0n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool),c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Earithmetic_2EODD_2E1(V0n_2E0),c_2Eint__bitwise_2Ebits__of__num_2E1(c_2Earithmetic_2EDIV_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ) ).

tff(thm_2Eint__bitwise_2Enum__of__bits__ind,axiom,
    ! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] :
      ( ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool)))
        & ! [V1bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V1bs_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,V1bs_2E0))) )
        & ! [V2bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] :
            ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V2bs_2E0))
           => p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,V2bs_2E0))) ) )
     => ! [V3v_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V0P_2E0,V3v_2E0)) ) ).

tff(thm_2Eint__bitwise_2Enum__of__bits__def,axiom,
    ( ( c_2Eint__bitwise_2Enum__of__bits_2E1(c_2Elist_2ENIL_2E0(tyop_2Emin_2Ebool)) = c_2Enum_2E0_2E0 )
    & ! [V0bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Enum__of__bits_2E1(c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0,V0bs_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eint__bitwise_2Enum__of__bits_2E1(V0bs_2E0)) )
    & ! [V1bs_2E0: tyop_2Elist_2Elist(tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Enum__of__bits_2E1(c_2Elist_2ECONS_2E2(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0,V1bs_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Eint__bitwise_2Enum__of__bits_2E1(V1bs_2E0))) ) ) ).

tff(thm_2Eint__bitwise_2Ebits__bitwise__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)))] :
      ( ( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V2r1_2E0: A_27b,V3r2_2E0: A_27c] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V1f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V2r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V3r2_2E0)))
        & ! [V4f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V5r1_2E0: A_27b,V6b2_2E0: A_27c,V7bs2_2E0: tyop_2Elist_2Elist(A_27c),V8r2_2E0: A_27c] :
            ( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V4f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V5r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,V7bs2_2E0,V8r2_2E0)))
           => p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V4f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V5r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ECONS_2E2(A_27c,V6b2_2E0,V7bs2_2E0),V8r2_2E0))) )
        & ! [V9f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V10b1_2E0: A_27b,V11bs1_2E0: tyop_2Elist_2Elist(A_27b),V12r1_2E0: A_27b,V13r2_2E0: A_27c] :
            ( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V9f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,V11bs1_2E0,V12r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V13r2_2E0)))
           => p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V9f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ECONS_2E2(A_27b,V10b1_2E0,V11bs1_2E0),V12r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V13r2_2E0))) )
        & ! [V14f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V15b1_2E0: A_27b,V16bs1_2E0: tyop_2Elist_2Elist(A_27b),V17r1_2E0: A_27b,V18b2_2E0: A_27c,V19bs2_2E0: tyop_2Elist_2Elist(A_27c),V20r2_2E0: A_27c] :
            ( p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V14f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,V16bs1_2E0,V17r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,V19bs2_2E0,V20r2_2E0)))
           => p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V14f_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ECONS_2E2(A_27b,V15b1_2E0,V16bs1_2E0),V17r1_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ECONS_2E2(A_27c,V18b2_2E0,V19bs2_2E0),V20r2_2E0))) ) )
     => ! [V21v_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V22v1_2E0: tyop_2Elist_2Elist(A_27b),V23v2_2E0: A_27b,V24v3_2E0: tyop_2Elist_2Elist(A_27c),V25v4_2E0: A_27c] : p(app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27c),A_27c),tyop_2Emin_2Ebool)),V0P_2E0,V21v_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,V22v1_2E0,V23v2_2E0)),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,V24v3_2E0,V25v4_2E0))) ) ).

tff(thm_2Eint__bitwise_2Ebits__bitwise__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))))] :
      ( ! [V19f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V23b1_2E0: A_27b,V22b2_2E0: A_27c,V24bs_2E0: tyop_2Elist_2Elist(A_27a),V25r_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F2_2E0,V19f_2E0),V23b1_2E0),V22b2_2E0),V24bs_2E0),V25r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V19f_2E0,V23b1_2E0),V22b2_2E0),V24bs_2E0),V25r_2E0) )
     => ( ! [V12f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V14b1_2E0: A_27b,V10r2_2E0: A_27c,V15bs_2E0: tyop_2Elist_2Elist(A_27a),V16r_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F1_2E0,V12f_2E0),V14b1_2E0),V10r2_2E0),V15bs_2E0),V16r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V12f_2E0,V14b1_2E0),V10r2_2E0),V15bs_2E0),V16r_2E0) )
       => ( ! [V5f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V4r1_2E0: A_27b,V7b2_2E0: A_27c,V8bs_2E0: tyop_2Elist_2Elist(A_27a),V9r_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F0_2E0,V5f_2E0),V4r1_2E0),V7b2_2E0),V8bs_2E0),V9r_2E0) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ECONS_2E2(A_27a,app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V5f_2E0,V4r1_2E0),V7b2_2E0),V8bs_2E0),V9r_2E0) )
         => ( ! [V0r2_2E0: A_27c,V1r1_2E0: A_27b,V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a))] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V2f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V1r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V0r2_2E0)) = c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),A_27a,c_2Elist_2ENIL_2E0(A_27a),app_2E2(A_27c,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27a),V2f_2E0,V1r1_2E0),V0r2_2E0)) )
            & ! [V3r2_2E0: A_27c,V4r1_2E0: A_27b,V5f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V6bs2_2E0: tyop_2Elist_2Elist(A_27c),V7b2_2E0: A_27c] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V5f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V4r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ECONS_2E2(A_27c,V7b2_2E0,V6bs2_2E0),V3r2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F0_2E0,V5f_2E0),V4r1_2E0),V7b2_2E0)),c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V5f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ENIL_2E0(A_27b),V4r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,V6bs2_2E0,V3r2_2E0))) )
            & ! [V10r2_2E0: A_27c,V11r1_2E0: A_27b,V12f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V13bs1_2E0: tyop_2Elist_2Elist(A_27b),V14b1_2E0: A_27b] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V12f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ECONS_2E2(A_27b,V14b1_2E0,V13bs1_2E0),V11r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V10r2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F1_2E0,V12f_2E0),V14b1_2E0),V10r2_2E0)),c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V12f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,V13bs1_2E0,V11r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ENIL_2E0(A_27c),V10r2_2E0))) )
            & ! [V17r2_2E0: A_27c,V18r1_2E0: A_27b,V19f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),V20bs2_2E0: tyop_2Elist_2Elist(A_27c),V21bs1_2E0: tyop_2Elist_2Elist(A_27b),V22b2_2E0: A_27c,V23b1_2E0: A_27b] : ( c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V19f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,c_2Elist_2ECONS_2E2(A_27b,V23b1_2E0,V21bs1_2E0),V18r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,c_2Elist_2ECONS_2E2(A_27c,V22b2_2E0,V20bs2_2E0),V17r2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Elist_2Elist(A_27a),A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),A_27a))))),F2_2E0,V19f_2E0),V23b1_2E0),V22b2_2E0)),c_2Eint__bitwise_2Ebits__bitwise_2E3(A_27a,A_27b,A_27c,V19f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27b),A_27b,V21bs1_2E0,V18r1_2E0),c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27c),A_27c,V20bs2_2E0,V17r2_2E0))) ) ) ) ) ) ).

tff(thm_2Eint__bitwise_2Eint__not,axiom,
    ! [F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool))] :
      ( ! [V0x_2E0: tyop_2Emin_2Ebool,V1y_2E0: tyop_2Emin_2Ebool] :
          ( p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),F0_2E0,V0x_2E0),V1y_2E0))
        <=> ~ p(V1y_2E0) )
     => ( c_2Eint__bitwise_2Eint__not_2E0 = c_2Eint__bitwise_2Eint__bitwise_2E2(F0_2E0,c_2Einteger_2Eint__of__num_2E1(c_2Enum_2E0_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__int__of__bits,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1b_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)] : ( c_2Eint__bitwise_2Eint__bit_2E2(V0n_2E0,c_2Eint__bitwise_2Eint__of__bits_2E1(V1b_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(tyop_2Emin_2Ebool,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1b_2E0))),c_2Elist_2EEL_2E2(tyop_2Emin_2Ebool,V0n_2E0,c_2Epair_2EFST_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1b_2E0)),c_2Epair_2ESND_2E1(tyop_2Elist_2Elist(tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,V1b_2E0)) ) ).

tff(thm_2Eint__bitwise_2Eint__of__bits__bits__of__int,axiom,
    ! [V0i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__of__bits_2E1(c_2Eint__bitwise_2Ebits__of__int_2E1(V0i_2E0)) = V0i_2E0 ) ).

tff(thm_2Eint__bitwise_2Eint__bit__bitwise,axiom,
    ! [V0n_2E0: tyop_2Enum_2Enum,V1f_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),V2i_2E0: tyop_2Einteger_2Eint,V3j_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bit_2E2(V0n_2E0,c_2Eint__bitwise_2Eint__bitwise_2E3(V1f_2E0,V2i_2E0,V3j_2E0)) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),V1f_2E0,c_2Eint__bitwise_2Eint__bit_2E2(V0n_2E0,V2i_2E0)),c_2Eint__bitwise_2Eint__bit_2E2(V0n_2E0,V3j_2E0)) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__and,axiom,
    ! [V0j_2E0: tyop_2Einteger_2Eint,V1i_2E0: tyop_2Einteger_2Eint,V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,c_2Eint__bitwise_2Eint__and_2E2(V1i_2E0,V0j_2E0)))
    <=> ( p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V1i_2E0))
        & p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V0j_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__or,axiom,
    ! [V0j_2E0: tyop_2Einteger_2Eint,V1i_2E0: tyop_2Einteger_2Eint,V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,c_2Eint__bitwise_2Eint__or_2E2(V1i_2E0,V0j_2E0)))
    <=> ( p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V1i_2E0))
        | p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V0j_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__xor,axiom,
    ! [V0j_2E0: tyop_2Einteger_2Eint,V1i_2E0: tyop_2Einteger_2Eint,V2n_2E0: tyop_2Enum_2Enum] :
      ( p(c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,c_2Eint__bitwise_2Eint__xor_2E2(V1i_2E0,V0j_2E0)))
    <=> ( c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V1i_2E0) != c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V0j_2E0) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__equiv,axiom,
    ! [V0i_2E0: tyop_2Einteger_2Eint,V1j_2E0: tyop_2Einteger_2Eint] :
      ( ( V0i_2E0 = V1j_2E0 )
    <=> ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V0i_2E0) = c_2Eint__bitwise_2Eint__bit_2E2(V2n_2E0,V1j_2E0) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__shift__left,axiom,
    ! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Einteger_2Eint] :
      ( p(c_2Eint__bitwise_2Eint__bit_2E2(V0b_2E0,c_2Eint__bitwise_2Eint__shift__left_2E2(V1n_2E0,V2i_2E0)))
    <=> ( p(c_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,V0b_2E0))
        & p(c_2Eint__bitwise_2Eint__bit_2E2(c_2Earithmetic_2E_2D_2E2(V0b_2E0,V1n_2E0),V2i_2E0)) ) ) ).

tff(thm_2Eint__bitwise_2Eint__bit__shift__right,axiom,
    ! [V0b_2E0: tyop_2Enum_2Enum,V1n_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Einteger_2Eint] : ( c_2Eint__bitwise_2Eint__bit_2E2(V0b_2E0,c_2Eint__bitwise_2Eint__shift__right_2E2(V1n_2E0,V2i_2E0)) = c_2Eint__bitwise_2Eint__bit_2E2(c_2Earithmetic_2E_2B_2E2(V0b_2E0,V1n_2E0),V2i_2E0) ) ).

%------------------------------------------------------------------------------