ITP001 Axioms: ITP062_7.ax


%------------------------------------------------------------------------------
% File     : ITP062_7 : TPTP v9.0.0. 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    : bft.ax [Gau19]
%          : HL4062_7.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  115 (  31 unt;  61 typ;   0 def)
%            Number of atoms       :  100 (  45 equ)
%            Maximal formula atoms :    9 (   0 avg)
%            Number of connectives :   51 (   5   ~;   4   |;  13   &)
%                                         (  13 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :   11 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   51 (  29   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   58 (  58 usr;   6 con; 0-7 aty)
%            Number of variables   :  271 ( 203   !;   1   ?; 271   :)
%                                         (  67  !>;   0  ?*;   0  @-;   0  @+)
% SPC      : TF1_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
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_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_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_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_2Elist_2EALL__DISTINCT_2E0,type,
    c_2Elist_2EALL__DISTINCT_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).

tff(c_2Elist_2EALL__DISTINCT_2E1,type,
    c_2Elist_2EALL__DISTINCT_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).

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_2Ebft_2EBFT_2E0,type,
    c_2Ebft_2EBFT_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(A_27a,A_27a))))) ).

tff(c_2Ebft_2EBFT_2E5,type,
    c_2Ebft_2EBFT_2E5: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27b)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)) * tyop_2Elist_2Elist(A_27b) * tyop_2Elist_2Elist(A_27b) * A_27a ) > A_27a ) ).

tff(c_2Epred__set_2ECARD_2E0,type,
    c_2Epred__set_2ECARD_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).

tff(c_2Epred__set_2ECARD_2E1,type,
    c_2Epred__set_2ECARD_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > 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_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2EdirGraph_2EEXCLUDE_2E0,type,
    c_2EdirGraph_2EEXCLUDE_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)))) ).

tff(c_2EdirGraph_2EEXCLUDE_2E2,type,
    c_2EdirGraph_2EEXCLUDE_2E2: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Elist_2Elist(A_27a)) ) ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(c_2Epred__set_2EFINITE_2E0,type,
    c_2Epred__set_2EFINITE_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(c_2Epred__set_2EFINITE_2E1,type,
    c_2Epred__set_2EFINITE_2E1: 
      !>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(c_2Elist_2EFOLDR_2E0,type,
    c_2Elist_2EFOLDR_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).

tff(c_2Elist_2EFOLDR_2E3,type,
    c_2Elist_2EFOLDR_2E3: 
      !>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(c_2Ebool_2EIN_2E2,type,
    c_2Ebool_2EIN_2E2: 
      !>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

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_2Elist_2ELIST__TO__SET_2E0,type,
    c_2Elist_2ELIST__TO__SET_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2Elist_2ELIST__TO__SET_2E1,type,
    c_2Elist_2ELIST__TO__SET_2E1: 
      !>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

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

tff(c_2EdirGraph_2EParents_2E0,type,
    c_2EdirGraph_2EParents_2E0: 
      !>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).

tff(c_2EdirGraph_2EParents_2E1,type,
    c_2EdirGraph_2EParents_2E1: 
      !>[A_27a: $tType,A_27b: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2EdirGraph_2EREACH__LIST_2E0,type,
    c_2EdirGraph_2EREACH__LIST_2E0: 
      !>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).

tff(c_2EdirGraph_2EREACH__LIST_2E2,type,
    c_2EdirGraph_2EREACH__LIST_2E2: 
      !>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).

tff(c_2Ebft_2ERel_2E0,type,
    c_2Ebft_2ERel_2E0: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).

tff(c_2Ebft_2ERel_2E1,type,
    c_2Ebft_2ERel_2E1: 
      !>[A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType] : ( tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))) > tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ) ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

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_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_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29,axiom,
    ! [A_27a: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: A_27c,X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))] : ( c_2Epair_2E_2C_2E2(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),app_2E2(A_27c,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),c_2Epair_2E_2C_2E0(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29_29,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),X1_2E0: tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))] : ( c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))))),c_2Epair_2E_2C_2E0(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29,axiom,
    ! [A_27a: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),X0_2E0,X1_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2EA_27e,axiom,
    ! [A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Elist_2Elist(A_27d),X1_2E0: A_27e] : ( c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27d),A_27e,X0_2E0,X1_2E0) = app_2E2(A_27e,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(A_27e,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),c_2Epair_2E_2C_2E0(tyop_2Elist_2Elist(A_27d),A_27e),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),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_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_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EALL__DISTINCT_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(A_27a),X0_2E0) ) ).

tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27a),X4_2E0: A_27b] : ( c_2Ebft_2EBFT_2E5(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(A_27b,A_27b,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,A_27b)))),c_2Ebft_2EBFT_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).

tff(arityeq5_2Ec_2Ebft_2EBFT_2E5_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),X2_2E0: tyop_2Elist_2Elist(A_27a),X3_2E0: tyop_2Elist_2Elist(A_27a),X4_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))))),c_2Ebft_2EBFT_2E0(tyop_2Elist_2Elist(A_27a),A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: A_27b,X2_2E0: A_27b] : ( c_2Ebool_2ECOND_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ebool_2ECOND_2E0(A_27b),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_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2EdirGraph_2EEXCLUDE_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2EdirGraph_2EEXCLUDE_2E2(A_27a,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))),c_2EdirGraph_2EEXCLUDE_2E0(A_27a,A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(A_27a),X0_2E0) ) ).

tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDR_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),c_2Elist_2EFOLDR_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27d,axiom,
    ! [A_27d: $tType,X0_2E0: tyop_2Elist_2Elist(A_27d)] : ( c_2Elist_2ELENGTH_2E1(A_27d,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27d),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27d),X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))] : ( c_2EdirGraph_2EParents_2E1(A_27a,A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E0(A_27a,A_27a),X0_2E0) ) ).

tff(arityeq1_2Ec_2EdirGraph_2EParents_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b))] : ( c_2EdirGraph_2EParents_2E1(A_27a,A_27b,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2EdirGraph_2EParents_2E0(A_27a,A_27b),X0_2E0) ) ).

tff(arityeq2_2Ec_2EdirGraph_2EREACH__LIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2EdirGraph_2EREACH__LIST_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2EdirGraph_2EREACH__LIST_2E0(A_27a),X0_2E0),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ebft_2ERel_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d_20mono_2EA_27e,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))))] : ( c_2Ebft_2ERel_2E1(A_27a,A_27b,A_27c,A_27d,A_27e,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)))),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Ebft_2ERel_2E0(A_27a,A_27b,A_27c,A_27d,A_27e),X0_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(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_2Ebft_2ERel__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,A_27c: $tType,A_27d: $tType,A_27e: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),V1f_2E0: A_27c,V2seen_2E0: tyop_2Elist_2Elist(A_27a),V3fringe_2E0: tyop_2Elist_2Elist(A_27d),V4acc_2E0: A_27e] : ( c_2Ebft_2ERel_2E1(A_27a,A_27b,A_27c,A_27d,A_27e,c_2Epair_2E_2C_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27b)),tyop_2Epair_2Eprod(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e))),V0G_2E0,c_2Epair_2E_2C_2E2(A_27c,tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e)),V1f_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),A_27e),V2seen_2E0,c_2Epair_2E_2C_2E2(tyop_2Elist_2Elist(A_27d),A_27e,V3fringe_2E0,V4acc_2E0))))) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(A_27a,c_2Epred__set_2EDIFF_2E2(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27b,V0G_2E0),c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2seen_2E0))),c_2Elist_2ELENGTH_2E1(A_27d,V3fringe_2E0)) ) ).

tff(thm_2Ebft_2EBFT__def,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Elist_2Elist(A_27a),V1seen_2E0: tyop_2Elist_2Elist(A_27a),V2h_2E0: A_27a,V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V4acc_2E0: A_27b,V5G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a))] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V5G_2E0)))
     => ( ( c_2Ebft_2EBFT_2E5(A_27b,A_27a,V5G_2E0,V3f_2E0,V1seen_2E0,c_2Elist_2ENIL_2E0(A_27a),V4acc_2E0) = V4acc_2E0 )
        & ( c_2Ebft_2EBFT_2E5(A_27b,A_27a,V5G_2E0,V3f_2E0,V1seen_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V0t_2E0),V4acc_2E0) = c_2Ebool_2ECOND_2E3(A_27b,c_2Ebool_2EIN_2E2(A_27a,V2h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V1seen_2E0)),c_2Ebft_2EBFT_2E5(A_27b,A_27a,V5G_2E0,V3f_2E0,V1seen_2E0,V0t_2E0,V4acc_2E0),c_2Ebft_2EBFT_2E5(A_27b,A_27a,V5G_2E0,V3f_2E0,c_2Elist_2ECONS_2E2(A_27a,V2h_2E0,V1seen_2E0),c_2Elist_2EAPPEND_2E2(A_27a,V0t_2E0,app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),V5G_2E0,V2h_2E0)),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V3f_2E0,V2h_2E0),V4acc_2E0))) ) ) ) ).

tff(thm_2Ebft_2EBFT__ind,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))))] :
      ( ! [V1G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V3seen_2E0: tyop_2Elist_2Elist(A_27a),V4h_2E0: A_27a,V5t_2E0: tyop_2Elist_2Elist(A_27a),V6acc_2E0: A_27b] :
          ( p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0P_2E0,V1G_2E0),V2f_2E0),V3seen_2E0),c_2Elist_2ENIL_2E0(A_27a)),V6acc_2E0))
          & ( ( ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V1G_2E0)))
                  & ~ p(c_2Ebool_2EIN_2E2(A_27a,V4h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3seen_2E0))) )
               => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0P_2E0,V1G_2E0),V2f_2E0),c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V3seen_2E0)),c_2Elist_2EAPPEND_2E2(A_27a,V5t_2E0,app_2E2(A_27a,tyop_2Elist_2Elist(A_27a),V1G_2E0,V4h_2E0))),app_2E2(A_27b,A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V2f_2E0,V4h_2E0),V6acc_2E0))) )
              & ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V1G_2E0)))
                  & p(c_2Ebool_2EIN_2E2(A_27a,V4h_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V3seen_2E0))) )
               => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0P_2E0,V1G_2E0),V2f_2E0),V3seen_2E0),V5t_2E0),V6acc_2E0)) ) )
           => p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0P_2E0,V1G_2E0),V2f_2E0),V3seen_2E0),c_2Elist_2ECONS_2E2(A_27a,V4h_2E0,V5t_2E0)),V6acc_2E0)) ) )
     => ! [V7v_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V8v1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V9v2_2E0: tyop_2Elist_2Elist(A_27a),V10v3_2E0: tyop_2Elist_2Elist(A_27a),V11v4_2E0: A_27b] : p(app_2E2(A_27b,tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)))),V0P_2E0,V7v_2E0),V8v1_2E0),V9v2_2E0),V10v3_2E0),V11v4_2E0)) ) ).

tff(thm_2Ebft_2EBFT__CONS,axiom,
    ! [A_27a: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V2seen_2E0: tyop_2Elist_2Elist(A_27a),V3fringe_2E0: tyop_2Elist_2Elist(A_27a),V4acc_2E0: tyop_2Elist_2Elist(A_27a),V5a_2E0: tyop_2Elist_2Elist(A_27a),V6b_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
        & ( V1f_2E0 = c_2Elist_2ECONS_2E0(A_27a) )
        & ( V4acc_2E0 = c_2Elist_2EAPPEND_2E2(A_27a,V5a_2E0,V6b_2E0) ) )
     => ( c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V5a_2E0),V6b_2E0) ) ) ).

tff(thm_2Ebft_2EBFT__FOLD,axiom,
    ! [A_27a: $tType,A_27b: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),V2seen_2E0: tyop_2Elist_2Elist(A_27a),V3fringe_2E0: tyop_2Elist_2Elist(A_27a),V4acc_2E0: A_27b] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
     => ( c_2Ebft_2EBFT_2E5(A_27b,A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0) = c_2Elist_2EFOLDR_2E3(A_27a,A_27b,V1f_2E0,V4acc_2E0,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,c_2Elist_2ECONS_2E0(A_27a),V2seen_2E0,V3fringe_2E0,c_2Elist_2ENIL_2E0(A_27a))) ) ) ).

tff(thm_2Ebft_2EBFT__ALL__DISTINCT,axiom,
    ! [A_27a: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1seen_2E0: tyop_2Elist_2Elist(A_27a),V2fringe_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
     => p(c_2Elist_2EALL__DISTINCT_2E1(A_27a,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,c_2Elist_2ECONS_2E0(A_27a),V1seen_2E0,V2fringe_2E0,c_2Elist_2ENIL_2E0(A_27a)))) ) ).

tff(thm_2Ebft_2EBFT__REACH__1,axiom,
    ! [A_27a: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V2seen_2E0: tyop_2Elist_2Elist(A_27a),V3fringe_2E0: tyop_2Elist_2Elist(A_27a),V4acc_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
        & ( V1f_2E0 = c_2Elist_2ECONS_2E0(A_27a) ) )
     => ! [V5x_2E0: A_27a] :
          ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0))))
         => ( p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2EdirGraph_2EREACH__LIST_2E2(A_27a,V0G_2E0,V3fringe_2E0)))
            | p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V4acc_2E0))) ) ) ) ).

tff(thm_2Ebft_2EBFT__REACH__2,axiom,
    ! [A_27a: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))),V2seen_2E0: tyop_2Elist_2Elist(A_27a),V3fringe_2E0: tyop_2Elist_2Elist(A_27a),V4acc_2E0: tyop_2Elist_2Elist(A_27a),V5x_2E0: A_27a] :
      ( ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
        & ( V1f_2E0 = c_2Elist_2ECONS_2E0(A_27a) )
        & p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2EdirGraph_2EREACH__LIST_2E2(A_27a,c_2EdirGraph_2EEXCLUDE_2E2(A_27a,A_27a,V0G_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2seen_2E0)),V3fringe_2E0)))
        & ~ p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,V2seen_2E0))) )
     => p(c_2Ebool_2EIN_2E2(A_27a,V5x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,V1f_2E0,V2seen_2E0,V3fringe_2E0,V4acc_2E0)))) ) ).

tff(thm_2Ebft_2EBFT__REACH__THM,axiom,
    ! [A_27a: $tType,V0G_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Elist_2Elist(A_27a)),V1fringe_2E0: tyop_2Elist_2Elist(A_27a)] :
      ( p(c_2Epred__set_2EFINITE_2E1(A_27a,c_2EdirGraph_2EParents_2E1(A_27a,A_27a,V0G_2E0)))
     => ! [V2x_2E0: A_27a] : ( c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2EdirGraph_2EREACH__LIST_2E2(A_27a,V0G_2E0,V1fringe_2E0)) = c_2Ebool_2EIN_2E2(A_27a,V2x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Ebft_2EBFT_2E5(tyop_2Elist_2Elist(A_27a),A_27a,V0G_2E0,c_2Elist_2ECONS_2E0(A_27a),c_2Elist_2ENIL_2E0(A_27a),V1fringe_2E0,c_2Elist_2ENIL_2E0(A_27a)))) ) ) ).

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