%------------------------------------------------------------------------------
% File     : ITP006^5 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 set theory export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : normalForms^2.ax [Gau20]
%          : HL4006^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    8 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :   51 (   4 equ;   0 cnn)
%            Maximal formula atoms :    9 (   6 avg)
%            Number of connectives :  109 (   0   ~;   0   |;   0   &;  97   @)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   9 avg;  97 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   17 (   0   ^  17   !;   0   ?;  17   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2EnormalForms_2EEXT__POINT,type,
    c_2EnormalForms_2EEXT__POINT: del > del > $i ).

thf(mem_c_2EnormalForms_2EEXT__POINT,axiom,
    ! [A_27a: del,A_27b: del] : ( mem @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ ( arr @ ( arr @ A_27a @ A_27b ) @ A_27a ) ) ) ).

thf(tp_c_2EnormalForms_2EUNIV__POINT,type,
    c_2EnormalForms_2EUNIV__POINT: del > $i ).

thf(mem_c_2EnormalForms_2EUNIV__POINT,axiom,
    ! [A_27a: del] : ( mem @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).

thf(ax_thm_2EnormalForms_2EEXT__POINT__DEF,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
         => ( ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
              = ( ap @ V1g @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) )
           => ( V0f = V1g ) ) ) ) ).

thf(conj_thm_2EnormalForms_2EEXT__POINT,axiom,
    ! [A_27a: del,A_27b: del,V0f: $i] :
      ( ( mem @ V0f @ ( arr @ A_27a @ A_27b ) )
     => ! [V1g: $i] :
          ( ( mem @ V1g @ ( arr @ A_27a @ A_27b ) )
         => ( ( ( ap @ V0f @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) )
              = ( ap @ V1g @ ( ap @ ( ap @ ( c_2EnormalForms_2EEXT__POINT @ A_27a @ A_27b ) @ V0f ) @ V1g ) ) )
          <=> ( V0f = V1g ) ) ) ) ).

thf(ax_thm_2EnormalForms_2EUNIV__POINT__DEF,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ V0p @ ( ap @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ V0p ) ) )
       => ! [V1x: $i] :
            ( ( mem @ V1x @ A_27a )
           => ( p @ ( ap @ V0p @ V1x ) ) ) ) ) ).

thf(conj_thm_2EnormalForms_2EUNIV__POINT,axiom,
    ! [A_27a: del,V0p: $i] :
      ( ( mem @ V0p @ ( arr @ A_27a @ bool ) )
     => ( ( p @ ( ap @ V0p @ ( ap @ ( c_2EnormalForms_2EUNIV__POINT @ A_27a ) @ V0p ) ) )
      <=> ! [V1x: $i] :
            ( ( mem @ V1x @ A_27a )
           => ( p @ ( ap @ V0p @ V1x ) ) ) ) ) ).

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