%------------------------------------------------------------------------------
% File     : ITP002^5 : 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    : min^2.ax [Gau20]
%          : HL4002^5.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    8 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :   29 (   1 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :   48 (   0   ~;   0   |;   0   &;  41   @)
%                                         (   2 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   8 avg;  41 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :    7 (   0   ^   7   !;   0   ?;   7   :)
% SPC      : TH0_SAT_EQU_NAR

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2Emin_2E_3D,type,
    c_2Emin_2E_3D: del > $i ).

thf(mem_c_2Emin_2E_3D,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Emin_2E_3D @ A_27a ) @ ( arr @ A_27a @ ( arr @ A_27a @ bool ) ) ) ).

thf(ax_eq_p,axiom,
    ! [A: del,X: $i] :
      ( ( mem @ X @ A )
     => ! [Y: $i] :
          ( ( mem @ Y @ A )
         => ( ( p @ ( ap @ ( ap @ ( c_2Emin_2E_3D @ A ) @ X ) @ Y ) )
          <=> ( X = Y ) ) ) ) ).

thf(tp_c_2Emin_2E_3D_3D_3E,type,
    c_2Emin_2E_3D_3D_3E: $i ).

thf(mem_c_2Emin_2E_3D_3D_3E,axiom,
    mem @ c_2Emin_2E_3D_3D_3E @ ( arr @ bool @ ( arr @ bool @ bool ) ) ).

thf(ax_imp_p,axiom,
    ! [Q: $i] :
      ( ( mem @ Q @ bool )
     => ! [R: $i] :
          ( ( mem @ R @ bool )
         => ( ( p @ ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ Q ) @ R ) )
          <=> ( ( p @ Q )
             => ( p @ R ) ) ) ) ) ).

thf(tp_c_2Emin_2E_40,type,
    c_2Emin_2E_40: del > $i ).

thf(mem_c_2Emin_2E_40,axiom,
    ! [A_27a: del] : ( mem @ ( c_2Emin_2E_40 @ A_27a ) @ ( arr @ ( arr @ A_27a @ bool ) @ A_27a ) ) ).

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