%------------------------------------------------------------------------------
% File     : SEU864^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (Finite sets)
% Problem  : TPS problem from FINITE-SET-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0863 [Bro09]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    4 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :   10 (   0   ~;   1   |;   1   &;   5   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (  12 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1 usr;   2 con; 0-2 aty)
%            Number of variables   :    6 (   3   ^;   3   !;   0   ?;   6   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
%            project in the Department of Mathematical Sciences at Carnegie
%            Mellon University. Distributed under the Creative Commons copyleft
%            license: http://creativecommons.org/licenses/by-sa/3.0/
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(t,type,
    t: a ).

thf(cDOMLEMMA1_pme,conjecture,
    ! [X: ( a > $o ) > $o] :
      ( ( ( X
          @ ^ [Xy: a] : $false )
        & ! [Xx: a > $o] :
            ( ( X @ Xx )
           => ! [Xt_0: a] :
                ( ( t = Xt_0 )
               => ( X
                  @ ^ [Xz: a] :
                      ( ( Xx @ Xz )
                      | ( Xt_0 = Xz ) ) ) ) ) )
     => ( X
        @ ^ [Xy: a] : ( t = Xy ) ) ) ).

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