%------------------------------------------------------------------------------
% File     : SEV273^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem THM542
% Version  : Especial.
% English  : A well-ordering is reflexive.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0569 [Bro09]
%          : THM542 [TPS]

% Status   : Theorem
% Rating   : 0.20 v8.2.0, 0.38 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 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, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    4 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :   19 (   0   ~;   0   |;   3   &;  11   @)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (  14 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :    7 (   0   ^;   5   !;   2   ?;   7   :)
% 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/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(cR,type,
    cR: a > a > $o ).

thf(cTHM542_pme,conjecture,
    ( ! [X: a > $o] :
        ( ? [Xz: a] : ( X @ Xz )
       => ? [Xz: a] :
            ( ( X @ Xz )
            & ! [Xx: a] :
                ( ( X @ Xx )
               => ( cR @ Xz @ Xx ) )
            & ! [Xy: a] :
                ( ( ( X @ Xy )
                  & ! [Xx: a] :
                      ( ( X @ Xx )
                     => ( cR @ Xy @ Xx ) ) )
               => ( Xy = Xz ) ) ) )
   => ! [Xx: a] : ( cR @ Xx @ Xx ) ) ).

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