%------------------------------------------------------------------------------
% File     : SEV119^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory (Relations)
% Problem  : TPS problem THM252
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0371 [Bro09]
%          : THM252 [TPS]
%          : THM252C [TPS]

% Status   : Theorem
% Rating   : 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.56 v7.3.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   1 unt;   1 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   42 (   0   ~;   2   |;   4   &;  28   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :   19 (   4   ^;  15   !;   0   ?;  19   :)
% 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(cTHM252_pme,conjecture,
    ! [PROP: ( a > a > $o ) > $o,R: a > a > $o,S: a > a > $o] :
      ( ( ^ [Xx: a,Xy: a] :
          ! [Xp: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a] :
                  ( ( ( R @ Xx0 @ Xy0 )
                    | ( S @ Xx0 @ Xy0 ) )
                 => ( Xp @ Xx0 @ Xy0 ) )
              & ( PROP @ Xp ) )
           => ( Xp @ Xx @ Xy ) ) )
      = ( ^ [Xx: a,Xy: a] :
          ! [Xp: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a] :
                  ( ( ! [Xp0: a > a > $o] :
                        ( ( ! [Xx1: a,Xy1: a] :
                              ( ( R @ Xx1 @ Xy1 )
                             => ( Xp0 @ Xx1 @ Xy1 ) )
                          & ( PROP @ Xp0 ) )
                       => ( Xp0 @ Xx0 @ Xy0 ) )
                    | ! [Xp0: a > a > $o] :
                        ( ( ! [Xx1: a,Xy1: a] :
                              ( ( S @ Xx1 @ Xy1 )
                             => ( Xp0 @ Xx1 @ Xy1 ) )
                          & ( PROP @ Xp0 ) )
                       => ( Xp0 @ Xx0 @ Xy0 ) ) )
                 => ( Xp @ Xx0 @ Xy0 ) )
              & ( PROP @ Xp ) )
           => ( Xp @ Xx @ Xy ) ) ) ) ).

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