%------------------------------------------------------------------------------
% File     : SEV417^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0953 [Bro09]

% Status   : Theorem
% Rating   : 0.10 v8.2.0, 0.15 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, 0.20 v5.3.0, 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       :    7 (   2 equ;   0 cnn)
%            Maximal formula atoms :    5 (   7 avg)
%            Number of connectives :   19 (   0   ~;   0   |;   6   &;  10   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (  12 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1 usr;   1 con; 0-2 aty)
%            Number of variables   :   10 (   5   ^;   5   !;   0   ?;  10   :)
% 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(cP,type,
    cP: ( a > $o ) > $o ).

thf(cTHM502_pme,conjecture,
    ! [X: a > $o,Y: a > $o,Z: a > $o] :
      ( ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
        & ! [Xx: a] :
            ( ( X @ Xx )
           => ( Z @ Xx ) )
        & ( ( ^ [Xx: a] :
                ( ( Y @ Xx )
                & ( Z @ Xx ) ) )
          = ( ^ [Xx: a] : $false ) )
        & ( cP
          @ ^ [Xx: a] :
              ( ( Y @ Xx )
              & ( Z @ Xx ) ) ) )
     => ( ( X
          = ( ^ [Xx: a] : $false ) )
        & ( cP
          @ ^ [Xx: a] : $false ) ) ) ).

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