%------------------------------------------------------------------------------
% File     : SYO148^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem from BASIC-FO-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0794 [Bro09]

% Status   : Theorem
% Rating   : 0.00 v9.0.0, 0.10 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    5 (   0 unt;   4 typ;   0 def)
%            Number of atoms       :    7 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   7 avg)
%            Number of connectives :   11 (   2   ~;   0   |;   0   &;   5   @)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   3 usr;   0 con; 1-2 aty)
%            Number of variables   :    2 (   1   ^;   1   !;   0   ?;   2   :)
% 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(cZ,type,
    cZ: a > $o ).

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

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

thf(cBOOL25,conjecture,
    ( ! [U: a] :
        ( ~ ( cX @ U )
      <=> ( ( cY @ U )
        <=> ( cZ @ U ) ) )
   => ( cX
      = ( ^ [U: a] :
            ~ ( ( cY @ U )
            <=> ( cZ @ U ) ) ) ) ) ).

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