%------------------------------------------------------------------------------
% File     : SEU844^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem GAZING-THM8
% Version  : Especial.
% English  :

% Refs     : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0208 [Bro09]
%          : 8 [Bar92]
%          : GAZING-THM8 [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.20 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :    5 (   1 equ;   0 cnn)
%            Maximal formula atoms :    5 (   5 avg)
%            Number of connectives :    8 (   0   ~;   0   |;   1   &;   4   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   2 usr;   0 con; 1-2 aty)
%            Number of variables   :    4 (   0   ^;   4   !;   0   ?;   4   :)
% 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(cS,type,
    cS: a > $o ).

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

thf(cGAZING_THM8_pme,conjecture,
    ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
   => ( ! [Xx: a] :
          ( ( cS @ Xx )
         => ( cT @ Xx ) )
      & ! [Xx: a] :
          ( ( cT @ Xx )
         => ( cS @ Xx ) ) ) ) ).

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