%------------------------------------------------------------------------------
% File     : SYO348^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem E1EXT
% Version  : Especial.
% English  : Example from [Ben99] p.115.

% Refs     : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0054 [Bro09]
%          : E1EXT [TPS]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.33 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    4 (   0 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :    5 (   0   ~;   0   |;   0   &;   2   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   5 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :    1 (   0   ^;   1   !;   0   ?;   1   :)
% SPC      : TH0_THM_NEQ_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(b,type,
    b: $o ).

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

thf(cE1EXT,conjecture,
    ( ( a
    <=> b )
   => ! [P: $o > $o] :
        ( ( P @ a )
       => ( P @ b ) ) ) ).

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