%------------------------------------------------------------------------------
% File     : SYO354^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : TPS problem E4EXT
% Version  : Especial.
% English  : 

% Refs     : [Ben99] Benzmueller (1999), Equality and Extensionality in Hig
%          : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0125 [Bro09]
%          : E4ext [Ben99]
%          : E4EXT [TPS]

% Status   : Theorem
% Rating   : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.3.0, 0.50 v4.1.0, 0.67 v4.0.1, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :    0 (   0 equ;   0 cnn)
%            Maximal formula atoms :    0 (   0 avg)
%            Number of connectives :   11 (   0   ~;   0   |;   0   &;   8   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   2 usr;   0 con; 1-1 aty)
%            Number of variables   :    5 (   2   ^;   3   !;   0   ?;   5   :)
% 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(n,type,
    n: $i > $i ).

thf(m,type,
    m: $i > $i ).

thf(cE4EXT,conjecture,
    ( ! [X: $i,P: $i > $o] :
        ( ( P @ ( m @ X ) )
       => ( P @ ( n @ X ) ) )
   => ! [Q: ( $i > $i ) > $o] :
        ( ( Q
          @ ^ [X: $i] : ( m @ X ) )
       => ( Q
          @ ^ [X: $i] : ( n @ X ) ) ) ) ).

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