%------------------------------------------------------------------------------
% File     : SEV171^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from PAIRS-FUNS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0844 [Bro09]

% Status   : Theorem
% Rating   : 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    2 (   0 unt;   1 typ;   0 def)
%            Number of atoms       :    3 (   3 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :    7 (   0   ~;   0   |;   1   &;   5   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   6 avg)
%            Number of types       :    1 (   1 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :    7 (   1   ^;   3   !;   3   ?;   7   :)
% 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(cTHM33_pme,conjecture,
    ? [F: a > ( a > a > a ) > a] :
      ( ! [Xx: a,Xy: a] :
          ( ( ( F @ Xx )
            = ( F @ Xy ) )
         => ( Xx = Xy ) )
      & ! [X: a] :
        ? [Y: a,Z: a] :
          ( ( F @ X )
          = ( ^ [G: a > a > a] : ( G @ X @ Y ) ) ) ) ).

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