%------------------------------------------------------------------------------
% File     : SEV401^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM67
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0490 [Bro09]
%          : THM67 [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 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :   10 (   0 equ;   0 cnn)
%            Maximal formula atoms :   10 (  10 avg)
%            Number of connectives :   29 (   0   ~;   0   |;   2   &;  20   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (  10 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   10 (   0   ^;  10   !;   0   ?;  10   :)
% 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/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

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

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

thf(cTHM67_pme,conjecture,
    ( ( ! [S: a > $o,T: a > $o] :
          ( ! [Xx: a] :
              ( ( S @ Xx )
             => ( T @ Xx ) )
         => ! [Xx: a] :
              ( ( cF @ T @ Xx )
             => ( cF @ S @ Xx ) ) )
      & ! [S: a > $o,Xx: a] :
          ( ( S @ Xx )
         => ( cF @ ( cG @ S ) @ Xx ) )
      & ! [S: a > $o,Xx: a] :
          ( ( S @ Xx )
         => ( cG @ ( cF @ S ) @ Xx ) ) )
   => ! [S: a > $o,Xx: a] :
        ( ( cF @ ( cG @ ( cF @ S ) ) @ Xx )
      <=> ( cF @ S @ Xx ) ) ) ).

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