%------------------------------------------------------------------------------
% File     : SEV416^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem from SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0880 [Bro09]

% Status   : Theorem
% Rating   : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% Syntax   : Number of formulae    :    4 (   0 unt;   3 typ;   0 def)
%            Number of atoms       :   11 (   0 equ;   0 cnn)
%            Maximal formula atoms :   11 (  11 avg)
%            Number of connectives :   18 (   0   ~;   1   |;   1   &;   8   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :    4 (   0   ^;   4   !;   0   ?;   4   :)
% 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(cG,type,
    cG: $o ).

thf(cB,type,
    cB: $i > $o ).

thf(cA,type,
    cA: $i > $o ).

thf(cDUAL_EG3_pme,conjecture,
    ( ( ( ( ! [Xx: $i] :
              ( ( cA @ Xx )
             => ( cB @ Xx ) )
          & ! [Xx: $i] :
              ( ( cA @ Xx )
             => ( cB @ Xx ) ) )
       => cG )
      | ( ! [Xx: $i] :
            ( ( cA @ Xx )
           => ( cB @ Xx ) )
       => cG ) )
   => ( ! [Xx: $i] :
          ( ( cA @ Xx )
         => ( cB @ Xx ) )
     => cG ) ) ).

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