%------------------------------------------------------------------------------
% File     : SEV281^5 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from WELL-ORD-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_1151 [Bro09]

% Status   : Unknown
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unt;   2 typ;   0 def)
%            Number of atoms       :   12 (   2 equ;   0 cnn)
%            Maximal formula atoms :   12 (  12 avg)
%            Number of connectives :   63 (   0   ~;   2   |;  12   &;  37   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (  16 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   21 (   0   ^;  17   !;   4   ?;  21   :)
% SPC      : TH0_UNK_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(cR,type,
    cR: a > a > $o ).

thf(cTHM548_pme,conjecture,
    ( ( ? [W: a > a > $o] :
        ! [X: a > $o] :
          ( ? [Xz: a] : ( X @ Xz )
         => ? [Xz: a] :
              ( ( X @ Xz )
              & ! [Xx: a] :
                  ( ( X @ Xx )
                 => ( W @ Xz @ Xx ) )
              & ! [Xy: a] :
                  ( ( ( X @ Xy )
                    & ! [Xx: a] :
                        ( ( X @ Xx )
                       => ( W @ Xy @ Xx ) ) )
                 => ( Xy = Xz ) ) ) )
      & ! [Xx: a,Xy: a,Xz: a] :
          ( ( ( cR @ Xx @ Xy )
            & ( cR @ Xy @ Xz ) )
         => ( cR @ Xx @ Xz ) )
      & ! [Xx: a] : ( cR @ Xx @ Xx )
      & ! [Xx: a,Xy: a] :
          ( ( ( cR @ Xx @ Xy )
            & ( cR @ Xy @ Xx ) )
         => ( Xx = Xy ) ) )
   => ? [S: a > $o] :
        ( ! [Xx: a,Xy: a] :
            ( ( ( S @ Xx )
              & ( S @ Xy ) )
           => ( ( cR @ Xx @ Xy )
              | ( cR @ Xy @ Xx ) ) )
        & ! [T: a > $o] :
            ( ( ! [Xx: a,Xy: a] :
                  ( ( ( T @ Xx )
                    & ( T @ Xy ) )
                 => ( ( cR @ Xx @ Xy )
                    | ( cR @ Xy @ Xx ) ) )
              & ! [Xx: a] :
                  ( ( S @ Xx )
                 => ( T @ Xx ) ) )
           => ! [Xx: a] :
                ( ( T @ Xx )
               => ( S @ Xx ) ) ) ) ) ).

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