TPTP Problem File: SEV244^5.p

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% File     : SEV244^5 : TPTP v7.0.0. Released v4.0.0.
% Domain   : Set Theory (Sets of sets)
% Problem  : TPS problem from SETS-OF-SETS-THMS
% Version  : Especial.
% English  :

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0966 [Bro09]

% Status   : Theorem
% Rating   : 0.71 v7.0.0, 0.75 v6.4.0, 0.86 v6.3.0, 0.83 v6.0.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.75 v5.2.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :    3 (   0 unit;   2 type;   0 defn)
%            Number of atoms       :   26 (   0 equality;  21 variable)
%            Maximal formula depth :   13 (   6 average)
%            Number of connectives :   25 (   0   ~;   0   |;   2   &;  16   @)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   2   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   7   !;   2   ?;   1   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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/
%          : 
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thf(a_type,type,(
    a: $tType )).

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

thf(cTHM116_pme,conjecture,
    ( ! [X: a > $o,Y: a > $o] :
        ( ! [Xx: a] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: a] :
            ( ( cK @ X @ Xx )
           => ( cK @ Y @ Xx ) ) )
   => ! [Xx: a] :
        ( ( cK
          @ ^ [Xx0: a] :
            ? [S: a > $o] :
              ( ! [Xx1: a] :
                  ( ( S @ Xx1 )
                 => ( cK @ S @ Xx1 ) )
              & ( S @ Xx0 ) )
          @ Xx )
      <=> ? [S: a > $o] :
            ( ! [Xx0: a] :
                ( ( S @ Xx0 )
               => ( cK @ S @ Xx0 ) )
            & ( S @ Xx ) ) ) )).

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