TPTP Problem File: SEV305^6.p

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% File     : SEV305^6 : TPTP v7.1.0. Released v5.1.0.
% Domain   : Set Theory
% Problem  : TPS problem THM2E
% Version  : Especial.
% English  : Related to the Knaster-Tarski theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0306 [Bro09]
%          : THM2E [TPS]

% Status   : Theorem
% Rating   : 0.88 v7.1.0, 0.86 v7.0.0, 0.88 v6.4.0, 0.86 v6.3.0, 0.83 v5.5.0, 0.80 v5.4.0, 0.75 v5.1.0
% Syntax   : Number of formulae    :    2 (   0 unit;   1 type;   0 defn)
%            Number of atoms       :   15 (   0 equality;  12 variable)
%            Maximal formula depth :    9 (   6 average)
%            Number of connectives :   14 (   0   ~;   0   |;   0   &;   9   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   1   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   5   !;   1   ?;   0   ^)
%                                         (   6   :;   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/
%          : Polymorphic definitions expanded.
%          : 
%          : Renamed from SEV307^5 
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thf(cK,type,(
    cK: ( $i > $o ) > $i > $o )).

thf(cTHM2E_pme,conjecture,
    ( ! [X: $i > $o,Y: $i > $o] :
        ( ! [Xx: $i] :
            ( ( X @ Xx )
           => ( Y @ Xx ) )
       => ! [Xx: $i] :
            ( ( cK @ X @ Xx )
           => ( cK @ Y @ Xx ) ) )
   => ? [U: $i > $o] :
      ! [Xx: $i] :
        ( ( cK @ U @ Xx )
      <=> ( U @ Xx ) ) )).

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