%------------------------------------------------------------------------------
% File     : SEV308^5 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM1A
% Version  : Especial.
% English  : Related to the Knaster-Tarski theorem.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0446 [Bro09]
%          : THM1A [TPS]

% Status   : Theorem
% Rating   : 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   1 unt;   0 typ;   0 def)
%            Number of atoms       :    1 (   1 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   12 (   1   ~;   1   |;   1   &;   7   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (  11 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0 usr;   0 con; 2-2 aty)
%            Number of variables   :    6 (   0   ^;   3   !;   3   ?;   6   :)
% SPC      : TH0_THM_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/
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM1A_pme,conjecture,
    ! [K: ( $i > $o ) > $i > $o] :
      ( ? [X: $i > $o,Y: $i > $o] :
          ( ! [Xx: $i] :
              ( ( X @ Xx )
             => ( Y @ Xx ) )
          & ~ ! [Xx: $i] :
                ( ( K @ X @ Xx )
               => ( K @ Y @ Xx ) ) )
      | ? [U: $i > $o] :
          ( ( K @ U )
          = U ) ) ).

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