## TPTP Problem File: SEV402^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEV402^5 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Set Theory
% Problem  : TPS problem THM596
% Version  : Especial.
% English  : If a set function K is order reversing, then K o K has a fixed
%            point. This is a special case of Knaster-Tarski.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0508 [Bro09]
%          : THM596 [TPS]

% Status   : Theorem
% Rating   : 1.00 v5.1.0, 0.80 v4.1.0, 0.67 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   15 (   1 equality;  14 variable)
%            Maximal formula depth :   10 (  10 average)
%            Number of connectives :   12 (   0   ~;   0   |;   0   &;   8   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    2 (   0   :;   0   =)
%            Number of variables   :    6 (   0 sgn;   5   !;   1   ?;   0   ^)
%                                         (   6   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% 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
%          : Polymorphic definitions expanded.
%------------------------------------------------------------------------------
thf(cTHM596_pme,conjecture,(
! [K: ( \$i > \$o ) > \$i > \$o] :
( ! [Xu: \$i > \$o,Xv: \$i > \$o] :
( ! [Xx: \$i] :
( ( Xu @ Xx )
=> ( Xv @ Xx ) )
=> ! [Xx: \$i] :
( ( K @ Xv @ Xx )
=> ( K @ Xu @ Xx ) ) )
=> ? [Xw: \$i > \$o] :
( ( K @ ( K @ Xw ) )
= Xw ) ) )).

%------------------------------------------------------------------------------
```