## TPTP Problem File: SEU932^5.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SEU932^5 : TPTP v7.2.0. Released v4.0.0.
% Domain   : Set Theory (Functions)
% Problem  : TPS problem THM141
% Version  : Especial.
% English  : If some function which commutes with f has a unique fixed point,
%            then f has a fixed point.

% Refs     : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% Source   : [Bro09]
% Names    : tps_0265 [Bro09]
%          : THM141 [TPS]

% Status   : Theorem
% Rating   : 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :   22 (   5 equality;  17 variable)
%            Maximal formula depth :   11 (  11 average)
%            Number of connectives :   11 (   0   ~;   0   |;   2   &;   7   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    1 (   0   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   2   !;   3   ?;   2   ^)
%                                         (   7   :;   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(cTHM141_pme,conjecture,(
! [Xf: \$i > \$i] :
( ? [Xg: \$i > \$i] :
( ( ( ^ [Xx: \$i] :
( Xf @ ( Xg @ Xx ) ) )
= ( ^ [Xx: \$i] :
( Xg @ ( Xf @ Xx ) ) ) )
& ? [Xx: \$i] :
( ( ( Xg @ Xx )
= Xx )
& ! [Xz: \$i] :
( ( ( Xg @ Xz )
= Xz )
=> ( Xz = Xx ) ) ) )
=> ? [Xy: \$i] :
( ( Xf @ Xy )
= Xy ) ) )).

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