## TPTP Problem File: KLE040+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE040+2 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra
% Problem  : The star of an element is multiplicatively idempotent
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [Koz94] Kozen (1994), A Completeness Theorem for Kleene Algebr
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.33 v7.5.0, 0.41 v7.4.0, 0.30 v7.3.0, 0.34 v7.2.0, 0.38 v7.1.0, 0.30 v7.0.0, 0.33 v6.4.0, 0.42 v6.3.0, 0.38 v6.2.0, 0.48 v6.1.0, 0.47 v6.0.0, 0.43 v5.5.0, 0.56 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.55 v5.1.0, 0.57 v5.0.0, 0.58 v4.1.0, 0.57 v4.0.1, 0.52 v4.0.0
% Syntax   : Number of formulae    :   17 (  13 unit)
%            Number of atoms       :   21 (  12 equality)
%            Maximal formula depth :    5 (   3 average)
%            Number of connectives :    4 (   0   ~;   0   |;   1   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    2 (   0 propositional; 2-2 arity)
%            Number of functors    :    5 (   2 constant; 0-2 arity)
%            Number of variables   :   31 (   0 sgn;  31   !;   0   ?)
%            Maximal term depth    :    4 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding : proof goal is split into 2 inequations
%------------------------------------------------------------------------------
%---Include axioms for Kleene algebra
include('Axioms/KLE002+0.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0] :
( leq(multiplication(star(X0),star(X0)),star(X0))
& leq(star(X0),multiplication(star(X0),star(X0))) ) )).

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