## TPTP Problem File: KLE043+2.p

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```%------------------------------------------------------------------------------
% File     : KLE043+2 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra
% Problem  : Star recursion
% Version  : [Hoe08] axioms.
% English  : Classical recursion equation for star of x followed by y.

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

% Status   : Theorem
% Rating   : 0.61 v7.5.0, 0.62 v7.4.0, 0.50 v7.3.0, 0.52 v7.2.0, 0.55 v7.1.0, 0.48 v7.0.0, 0.60 v6.4.0, 0.62 v6.3.0, 0.54 v6.2.0, 0.60 v6.1.0, 0.70 v5.5.0, 0.81 v5.4.0, 0.82 v5.3.0, 0.85 v5.2.0, 0.75 v5.1.0, 0.81 v5.0.0, 0.92 v4.1.0, 0.91 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   :   32 (   0 sgn;  32   !;   0   ?)
%            Maximal term depth    :    5 (   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,X1] :