## TPTP Problem File: KLE027+4.p

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```%------------------------------------------------------------------------------
% File     : KLE027+4 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Test Semirings)
% Problem  : Simplify conditional
% Version  : [Hoe08] axioms : Augmented.
% English  : Simplify conditional: if p then (if p then x else y) else
%            z = if p then x else z.

% Refs     : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.50 v7.5.0, 0.56 v7.4.0, 0.40 v7.3.0, 0.45 v7.2.0, 0.48 v7.1.0, 0.39 v7.0.0, 0.47 v6.4.0, 0.42 v6.3.0, 0.38 v6.2.0, 0.44 v6.1.0, 0.53 v6.0.0, 0.48 v5.5.0, 0.56 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.52 v5.0.0, 0.46 v4.1.0, 0.43 v4.0.1, 0.48 v4.0.0
% Syntax   : Number of formulae    :   19 (  11 unit)
%            Number of atoms       :   34 (  19 equality)
%            Maximal formula depth :    8 (   4 average)
%            Number of connectives :   16 (   1   ~;   0   |;   6   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    4 (   0 propositional; 1-2 arity)
%            Number of functors    :    5 (   2 constant; 0-2 arity)
%            Number of variables   :   38 (   0 sgn;  37   !;   1   ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding : additionally the de Morgan laws : proof
%            goal is split into 2 inequations.
%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
include('Axioms/KLE001+2.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4) )