TPTP Problem File: KLE021+3.p

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%------------------------------------------------------------------------------
% File     : KLE021+3 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Test Semirings)
% Problem  : Decompose splitting
% Version  : [Hoe08] axioms : Augmented.
% English  : Decompose x into the part starting in p and the one starting in
%            p's complement; also the rule if p then x else x = x where if p
%            then y else z = p;y + c(p);z.

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

% Status   : Theorem
% Rating   : 0.25 v7.5.0, 0.28 v7.4.0, 0.10 v7.3.0, 0.21 v7.1.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.17 v6.2.0, 0.24 v6.1.0, 0.30 v5.4.0, 0.32 v5.3.0, 0.41 v5.2.0, 0.30 v5.1.0, 0.33 v4.1.0, 0.26 v4.0.1, 0.30 v4.0.0
% Syntax   : Number of formulae    :   19 (  11 unit)
%            Number of atoms       :   32 (  20 equality)
%            Maximal formula depth :    6 (   4 average)
%            Number of connectives :   14 (   1   ~;   0   |;   4   &)
%                                         (   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   :   35 (   0 sgn;  34   !;   1   ?)
%            Maximal term depth    :    4 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding : additionally the de Morgan laws
%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%---Include additionally axioms
include('Axioms/KLE001+2.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
    ! [X0,X1] :
      ( test(X1)
     => X0 = addition(multiplication(X1,X0),multiplication(c(X1),X0)) ) )).

%------------------------------------------------------------------------------