## TPTP Problem File: KLE007+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE007+2 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Test Semirings)
% Problem  : Split 1 with q and split the parts with p
% Version  : [Hoe08] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.22 v7.5.0, 0.25 v7.4.0, 0.10 v7.3.0, 0.14 v7.1.0, 0.17 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.21 v6.2.0, 0.20 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.44 v5.2.0, 0.35 v5.1.0, 0.38 v4.1.0, 0.30 v4.0.1, 0.35 v4.0.0
% Syntax   : Number of formulae    :   17 (  11 unit)
%            Number of atoms       :   28 (  17 equality)
%            Maximal formula depth :    6 (   3 average)
%            Number of connectives :   12 (   1   ~;   0   |;   4   &)
%                                         (   4 <=>;   3  =>;   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   :   31 (   0 sgn;  30   !;   1   ?)
%            Maximal term depth    :    5 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding : 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').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ) )).

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