## TPTP Problem File: KLE033+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE033+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Test Semirings)
% Problem  : Disjoint tests induce disjoint restrictions
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [Mol04] Moeller (2004), Lazy Kleene Algebra
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.83 v7.5.0, 0.94 v7.4.0, 0.83 v7.3.0, 0.93 v7.1.0, 0.91 v7.0.0, 1.00 v6.4.0, 0.96 v6.1.0, 1.00 v4.0.0
% Syntax   : Number of formulae    :   19 (  11 unit)
%            Number of atoms       :   38 (  17 equality)
%            Maximal formula depth :   10 (   4 average)
%            Number of connectives :   20 (   1   ~;   0   |;   8   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    6 (   0 propositional; 1-3 arity)
%            Number of functors    :    5 (   2 constant; 0-2 arity)
%            Number of variables   :   40 (   0 sgn;  39   !;   1   ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Inequational encoding
%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%---define meet
include('Axioms/KLE001+3.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& ismeet(zero,X1,X2) )
=> ismeet(zero,multiplication(X1,X0),multiplication(X2,X0)) ) )).

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