## TPTP Problem File: KLE069+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE069+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Domain Semirings)
% Problem  : Domain elements satisfy the first lattice absorption law
% Version  : [Hoe08] axioms.
% English  :

% Refs     : [DS08]  Desharnais & Struth (2008), Modal Semirings Revisited
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 0.33 v7.5.0, 0.47 v7.4.0, 0.27 v7.3.0, 0.31 v7.2.0, 0.34 v7.1.0, 0.35 v7.0.0, 0.33 v6.4.0, 0.35 v6.3.0, 0.38 v6.2.0, 0.36 v6.1.0, 0.47 v6.0.0, 0.57 v5.5.0, 0.59 v5.4.0, 0.61 v5.3.0, 0.59 v5.2.0, 0.45 v5.1.0, 0.48 v5.0.0, 0.42 v4.1.0, 0.43 v4.0.0
% Syntax   : Number of formulae    :   18 (  17 unit)
%            Number of atoms       :   19 (  18 equality)
%            Maximal formula depth :    4 (   3 average)
%            Number of connectives :    1 (   0   ~;   0   |;   0   &)
%                                         (   1 <=>;   0  =>;   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   :   30 (   0 sgn;  30   !;   0   ?)
%            Maximal term depth    :    4 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Needed for showing that domain elements form a bounded
%            distributive lattice.
%          : Equational encoding
%------------------------------------------------------------------------------
%---Include axioms for domain semiring
include('Axioms/KLE001+0.ax').
%---Include axioms for domain
include('Axioms/KLE001+5.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1] : multiplication(domain(X0),addition(domain(X0),domain(X1))) = domain(X0) )).

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