## TPTP Problem File: KLE062+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE062+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Domain Semirings)
% Problem  : Domain elements are multiplicatively commutative
% 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   : 0.47 v7.5.0, 0.59 v7.4.0, 0.43 v7.3.0, 0.48 v7.2.0, 0.52 v7.1.0, 0.43 v7.0.0, 0.53 v6.4.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.80 v6.0.0, 0.74 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.70 v5.1.0, 0.71 v5.0.0, 0.67 v4.1.0, 0.61 v4.0.1, 0.65 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 : 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),domain(X1)) = multiplication(domain(X1),domain(X0)) )).

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