## TPTP Problem File: KLE008+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE008+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (Idempotent Test Semirings)
% Problem  : A simple law to eliminate the complement
% Version  : [Hoe08] axioms.
% English  :

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

% Status   : Theorem
% Rating   : 0.56 v7.5.0, 0.66 v7.4.0, 0.50 v7.3.0, 0.55 v7.1.0, 0.57 v6.4.0, 0.54 v6.3.0, 0.58 v6.2.0, 0.68 v6.1.0, 0.77 v6.0.0, 0.70 v5.5.0, 0.74 v5.4.0, 0.82 v5.3.0, 0.85 v5.2.0, 0.70 v5.1.0, 0.76 v5.0.0, 0.79 v4.1.0, 0.83 v4.0.1, 0.78 v4.0.0
% Syntax   : Number of formulae    :   17 (  11 unit)
%            Number of atoms       :   28 (  17 equality)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :   12 (   1   ~;   0   |;   3   &)
%                                         (   5 <=>;   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   :   32 (   0 sgn;  31   !;   1   ?)
%            Maximal term depth    :    3 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%---Include axioms for idempotent test semiring
include('Axioms/KLE001+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(X0,X1)
& leq(multiplication(c(X2),X0),zero) ) ) ) )).

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