## TPTP Problem File: KLE049+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : KLE049+1 : TPTP v7.5.0. Released v4.0.0.
% Domain   : Kleene Algebra (with Tests)
% Problem  : Hoare rule while
% Version  : [Hoe08] axioms.
% English  : Encoding of Hoare rule {p;q}x{q} -> {q} while p  do x {c(p);q},
%            where while p do x = (p;x)*;c(p).

% Refs     : [Koz00] Kozen (2000), On Hoare Logic and Kleene Algebra with T
%          : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% Source   : [Hoe08]
% Names    :

% Status   : Theorem
% Rating   : 1.00 v4.0.0
% Syntax   : Number of formulae    :   21 (  13 unit)
%            Number of atoms       :   34 (  17 equality)
%            Maximal formula depth :    7 (   4 average)
%            Number of connectives :   14 (   1   ~;   0   |;   4   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    4 (   0 propositional; 1-2 arity)
%            Number of functors    :    6 (   2 constant; 0-2 arity)
%            Number of variables   :   40 (   0 sgn;  39   !;   1   ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%---Include axioms for Kleene algebra with tests
include('Axioms/KLE002+0.ax').
%---Include test axioms
include('Axioms/KLE001+1.ax').
%------------------------------------------------------------------------------
fof(goals,conjecture,(
! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& leq(multiplication(multiplication(multiplication(X2,X1),X0),c(X2)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,star(multiplication(X1,X0))),c(X1)),c(X2)),zero) ) )).

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