## Section: New Software and Platforms

*Super Zenon* and *Zenon Modulo*

Several extensions of the *Zenon* automated theorem prover (developed
by Damien Doligez at *Inria* in the *Gallium* team) to Deduction
modulo have been studied. These extensions intend to be applied in the
context of the automatic verification of proof rules and obligations
coming from industrial applications formalized using the *B*
method.

The first extension, developed by Mélanie Jacquel and David Delahaye,
is called *Super Zenon*
and is an extension of *Zenon* to superdeduction, which can be seen
as a variant of Deduction modulo. This extension is a generalization
of previous experiments [42] together with
Catherine Dubois and Karim Berkani (*Siemens*), where *Zenon* has
been used and extended to superdeduction to deal with the *B* set
theory and automatically prove proof rules of *Atelier B*. This
generalization consists in allowing us to apply the extension of
*Zenon* to superdeduction to any first order theory by means of a
heuristic that automatically transforms axioms of the theory into
rewrite rules. This work is described
in [13] [35] , which also
proposes a study of the possibility of recovering intuition from
automated proofs using superdeduction.

The second extension, developed by Pierre Halmagrand, David Delahaye,
Damien Doligez, and Olivier Hermant, is called *Zenon Modulo* and is an
extension of *Zenon* to Deduction modulo. Compared to *Super Zenon*, this
extension allows us to deal with rewrite rules both over propositions
and terms. Like *Super Zenon*, *Zenon Modulo* is able to deal with any first order
theory by means of a similar heuristic. To assess the approach of
*Zenon Modulo*, we have applied this extension to the first order problems
coming from the TPTP library. An increase of the number of proved
problems has been observed, with in particular a significant increase
in the category of set theory. Over these problems of the TPTP
library, we have also observed a significant proof size reduction,
which confirms this aspect of Deduction modulo. These results are
gathered into two
publications [33] , [34] .

The third extension, developed by Guillaume Bury and David Delahaye,
is an extension of *Zenon* to (rational and integer) linear
arithmetic (using the simplex algorithm), that has been integrated
to *Zenon Modulo* by Guillaume Bury and Pierre Halmagrand, in order to be
applied in the framework of the *B* set theory to the
verification of proof obligations of
*Atelier B* [17] . Experiments have been
conducted over the benchmarks of the *BWare* project, and it turns
out that more than 95% of the proof obligations are proved thanks
to this extension.