Tuesday 8 January 2019, 14:00, ENS Cachan, Pavillon des Jardins: Integrating Rewriting, Tableau and Superposition into SMT, PhD defense of Guillaume Bury.

This PhD thesis presents ArchSAT, an automated theorem prover with formal proof outputs, which is used to study the integration of some first-order reasoning methods into SMT solvers. ArchSAT integrates the notion of rewriting as a regular SMT theory, which allows us to speed up reasoning on problems whose axioms can be turned into rewrite rules. Additionally, an extension of the rewriting theory for the underlying McSAT architecture enables ArchSAT to consider conditional rewrite systems as well. ArchSAT also integrates a tableau method presented as a SMT theory able to handle generic first-order reasoning, replacing the conjunctive normal form transformation and trigger mechanism traditionally used in SMT solvers. This tableau theory uses a variant of superposition in order to perform unification modulo equalities and modulo rewrite rules. Finally, ArchSAT is able to generate formal proofs for the Coq proof assistant and the Dedukti logical framework, ensuring the correctness of its results.