Embedding deduction modulo into a prover

Deduction modulo consists in presenting a theory through rewrite rules to support automatic and interactive proof search. It induces proof search methods based on narrowing, such as the polarized resolution modulo. We show how to combine this method with more traditional ordering restrictions. Interestingly, no compatibility between the rewriting and the ordering is requested to ensure completeness. We also show that some simplification rules, such as strict subsumption eliminations and demodulations, preserve completeness. For this purpose, we use a new framework based on a proof ordering. These results show that polarized resolution modulo can be integrated into existing provers, where these restrictions and simplifications are present. We also discuss how this integration can actually be done by diverting the main algorithm of state-of-the-art provers.