Section: Overall Objectives

Automated theorem proving

Deduction modulo has originally been proposed to solve a problem in automated theorem proving and some of the early work in this area focused on the design of an automated theorem proving method called Resolution modulo, but this method was so complex that it was never implemented. This method was simplified in 2010 [4] and it could then be implemented. This implementation that builds on the iProver effort [52] is called iProver modulo.

iProver modulo gave surprisingly good results [2] , so that we use it now to search for proofs in many areas: in the theory of classes —also known as B-set theory—, on finite structures, etc. Similar ideas have also been exploited for tableaux methods leading to the systems ZenonB and super-Zenon.

More generally, we believe that proof-checking and automated theorem proving have a lot to learn from each other, because a proof is both a static linguistic object justifying the truth of a proposition and a dynamic process of proving this proposition.