Lemmas: Generation, Selection, Application

Michael Rawson, TU Wien
Christoph Wernhard, University of Potsdam
Zsolt Zombori, Rényi AI
Wolfgang Bibel, Technical University Darmstadt
Published at
14 September 2023

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search.