Lemmas: Generation, Selection, Application
This addresses the challenge of lemma generation in automated theorem proving, which is incremental as it builds on existing methods in a simplified setting.
The paper tackled the problem of generating useful lemmas for automated theorem provers, resulting in improvements for several systems and solving a hard problem unsolved for 20 years.
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.