Lemmas: Generation, Selection, Application

Rawson, Michael and Wernhard, Christoph and Zombori, Zsolt and Bibel, Wolfgang (2023) Lemmas: Generation, Selection, Application. In: Automated Reasoning with Analytic Tableaux and Related Methods. Lecture Notes in Computer Science . Springer, Cham, Cham. ISBN 9783031435133 (In Press)

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Abstract

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.

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