Towards Finding Longer Proofs

Zombori, Zsolt and Csiszárik, Adrián and Michalewski, Henryk and Kaliszyk, Cezary and Urban, Josef (2021) Towards Finding Longer Proofs. In: Automated Reasoning with Analytic Tableaux and Related Methods : 30th International Conference, TABLEAUX 2021, Birmingham, UK, September 6–9, 2021, Proceedings. Lecture Notes in Computer Science; Lecture Notes in Artificial Intelligence (12842). Springer Nature Switzerland AG. (Springer Nature), Cham, pp. 1-25. ISBN 978-3-030-86058-5 (softcover); 978-3-030-86059-2 (eBook)

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Abstract

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and achieving near complete confidence. We use several simple, structured datasets with very long proofs to show that FLoP can successfully generalise a single training proof to a large class of related problems. On these benchmarks, FLoP is competitive with strong theorem provers despite using very limited search, due to its ability to solve problems that are prohibitively long for other systems.

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