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arXiv · 2603.06849

Twitch: Learning Abstractions for Equational Theorem Proving

Guy Axelrod·Moa Johansson·Nicholas Smallbone
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Abstract

Several successful strategies in automated reasoning rely on human-supplied guidance about which term or clause shapes are interesting. In this paper we aim to discover interesting term shapes automatically. Specifically, we discover abstractions : term patterns that occur over and over again in relevant proofs. We present our tool Twitch which discovers abstractions with the help of Stitch, a tool originally developed for discovering reusable library functions in program synthesis tasks. Twitch can produce abstractions in two ways: (1) from a partial, failed proof of a conjecture; (2) from successful proofs of other theorems in the same domain. We have also extended Twee, an equational theorem prover, to use these abstractions. We evaluate Twitch on a set of unit equality (UEQ) problems from TPTP, and show that it can prove 12 rating-1 problems as well as yielding significant speed-ups on many other problems.

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Guy Axelrod, Moa Johansson, Nicholas Smallbone. 2026-03-06. Twitch: Learning Abstractions for Equational Theorem Proving. https://arxiv.org/abs/2603.06849

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