Twitch: Learning Abstractions for Equational Theorem Proving

Paper i proceeding, 2026

Automated theorem provers often perform better when told what shapes of terms are interesting. In this paper we discover interesting term shapes automatically, in the form of abstractions, term patterns that occur over and over again in proofs. Our tool Twitch produces abstractions automatically and can do so in two ways: (1) from a partial, failed proof of a conjecture; (2) from successful proofs of other theorems in the same domain. Twitch is built on top of Stitch, a tool designed for discovering reusable library functions in program synthesis tasks. We have also extended Twee, an equational theorem prover, to use the generated abstractions. We evaluate Twitch on a set of unit equality (UEQ) problems from TPTP, and show that it proves problems previously unsolved by Twee, as well as yielding speed-ups on many other problems.