Learning-assisted Theorem Proving with Millions of Lemmas
This work addresses the challenge of scaling automated theorem proving for formal mathematicians by efficiently leveraging large lemma sets, though it is incremental as it builds on existing methods with new criteria and filtering.
The authors tackled the problem of automated theorem proving in large formal mathematical libraries by identifying and reusing useful lemmas from millions of existing proofs, showing that this approach significantly strengthens theorem proving for new conjectures in libraries like Flyspeck.
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such statements is named and re-used in later proofs by formal mathematicians. In this work, we suggest and implement criteria defining the estimated usefulness of the HOL Light lemmas for proving further theorems. We use these criteria to mine the large inference graph of the lemmas in the HOL Light and Flyspeck libraries, adding up to millions of the best lemmas to the pool of statements that can be re-used in later proofs. We show that in combination with learning-based relevance filtering, such methods significantly strengthen automated theorem proving of new conjectures over large formal mathematical libraries such as Flyspeck.