ProofWatch: Watchlist Guidance for Large Theories in E

TL;DR

ProofWatch introduces watchlist-based heuristics and dynamic proof matching algorithms within the E ATP system, significantly enhancing automated theorem proving efficiency on large formal libraries.

Contribution

The paper presents novel watchlist-guided heuristics and proof matching algorithms tailored for large theories in the E ATP system, improving proof search guidance.

Findings

Significant improvement over standard E strategies.

Enhanced performance on Mizar library problems.

Outperforms previous evolutionary strategy sets.

Abstract

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E's standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.