# ENIGMAWatch: ProofWatch Meets ENIGMA

## TL;DR

ENIGMAWatch is a novel proof guidance system for saturation-style theorem provers that combines symbolic proof matching with statistical learning, leading to improved performance on large theorem sets.

## Contribution

It introduces a new learning-based proof guidance that integrates ProofWatch and ENIGMA methods for the first time in a saturation-style prover.

## Key findings

- ProofWatch and ENIGMA combined improve prover performance.
- Added proof-matching info is valuable for machine learning.
- System outperforms previous methods on Mizar Library problems.

## Abstract

In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system: ProofWatch and ENIGMA. ProofWatch is motivated by the watchlist (hints) method and based on symbolic matching of multiple related proofs, while ENIGMA is based on statistical machine learning. The two methods are combined by using the evolving information about symbolic proof matching as an additional information that characterizes the saturation-style proof search for the statistical learning methods. The new system is experimentally evaluated on a large set of problems from the Mizar Library. We show that the added proof-matching information is considered important by the statistical machine learners, and that it leads to improvements in E's Performance over ProofWatch and ENIGMA.