Improving ENIGMA-Style Clause Selection While Learning From History

TL;DR

This paper enhances ENIGMA-style clause selection in theorem proving by using recursive neural networks to classify clauses based on their derivation history, leading to significant performance improvements.

Contribution

It introduces a novel recursive neural network approach for clause classification and demonstrates its effectiveness in improving theorem prover performance.

Findings

41% performance improvement on SMT-LIB benchmarks

Effective use of derivation history and theory axioms in classification

Validation of neural network-based guidance in theorem proving

Abstract

We re-examine the topic of machine-learned clause selection guidance in saturation-based theorem provers. The central idea, recently popularized by the ENIGMA system, is to learn a classifier for recognizing clauses that appeared in previously discovered proofs. In subsequent runs, clauses classified positively are prioritized for selection. We propose several improvements to this approach and experimentally confirm their viability. For the demonstration, we use a recursive neural network to classify clauses based on their derivation history and the presence or absence of automatically supplied theory axioms therein. The automatic theorem prover Vampire guided by the network achieves a 41% improvement on a relevant subset of SMT-LIB in a real time evaluation.