Vampire With a Brain Is a Good ITP Hammer

TL;DR

This paper enhances the Vampire theorem prover's performance in proof automation by integrating an efficient neural guidance system, significantly improving its ability to prove theorems in the Mizar library.

Contribution

It introduces a novel neural guidance architecture based on recursive neural networks that improves clause evaluation efficiency in Vampire.

Findings

Outperforms previous neural methods in proof automation.

Proves more theorems in the Mizar library than ENIGMA.

Demonstrates good learning capability of the neural guidance system.

Abstract

Vampire has been for a long time the strongest first-order automatic theorem prover, widely used for hammer-style proof automation in ITPs such as Mizar, Isabelle, HOL, and Coq. In this work, we considerably improve the performance of Vampire in hammering over the full Mizar library by enhancing its saturation procedure with efficient neural guidance. In particular, we employ a recently proposed recursive neural network classifying the generated clauses based only on their derivation history. Compared to previous neural methods based on considering the logical content of the clauses, our architecture makes evaluating a single clause much less time consuming. The resulting system shows good learning capability and improves on the state-of-the-art performance on the Mizar library, while proving many theorems that the related ENIGMA system could not prove in a similar hammering evaluation.