Vampire With a Brain Is a Good ITP Hammer
This work provides an incremental improvement for users of interactive theorem provers who rely on automated provers like Vampire for proof automation.
This paper addresses the problem of improving the performance of the Vampire theorem prover in hammer-style proof automation for ITPs, specifically on the Mizar library. They achieved this by enhancing Vampire's saturation procedure with neural guidance, resulting in improved state-of-the-art performance on the Mizar library and proving theorems that previous systems could not.
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.