Vampire With a Brain Is a Good ITP Hammer

Vampire has been for a long time the strongest first-order automated 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 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, this leads to large real-time speedup of the neural guidance. The resulting system shows good learning capability and achieves 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.