Hammering with Vampire in Lean

Jonas Bodingbauer, Laura Kovács

We present Vampire-Hammer, a hammer for the Lean interactive theorem prover that discharges goals using the Vampire automated theorem prover and reconstructs proofs checked by the Lean kernel. Vampire-Hammer uses the Lean-auto framework to process goals and premises before dispatching them to Vampire for proof search. Doing so, we rely on standard TPTP problem formats and annotated TSTP proofs that support proof reconstruction. With a 10-second budget on 196,083 eligible Mathlib theorems, Vampire-Hammer solves 21,158 problems not solved by other evaluated tools within the same budget.