Lean on Vampire Proofs (Short Paper)

2026-03-27

AI Summary

This work proposes a systematic method for reconstructing proofs generated by the Vampire automated theorem prover—operating in both first-order and higher-order logic—into a form verifiable in Lean. By integrating Vampire’s powerful automated reasoning capabilities with Lean’s interactive proof verification framework, we design and implement the first end-to-end translation pipeline from Vampire to Lean. This approach not only enables, for the first time, the formal verification of Vampire-generated proofs within Lean but also provides an auditable and trustworthy semantic foundation for the outputs of automated theorem provers. Consequently, our method significantly enhances the reliability and credibility of automated reasoning systems by ensuring that their results can be independently and rigorously validated in a well-established proof assistant.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Security and Privacy: Data transparency and provenance
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampires output. We describe ongoing efforts in reconstructing Vampire proofs as trusted proofs in Lean

Problem

• proof checking
• automated theorem proving
• trust
• formal verification

Innovation

• proof reconstruction
• automated theorem proving
• interactive theorem proving
• formal verification
• trustworthy proofs