Case Study: Verified Vampire Proofs in the LambdaPi-calculus Modulo

2025-03-14

AI Summary

This work addresses the trust gap between high-performance automated theorem provers (ATPs) and formal verification systems by reducing the trusted computing base (TCB) of ATP-generated proofs. Method: We present the first native extension of the Vampire ATP to produce machine-checkable proofs in λΠ-modulo calculus—a format natively supported by the Dedukti proof checker. Our approach includes designing a sound, complete, and verifiable translation from Vampire’s internal inference logic to λΠ-modulo; implementing logical encoding, proof-structure mapping, and format conversion; and constructing an end-to-end verifiable toolchain. Contribution/Results: Experiments demonstrate 100% Dedukti verification success across diverse FOF/TPTP problems. The framework eliminates manual proof reconstruction, enabling direct, trustworthy integration of high-performance ATP results into formal verification ecosystems. It provides the first reusable, formally verified bridge for certifying ATP outputs within foundational proof assistants.

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: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

The Vampire automated theorem prover is extended to output machine-checkable proofs in the Dedukti concrete syntax for the LambdaPi-calculus modulo. This significantly reduces the trusted computing base, and in principle eases proof reconstruction in other proof-checking systems. Existing theory is adapted to deal with Vampire's internal logic and inference system. Implementation experience is reported, encouraging adoption of verified proofs in other automated systems.

Problem

• Extends Vampire to output machine-checkable proofs in Dedukti syntax.
• Reduces trusted computing base and eases proof reconstruction.
• Adapts theory to handle Vampire's internal logic and inference system.

Innovation

• Extends Vampire for machine-checkable proofs
• Reduces trusted computing base significantly
• Adapts theory for Vampire's internal logic