🤖 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.
📝 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.
