arXiv:2607.00815v1 Announce Type: cross Abstract: SAT solvers settle combinatorial problems beyond the reach of interactive theorem provers and produce LRAT certificates for independent verification. We present LRAT-Catcher, a standalone, general-purpose tool that imports a DIMACS formula together with an LRAT certificate into Lean 4 as a theorem. LRAT-Catcher runs the formally verified LRAT checker from Lean core as compiled native code via reflection. This scales to instances where Mathlib's explicit proof-term import exhausts memory. LRAT-Catcher also composes cube-and-conquer solving runs
The continuous development in formal verification and proof assistants like Lean 4 is pushing the boundaries of what can be formally proven and verified in computational logic.
This tool improves the reliability and trustworthiness of complex computational problem-solving by independently verifying the correctness of SAT solver outputs, which is crucial for safety-critical AI applications.
The ability to efficiently import and formally verify SAT solver certificates into Lean 4 via reflection changes how complex combinatorial problems can be rigorously proven, moving beyond traditional interactive methods.
- · Formal verification developers
- · High-assurance AI systems
- · Academic research in proof assistants
- · Aerospace and semiconductor industries
- · Systems relying solely on unverified SAT solver outputs
Increased adoption of formal verification for critical computational tasks.
Development of more robust and trustworthy AI models that can be formally audited.
Potential acceleration of AI safety and alignment research by providing a stronger verification backbone.
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Read at arXiv cs.AI