Hint-Based SMT Proof Reconstruction

2026-01-20

AI Summary

This work addresses the challenge of efficiently leveraging information from SMT solvers in interactive theorem provers without relying on their full proofs. We propose a lightweight proof reconstruction approach based on “hints”: by extracting derived facts generated during SMT solving, we guide Lean’s built-in automation tactics. This method offers a rich yet loosely coupled middle ground between depending entirely on SMT proofs and using only the original premise set. Integrating cvc5 with Lean, we implement the QuerySMT tactic, which significantly outperforms existing SMT integration tools on standard Lean benchmarks, thereby enhancing the automation capabilities of interactive proof development.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

There are several paradigms for integrating interactive and automated theorem provers, combining the convenience of powerful automation with strong soundness guarantees. We introduce a new approach for reconstructing proofs found by SMT solvers which we intend to be complementary with existing techniques. Rather than verifying or replaying a full proof produced by the SMT solver, or at the other extreme, rediscovering the solver's proof from just the set of premises it uses, we explore an approach which helps guide an interactive theorem prover's internal automation by leveraging derived facts during solving, which we call hints. This makes it possible to extract more information from the SMT solver's proof without the cost of retaining a dependency on the SMT solver itself. We implement a tactic in the Lean proof assistant, called QuerySMT, which leverages hints from the cvc5 SMT solver to improve existing Lean automation. We evaluate QuerySMT's performance on relevant Lean benchmarks, compare it to other tools available in Lean relating to SMT solving, and show that the hints generated by cvc5 produce a clear improvement in existing automation's performance.

Problem

• SMT proof reconstruction
• interactive theorem proving
• proof automation
• hint-based guidance
• formal verification

Innovation

• hint-based proof reconstruction
• SMT solver integration
• interactive theorem proving
• proof automation
• Lean