Maestro: Agentic Formal Proof Development by Coordination

Haoyu Li, Zeren Shui, Yuhao Zhang, Ferhat Erata, Benjamin Mikek +2

Lean is increasingly used to verify mathematical proofs and software produced by LLM agents, but writing formal proofs remains hard. Existing prover systems take a divide-and-conquer approach that recursively decomposes hard proof obligations into easier lemmas and splits again any lemma that resists proof. However, a lemma can resist proof for different reasons, including insufficient guidance, a false statement, or a flaw in the decomposition that produced it. Existing systems cannot tell these apart as a failed attempt reports little beyond its failure, and responses are confined to the failing node without considering the rest of the proof or revising the plan above it. The system may thus keep decomposing obligations along a flawed proof direction until the budget runs out, causing the whole proof attempt to fail. We introduce Maestro, a Lean prover harness that handles failures through global coordination. Provers report why they failed, not just that they failed, and a coordinator that sees the whole proof chooses an appropriate response, such as guiding a stuck prover, correcting a false lemma, or retracting a flawed subtree and replanning it. The same harness extends to…