MerLean-Prover: A Recursive Agent Harness for Lean 4 Theorem Proving Outperforms Baselines
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[Submitted on 26 May 2026 (v1), last revised 27 May 2026 (this version, v2)]
Properly proved. Has structure, has flavour, has a point.
Summary
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces 'sorry' declarations with kernel-checkable proofs using three agent types (Planning, Check, and Lean) composed by a recursive outer loop. It requires no fine-tuning, custom RL objective, or theorem-specific scaffolding. On FormalQualBench (23 PhD-qualifying-exam theorems), it solves 10/23, surpassing the strongest open-source baseline (OpenGauss, 8/23). On Putnam2025, it closes 12/12 with lower wall-clock time than the next-best system. The harness also transfers to smaller models (Sonnet and Haiku). Results suggest harness design is a central factor in Lean4 theorem proving alongside raw model capability.
Key quotes
· 5 pulledMerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs.
On FormalQualBench, a benchmark of 23 PhD-qualifying-exam theorems, MerLean-Prover solves 10/23, surpassing the strongest published open-source baseline (OpenGauss, 8/23).
On Putnam2025, the same harness closes 12/12 with substantially lower total wall-clock than the next-best system that closes the full set.
These results suggest that harness design is a central factor in end-to-end Lean4 theorem proving, alongside raw model capability.
The harness also transfers to smaller models: Sonnet closes all four tested FormalQualBench problems, and Haiku closes the two short ones.
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