When Does Collaboration Help in Lean Proof Search?

When two language models work on the same Lean theorem, they can help in two different ways. They can provide coverage, by trying different searches and succeeding on different problems, or transfer, by sending information that makes the other search more likely to succeed.

I built a compiler-guided proof-search harness around Qwen 3.5 Flash and GPT-OSS 120B and evaluated both mechanisms. Each model repeatedly proposed and repaired a Lean proof using compiler feedback.