I had the thought recently that theorem provers could be a neat source of synthetic data. Make an LLM generate a proof, run it to evaluate it and label it as va

I had the thought recently that theorem provers could be a neat source of synthetic data. Make an LLM generate a proof, run it to evaluate it and label it as valid/invalid, fine-tune the LLM on the results. In theory it should then more consistently create valid proofs.