A technology company is building a system to automatically generate and validate new mathematical theorems. Their plan is to use a powerful language model to generate a theorem and its corresponding proof, and then feed the proof directly into an automated proof-checking software. If the software confirms the proof is valid, the theorem is added to a database of verified knowledge. Critically evaluate this strategy. What is its most significant strength, and what is a major potential weakness or blind spot that could undermine the project's goal of creating a reliable database of new theorems?