That's not what I asked the LLM for. I asked it for a counterexample, not whether a counterexample is currently known to humans.

Is that the correct answer to "write a lock-free MPMC queue"? That is a coding problem that literally every LLM gets wrong, but has several well-known solutions.

There's merit to "I don't know" as a solution, but a lot of the knowledge encoded in LLMs is correlated with other LLMs, so more sampling isn't going to get rid of all the "I don't knows."