I don’t think this is the watertight case you think it is, furthermore good luck proving with closed models that your question that’s never been asked in any form or derivation (supposedly) is not in the training data.
It’s water tight if the claim is only LLMs CAN reason.
No one is making the claim that LLMs reason like humans or always reason correctly. Ask anyone who makes a claim similar to mine. We are all ONLY making the claim that LLMs can reason correctly. That is a small claim.
The counterclaim is LLMs can’t reason and that is a vastly expansive claim that is ludicrously unprovable.
