Using openrouter, a bunch of models fail on this. Sonnet 3.5 so far seems to be the best at saying it doesn't know, other than perhaps o1 pro, but once that has said "no" (which can be triggered more by telling it to respond very concisely) it seems very stuck and unable to say they don't exist. Letting it ramble more and so far it's been good.

Google's models for me have been the worst, lying about what's even been said in the messages so far, quoting me incorrectly.