@Poslovitch @lunareclipse I tested something similar but more obscure; I used Coquand's paradox (really, De Bruijn's paradox) and only about half of the chat.lmsys.org bots can get it right.

For reference, my prompt was, "In mathematics, consider rooted trees: a root and zero or more branches, each branch its own tree. Let a tree be normal iff it is not among its own branches. Is there a tree R such that every normal tree is a branch of R and every branch of R is normal?"

If the bot didn't get it immediately, I sent, "Hint: is R normal?" which is also how I would prompt a human. This worked sometimes.