This was fun. Here's my test session: https://debunkbot.com/chat/48a5ac29-2924-4689-b573-2c38a1cdd...
I don't know which model underlies this. It responded more quickly than the models I normally use. It made the mistake I expected it to make, since this misconception is very common in training data, and conceded the point from my follow-up.
(EDIT: It appears that this link is not accessible to people without my cookies, except the developer I'm responding to above.)
You can share the text from individual messages but full chat share feature is TBD :)
Glad you enjoyed!