Browsing the internet I found this quote:

1994 Miss America Contest--question posed to Miss Alabama:

Question: If you could live forever, would you and why?

Answer: I would not live forever, because we should not live forever, because if we were supposed to live forever, then we would live forever, but we cannot live forever, which is why I would not live forever.

It sounds pretty stupid, and the impression you'd get from it would be that her brain couldn't keep up with her mouth. But it is a surprisingly logical statement. We can interpret it as so:

P1) If we should not live forever, then I would not (choose to) live forever.
P2) If we should live forever, then we would live forever.
P3) We do not live forever.
Therefore 4) We should not live forever.
Therefore 5) I would not (choose to) live forever.

The argument-form makes use of both modus ponens and modus tollens, and she isn't guilty of affirming the consequent or denying the antecedent which a lot of supposedly more intelligent people get incorrect a lot.

I looked around the internet to find some sort of reference or confirmation that this ever actually happened, but didn't look long enough to find it. Instead I found a lot of comments about it, including:

"Sounds pretty dumb to me! I showed this to my English teacher before break. After she stopped laughing, she said if this were her student, they'd get a big fat F."

I only have a slight problem with P2 myself. But she is hardly alone by believing P2. Leibniz, who is believed to be one of the most intelligent people to ever live, notably argued for P2. it could even be argued that Descartes would also assert the truth of P2.