smart and graduate studies are mutually exclusive

Rest assured fellow graduate students:

Let $S$ be a set of smart individuals and $P$ be the set of PhD students, then we can safely assume that
\[S\cap P=\emptyset.\]

I have been reading advice from the following blog:

I'm not smart, so it has been very calming for me to hear that being smart is "neither sufficient nor necessary" to obtain a PhD. In fact, smart people don't go to graduate school.