(n.) An anti-pun is a totally random statement or comment--made when in the midst of Punning-- that is made to sound like a real pun. But It's Really Not!
This can be quite effective if done right; fellow punsters may try to get it at first, but the joke's on them--it's not a joke!
(Two students are making Geology puns)
Student 1: Geology Rocks, but it's a pretty Hard subject
Student 2: Haha Gneiss puns
Student 1: Wow i'm FLOORED
Student 2: ha? . . . wait that was an anti-pun. You got me!