There's irony in here somewhere

"Do you have a copy of today's paper?" I asked, in an office previously known to have several.

"No," was the reply. "It's online now. It's paperless."

"A paperless paper," I pondered.

Semantically, making a paper paperless would make it ( ). Kind of like when you take the cheese out of the cheeseburger, and then take the burger out.