A Flight Instructor reported during landing roll at a non-towered airport another aircraft landed behind them prior to their exit.

Narrative

Aircraft Y committed a runway incursion at ZZZ Airport. I was conducting pattern work with my student at ZZZ in Aircraft X. There were 2 other aircraft in the pattern in addition to us. We were in the downwind and abeam the numbers when we began to configure and start our descent. Upon beginning the descent; we heard a radio call for a '4 mile; straight-in final; runway XX.' They asked if we had them in sight. My student began to turn base. I reported back that I didn't have them in sight. A few seconds later; we located them; flying directly straight-in to the runway. I estimate they were 2NM away. Given that we had the right of way; there was another aircraft in the downwind behind us; the surface Bravo for ZZZ1 was in front of us; and we were roughly 500ft MSL; we opted to turn final instead of maneuver out of the pattern. Aircraft Y continued in behind us; closing the gap rapidly. My student landed and rolled out to the first taxiway exit. Before we reached the turnout; I looked back to see Aircraft Y touchdown on the runway behind us. We exited at the first turnout and they continued to the next and final exit.