C172 pilot trainee reported a ground conflict during the landing roll out. As the trainee and instructor landed; a single engine turboprop landed while the trainee was still on the runway. The instructor took control of the aircraft and exited quickly out of the turboprop's way. There was no communication after landing with the conflicting turboprop aircraft.

Narrative

On descent into ZZZ from the north; I noticed two other aircraft also on arrival into ZZZ. One coming from due west and another from the northwest (Aircraft Y; single engine turboprop). Myself and both other aircraft were all making correct radio calls stating our positions. As I entered the downwind; abeam the opposite end of the runway; my instructor made a call that we were entering left downwind for Runway XX. Aircraft Y called that he was northwest of the field to enter the left downwind for Runway XX. When we had reached abeam the numbers for [Runway] XX; Aircraft Y called on frequency asking if another aircraft was on downwind. My instructor responded that yes; we were; and restated our position. He did not respond to this. As we turned base; Aircraft Y called that they were on downwind to which my instructor attempted to spot the aircraft but could not see it; but on the traffic map it was midfield approaching the numbers. It appeared to extend its downwind approximately 2 miles past where we turned our base at before it turned base. The pilot made a call when he was on base and another when he was on final; which appeared to be approximately 2 miles behind us on final. Due to a strong headwind of approximately 25 knots; we had a slower ground speed and could see that he was shortening the distance between us. Due to Right of way regulations and us being the lower aircraft on approach; we continued. When we were on about a mile final; he asked us if we were landing long; to which my instructor replied yes; that we were aiming about two thousand feet down the runway (due to taxiway closures). There was no response from him and we continued. After we had touched down; we got a traffic alert about traffic at our 6 o'clock; same altitude. When my instructor turned around to see; he could see the aircraft approx. 1;000-1;500 feet behind us on the runway. My instructor immediately took controls and expedited our exit from the runway as to avoid losing anymore separation. We exited the runway at the next available taxiway and not long after; he exited; and his only other call was that he had cleared the runway.