At about 2125 Eastern time, the airplane was substantially damaged following an engine fire on the runway. The flight instructor and student were not injured. Night visual conditions prevailed at the time. Upon coming to a stop on the runway after landing, the engine quit. The pilots contacted the tower to inform them of the situation. Three restart attempts were performed, with about 20 seconds allowed between attempts. After the third attempt, flames were observed coming from the engine. The instructor cut the fuel mixture to idle, took the fire extinguisher and both pilots exited the airplane. The instructor attempted to put out the fire; however, the Halon extinguisher was inoperative.