Flight Instructor reported while on departure roll another aircraft took the runway and departed behind them resulting in a runway incursion.

Narrative

I was with a student holding short of runway XX at ZZZ; and my student broadcasted on CTAF for ZZZ that we were departing XX with a departure to the North East. By the time that we had advanced the throttle to full; the plane behind us (C172) decided they were going to takeoff as well. We were still on the runway while we were accelerating. This is a clear runway incursion. This left us with no room to go if we had to abort the takeoff (we would have gotten hit by them); and had no where to turn except straight out due to four other planes in the pattern. I tried to ask the C172 if they saw us; and what their intentions were; but my radio calls were ignored by them. They then said that they were turning left crosswind for runway XX so I know their radio was working. Another plane in the pattern also stated that this aircraft had done the same thing to them; or pulled out onto the runway while they were on final. I have witnessed this plane a few times at ZZZ in the past week causing runway incursions by lining up and waiting (which is only a ATC instruction). This probably was caused by the C172 being wanting to get out and not have to wait for a safe gap to takeoff. Just by them holding short and waiting for the runway to be clear would have avoided this situation.