Running shoes should in general be replaced after about 300 miles.
I doubt your treadmill is more abrasive thsn concrete and tarnac outside.
in fact, everything i have ted suggests running shoes last longer on a treadmill than outside. So i would rather question what shows you are wearing snd how you sre running?
I say this as a series run addict, i do about 5000km per year with a load of vertical. Next weekend i will be running 110km with 8700m of climbing in the alps.
shoes wear out quickly, they are expensive for good shoes. But it is cheaper than biking and more convenient than swimming. If i am marathon training s £150 pair lf shoes might be done in 5 weeks .