What is the ruling on a husband repeating to his wife "You are divorced" three times after she provokes him and demands a divorce?

If the situation is as you described, then this wife has been irrevocably divorced from you with a major divorce (baynunah kubra). She is not lawful for you until she marries another husband, and he consummates the marriage with her, and then he divorces her or dies. This is based on the Almighty's saying: "And if he has divorced her [for the third time], then she is not lawful to him afterward until she marries another husband. And if he [then new husband] divorces her, there is no blame upon them both if they return to each other (by marriage), if they think that they can keep [within] the limits of Allah." One must be cautious about divorce, as it is not the only solution to marital problems. Divine remedies for a wife's disobedience are necessary, and it is not sufficient to rely solely on a fatwa; rather, it is essential to refer to the Sharia court.