Is it permissible for a woman to seek divorce from her husband who beats her, insults her, and insults Allah and Muhammad, knowing that he had previously uttered a divorce and paid expiation?

It is obligatory to separate from the husband if it is proven that he curses the Divine Being and the Prophet, as this is an act of disbelief that expels one from the faith unless he repents. As for his statement "You are divorced," it is an actual divorce. However, "I will divorce you" is a promise of divorce that does not effect it. His cursing and beating his wife are forbidden. There is no good in remaining with him, and the matter must be referred to the judiciary to ascertain the legal ruling on the relationship.