Is a woman irrevocably divorced by three pronouncements from her husband who swore on the Qur'an that if he returned to adultery, she would be divorced, and then he returned to his act, and what are the implications of that?

Adultery is a major sin. If the husband commits it, it is preferable for the wife to seek divorce. If the husband has sworn to divorce three times in case he returns to adultery, the majority of jurists hold that the triple divorce occurs immediately upon his return. However, Shaykh al-Islam Ibn Taymiyyah is of the opinion that a conditional divorce intended for emphasis or threat does not occur, and the husband is liable for an expiation for breaking an oath (kaffarat yamin). If the wife is certain that her husband has committed indecency after the oath, then the triple divorce has occurred, and she is unlawful to him, and it is not permissible for her to remain with him. Since this issue is subject to scholarly disagreement, it is necessary to refer to a Sharia court for a ruling.