What is the ruling regarding a man's statement to his wife: "Then you are divorced," after he had said to her: "Do such-and-such or I will divorce you," and she refused to do it, given his doubt about the occurrence of this divorce?

If what was issued by the husband, whether verbally or in writing, was with the intention of divorce, then it is a conditional divorce, contingent upon the wife not doing what was requested of her. If the husband, by saying: "Then you are divorced," intended to link the divorce to her showing refusal and non-compliance, then she is divorced immediately. However, if he linked it to her not doing it, whether immediately or in the future, then he does not breach his oath unless he is certain that she will never do it at all.