Is a wife divorced if her husband tells her, in front of witnesses, "Life has become impossible between us," without uttering the oath of divorce, and what is the legal status of their cohabitation and intimacy in this situation?

A husband's statement to his wife, "Life has become impossible between us," is not considered a divorce unless the husband intends divorce by it. If he does intend divorce by it, then it is considered a divorce according to the Maliki school and some Shafi'is. However, the majority of scholars do not consider it a divorce even if the husband intends it, because the phrasing itself is not inherently suitable for divorce.