There are several synonyms for the phrase "not living together," depending on the context in which it is used. For instance, "living apart" is a straightforward synonym that simply means not living together in the same physical space. Another synonym is "separated," which implies that the individuals were previously living together, but are now living separately. "Disunited," "divided," and "estranged" are synonyms that suggest a deeper divide between individuals, such as a breakdown in a relationship or marriage. "Distant" and "removed" are synonyms that can be used to suggest a physical or emotional separation between individuals. Ultimately, the context in which the phrase is used will dictate the most appropriate synonym.