Is it permissible to marry another man, knowing that the husband divorced her by saying: "Go, and you are divorced (second divorce)," and he did not reconcile during the waiting period, and the wife has been living separately from him for years?

If your husband divorced you and your waiting period ('iddah (definition)) expired without him revoking the divorce, then you have become irrevocably separated from him, and it is permissible for you to marry someone else according to Islamic law. However, your marriage before the documentation of the divorce from the first husband carries legal risks, as you are still considered his wife legally. Therefore, it is essential to officially prove the divorce before documenting your new marriage, to ensure the preservation of rights and to avoid problems. If the husband refuses to prove the divorce, then take the matter to the Sharia (definition) court.