Consider the following premises. ~T(g_4). forall z: U(z) or ~T(z). forall z: U(z) -> T(z). Can we infer ~U(g_4) from them?
 From forall z: U(z) or ~T(z) we can infer forall z: T(z) -> U(z). From forall z: U(z) -> T(z), forall z: T(z) -> U(z) we can infer forall z: U(z) <-> T(z). From forall z: U(z) <-> T(z) we can infer U(g_4) <-> T(g_4). Finally, from U(g_4) <-> T(g_4), ~T(g_4) we can infer ~U(g_4). Therefore, the answer is yes.