Consider the following premises. forall x_2: ~S(x_2). forall x_2: U(x_2) <-> T_4(x_2). forall x_2: U(x_2) -> S(x_2). Can we infer exists x_2: T_4(x_2) from them?
 From forall x_2: U(x_2) -> S(x_2), forall x_2: ~S(x_2) we can infer forall x_2: ~U(x_2). Finally, from forall x_2: U(x_2) <-> T_4(x_2), forall x_2: ~U(x_2) we can infer forall x_2: ~T_4(x_2), which contradicts exists x_2: T_4(x_2). Therefore, the answer is no.