Consider the following premises. forall y_4: S(y_4) <-> T(y_4). forall y_4: S(y_4) -> U(y_4). forall y_4: ~U(y_4). Can we infer exists y_4: T(y_4) from them?
 From forall y_4: S(y_4) -> U(y_4), forall y_4: ~U(y_4) we can infer forall y_4: ~S(y_4). Finally, from forall y_4: S(y_4) <-> T(y_4), forall y_4: ~S(y_4) we can infer forall y_4: ~T(y_4), which contradicts exists y_4: T(y_4). Therefore, the answer is no.