Consider the following premises. forall y: T(y) -> U(y). forall y: T(y). exists y: U(y) -> R_4(y). Can we infer forall y: ~R_4(y) from them?
 From forall y: T(y) -> U(y), forall y: T(y) we can infer forall y: U(y). Finally, from exists y: U(y) -> R_4(y), forall y: U(y) we can infer exists y: R_4(y), which contradicts forall y: ~R_4(y). Therefore, the answer is no.