Consider the following premises. forall z: R(z) -> T(z). forall z: ~U_4(z). forall z: T(z) -> U_4(z). exists z: T(z) -> R(z). forall z: U_4(z) -> T(z). Can we infer exists z: ~R(z) from them?
 From forall z: U_4(z) -> T(z), forall z: T(z) -> U_4(z) we can infer forall z: U_4(z) <-> T(z). From forall z: U_4(z) <-> T(z), forall z: ~U_4(z) we can infer forall z: ~T(z). From forall z: R(z) -> T(z), exists z: T(z) -> R(z) we can infer exists z: R(z) <-> T(z). Finally, from exists z: R(z) <-> T(z), forall z: ~T(z) we can infer exists z: ~R(z). Therefore, the answer is yes.