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