Consider the following premises. forall z: U(z) or ~R_3(z). forall z: U(z) <-> S(z). exists z: ~S(z). Can we infer exists z: ~R_3(z) from them?
 From forall z: U(z) or ~R_3(z) we can infer forall z: R_3(z) -> U(z). From forall z: U(z) <-> S(z), exists z: ~S(z) we can infer exists z: ~U(z). Finally, from forall z: R_3(z) -> U(z), exists z: ~U(z) we can infer exists z: ~R_3(z). Therefore, the answer is yes.