Consider the following premises. forall x: U(x) -> R_4(x). forall x: R_4(x) -> R(x). exists x: R(x) <-> S(x). Can we infer exists x: U(x) -> S(x) from them?
 From forall x: U(x) -> R_4(x), forall x: R_4(x) -> R(x) we can infer forall x: U(x) -> R(x). From exists x: R(x) <-> S(x) we can infer exists x: R(x) -> S(x). Finally, from forall x: U(x) -> R(x), exists x: R(x) -> S(x) we can infer exists x: U(x) -> S(x). Therefore, the answer is yes.