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