Consider the following premises. exists y_3: R(y_3) <-> U(y_3). forall y_3: R(y_3) -> S(y_3). forall y_3: U(y_3) <-> S(y_3). Can we infer exists y_3: R(y_3) -> U(y_3) from them?
 From forall y_3: U(y_3) <-> S(y_3) we can infer forall y_3: S(y_3) -> U(y_3). From forall y_3: R(y_3) -> S(y_3), forall y_3: S(y_3) -> U(y_3) we can infer forall y_3: R(y_3) -> U(y_3). From exists y_3: R(y_3) <-> U(y_3) we can infer exists y_3: U(y_3) -> R(y_3). From exists y_3: U(y_3) -> R(y_3), forall y_3: R(y_3) -> U(y_3) we can infer exists y_3: U(y_3) <-> R(y_3). Finally, from exists y_3: U(y_3) <-> R(y_3) we can infer exists y_3: R(y_3) -> U(y_3). Therefore, the answer is yes.