Consider the following premises. forall y_4: U_1(y_4) or ~R(y_4). exists y_4: P(y_4) <-> U_1(y_4). Can we infer exists y_4: R(y_4) -> P(y_4) from them?
 From exists y_4: P(y_4) <-> U_1(y_4) we can infer exists y_4: U_1(y_4) -> P(y_4). From forall y_4: U_1(y_4) or ~R(y_4) we can infer forall y_4: R(y_4) -> U_1(y_4). Finally, from forall y_4: R(y_4) -> U_1(y_4), exists y_4: U_1(y_4) -> P(y_4) we can infer exists y_4: R(y_4) -> P(y_4). Therefore, the answer is yes.