Consider the following premises. exists y_1: S(y_1) <-> R_4(y_1). forall y_1: R_4(y_1) or ~S(y_1). Can we infer exists y_1: S(y_1) -> R_4(y_1) from them?
 From exists y_1: S(y_1) <-> R_4(y_1) we can infer exists y_1: R_4(y_1) -> S(y_1). From forall y_1: R_4(y_1) or ~S(y_1) we can infer forall y_1: S(y_1) -> R_4(y_1). From forall y_1: S(y_1) -> R_4(y_1), exists y_1: R_4(y_1) -> S(y_1) we can infer exists y_1: S(y_1) <-> R_4(y_1). Finally, from exists y_1: S(y_1) <-> R_4(y_1) we can infer exists y_1: S(y_1) -> R_4(y_1). Therefore, the answer is yes.