Consider the following premises. exists y: T_1(y) -> S(y). forall y: S(y) -> R_1(y). forall y: T_1(y) or ~R_1(y). Can we infer exists y: R_1(y) <-> T_1(y) from them?
 From forall y: T_1(y) or ~R_1(y) we can infer forall y: R_1(y) -> T_1(y). From exists y: T_1(y) -> S(y), forall y: S(y) -> R_1(y) we can infer exists y: T_1(y) -> R_1(y). Finally, from forall y: R_1(y) -> T_1(y), exists y: T_1(y) -> R_1(y) we can infer exists y: R_1(y) <-> T_1(y). Therefore, the answer is yes.