Consider the following premises. forall y: T_1(y) -> U_3(y). exists y: T_1(y) or ~S(y). forall y: U_3(y) -> S(y). Can we infer exists y: T_1(y) <-> U_3(y) from them?
 From exists y: T_1(y) or ~S(y) we can infer exists y: S(y) -> T_1(y). From forall y: U_3(y) -> S(y), exists y: S(y) -> T_1(y) we can infer exists y: U_3(y) -> T_1(y). Finally, from forall y: T_1(y) -> U_3(y), exists y: U_3(y) -> T_1(y) we can infer exists y: T_1(y) <-> U_3(y). Therefore, the answer is yes.