Consider the following premises. exists y: S_3(y) -> T(y). forall y: S_3(y) or S_2(y). forall y: S_2(y) -> T(y). forall y: T(y) -> S_3(y). Can we infer exists y: T(y) from them?
 From forall y: T(y) -> S_3(y), exists y: S_3(y) -> T(y) we can infer exists y: T(y) <-> S_3(y). From exists y: T(y) <-> S_3(y) we can infer exists y: S_3(y) -> T(y). Finally, from exists y: S_3(y) -> T(y), forall y: S_2(y) -> T(y), forall y: S_3(y) or S_2(y) we can infer exists y: T(y). Therefore, the answer is yes.