Consider the following premises. exists y: ~U_2(y). forall y: T(y) <-> U_2(y). forall y: U_2(y) -> T(y). Can we infer exists y: ~T(y) from them?
 From forall y: T(y) <-> U_2(y) we can infer forall y: T(y) -> U_2(y). From forall y: U_2(y) -> T(y), forall y: T(y) -> U_2(y) we can infer forall y: U_2(y) <-> T(y). Finally, from forall y: U_2(y) <-> T(y), exists y: ~U_2(y) we can infer exists y: ~T(y). Therefore, the answer is yes.