Consider the following premises. forall y_3: U_2(y_3) -> T(y_3). forall y_3: ~T(y_3). forall y_3: U_2(y_3) <-> T(y_3). Can we infer exists y_3: U_2(y_3) from them?
 From forall y_3: U_2(y_3) <-> T(y_3) we can infer forall y_3: T(y_3) -> U_2(y_3). From forall y_3: T(y_3) -> U_2(y_3), forall y_3: U_2(y_3) -> T(y_3) we can infer forall y_3: T(y_3) <-> U_2(y_3). Finally, from forall y_3: T(y_3) <-> U_2(y_3), forall y_3: ~T(y_3) we can infer forall y_3: ~U_2(y_3), which contradicts exists y_3: U_2(y_3). Therefore, the answer is no.