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