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