Consider the following premises. r -> T(b). forall z_3: T(z_3) -> U(z_3). U(b) -> r. Can we infer ~(T(b) <-> U(b)) from them?
 From forall z_3: T(z_3) -> U(z_3) we can infer T(b) -> U(b). From U(b) -> r, r -> T(b) we can infer U(b) -> T(b). Finally, from T(b) -> U(b), U(b) -> T(b) we can infer T(b) <-> U(b), which contradicts ~(T(b) <-> U(b)). Therefore, the answer is no.