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