Consider the following premises. forall z_4: U(z_4) -> S(z_4). forall z_4: ~S(z_4). forall z_4: S(z_4) -> U(z_4). Can we infer forall z_4: ~U(z_4) from them?
 From forall z_4: U(z_4) -> S(z_4), forall z_4: S(z_4) -> U(z_4) we can infer forall z_4: U(z_4) <-> S(z_4). From forall z_4: U(z_4) <-> S(z_4) we can infer forall z_4: U(z_4) -> S(z_4). Finally, from forall z_4: U(z_4) -> S(z_4), forall z_4: ~S(z_4) we can infer forall z_4: ~U(z_4). Therefore, the answer is yes.