Consider the following premises. exists z: W_2(z) -> T(z). forall z: U(z) -> W_2(z). forall z: T(z) -> S(z). forall z: ~S(z). Can we infer forall z: U(z) from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) -> S(z), forall z: ~S(z) we can infer forall z: ~T(z) via universal modus tollens. From forall z: U(z) -> W_2(z), exists z: W_2(z) -> T(z) we can infer exists z: U(z) -> T(z) via existential transitivity. Finally, from exists z: U(z) -> T(z), forall z: ~T(z) we can infer exists z: ~U(z) via existential modus tollens, which contradicts forall z: U(z). Therefore, the answer is no.