Consider the following premises. forall z: W(z) -> S_2(z). forall z: T(z) -> W(z). forall z: W_4(z) -> W_2(z). forall z: W_2(z) -> T(z). Can we infer exists z: ~(W_4(z) -> S_2(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: T(z) -> W(z), forall z: W(z) -> S_2(z) we can infer forall z: T(z) -> S_2(z) via universal transitivity. From forall z: W_4(z) -> W_2(z), forall z: W_2(z) -> T(z) we can infer forall z: W_4(z) -> T(z) via universal transitivity. Finally, from forall z: W_4(z) -> T(z), forall z: T(z) -> S_2(z) we can infer forall z: W_4(z) -> S_2(z) via universal transitivity, which contradicts exists z: ~(W_4(z) -> S_2(z)). Therefore, the answer is no.