Consider the following premises. forall z: Q(z) or ~S(z). forall z: W_3(z) -> S(z). forall z: T(z) -> W_3(z). Can we infer exists z: ~(T(z) -> Q(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: Q(z) or ~S(z) we can infer forall z: S(z) -> Q(z) via universal rewriting. From forall z: W_3(z) -> S(z), forall z: S(z) -> Q(z) we can infer forall z: W_3(z) -> Q(z) via universal transitivity. Finally, from forall z: T(z) -> W_3(z), forall z: W_3(z) -> Q(z) we can infer forall z: T(z) -> Q(z) via universal transitivity, which contradicts exists z: ~(T(z) -> Q(z)). Therefore, the answer is no.