Consider the following premises. exists z: P(z) -> U(z). forall z: U(z) -> T(z). forall z: T(z) -> W(z). forall z: W(z) -> P(z). Can we infer forall z: ~(P(z) -> U(z)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.