Consider the following premises. forall z: Q_1(z) -> W(z). forall z: W(z) -> Q_1(z). exists z: P(z) -> Q_1(z). forall z: ~W(z). forall z: Q_1(z) -> P(z). Can we infer forall z: ~W(z) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.