Consider the following premises. forall z: Q(z) -> P(z). forall z: ~Q(z). forall z: P(z) -> Q(z). forall z: W(z) -> P(z). forall z: Q(z) -> W(z). Can we infer forall z: ~P(z) from them?
 From forall z: Q(z) -> W(z), forall z: W(z) -> P(z) we can infer forall z: Q(z) -> P(z). From forall z: Q(z) -> P(z), forall z: P(z) -> Q(z) we can infer forall z: Q(z) <-> P(z). From forall z: Q(z) <-> P(z) we can infer forall z: P(z) -> Q(z). From forall z: P(z) -> Q(z), forall z: Q(z) -> P(z) we can infer forall z: P(z) <-> Q(z). Finally, from forall z: P(z) <-> Q(z), forall z: ~Q(z) we can infer forall z: ~P(z). Therefore, the answer is yes.