Consider the following premises. forall z: P_1(z) or ~R(z). forall z: P_1(z) -> W(z). forall z: W(z) -> R(z). Can we infer exists z: ~(W(z) -> P_1(z)) from them?
 From forall z: P_1(z) or ~R(z) we can infer forall z: R(z) -> P_1(z). From forall z: W(z) -> R(z), forall z: R(z) -> P_1(z) we can infer forall z: W(z) -> P_1(z). From forall z: P_1(z) -> W(z), forall z: W(z) -> P_1(z) we can infer forall z: P_1(z) <-> W(z). Finally, from forall z: P_1(z) <-> W(z) we can infer forall z: W(z) -> P_1(z), which contradicts exists z: ~(W(z) -> P_1(z)). Therefore, the answer is no.