Consider the following premises. forall z_1: W(z_1) -> S(z_1). forall z_1: P(z_1) -> W(z_1). forall z_1: S(z_1) -> P(z_1). Can we infer exists z_1: ~(W(z_1) -> P(z_1)) from them?
 From forall z_1: W(z_1) -> S(z_1), forall z_1: S(z_1) -> P(z_1) we can infer forall z_1: W(z_1) -> P(z_1). From forall z_1: P(z_1) -> W(z_1), forall z_1: W(z_1) -> P(z_1) we can infer forall z_1: P(z_1) <-> W(z_1). Finally, from forall z_1: P(z_1) <-> W(z_1) we can infer forall z_1: W(z_1) -> P(z_1), which contradicts exists z_1: ~(W(z_1) -> P(z_1)). Therefore, the answer is no.