Consider the following premises. forall z_1: P(z_1) <-> S(z_1). exists z_1: P(z_1) -> W_1(z_1). forall z_1: W_1(z_1) -> T(z_1). forall z_1: T(z_1) -> U(z_1). Can we infer forall z_1: ~(S(z_1) -> U(z_1)) from them?
That contradicts the premises. Therefore the answer is no.