Consider the following premises. forall z: R_2(z) -> T_3(z). forall z: T_3(z) -> P(z). exists z: R(z) -> W_3(z). forall z: W_3(z) -> R_2(z). Can we infer forall z: ~(R(z) -> P(z)) from them?
That contradicts the premises. Therefore the answer is no.