Consider the following premises. forall z_4: W_4(z_4) -> T(z_4). exists z_4: T(z_4) -> T_3(z_4). forall z_4: W_2(z_4) <-> T_3(z_4). Can we infer forall z_4: ~(W_4(z_4) -> W_2(z_4)) from them?
That contradicts the premises. Therefore the answer is no.