Consider the following premises. p_2 -> t. u_4 -> w. w -> p_2. t -> u_4. Can we infer ~(p_2 -> u_4) from them?
 From u_4 -> w, w -> p_2 we can infer u_4 -> p_2. Finally, from p_2 -> t, t -> u_4 we can infer p_2 -> u_4, which contradicts ~(p_2 -> u_4). Therefore, the answer is no.