Consider the following premises. p -> p_2. s -> u_2. p_2 -> s. s -> p_2. Can we infer ~(p -> u_2) from them?
 From p_2 -> s, s -> p_2 we can infer p_2 <-> s. From p_2 <-> s we can infer p_2 -> s. From p_2 -> s, s -> u_2 we can infer p_2 -> u_2. Finally, from p -> p_2, p_2 -> u_2 we can infer p -> u_2, which contradicts ~(p -> u_2). Therefore, the answer is no.