Consider the following premises. p_3 -> p_1. p_1 -> s. s -> p_3. Can we infer ~(p_1 <-> p_3) from them?
 From p_1 -> s, s -> p_3 we can infer p_1 -> p_3. Finally, from p_1 -> p_3, p_3 -> p_1 we can infer p_1 <-> p_3, which contradicts ~(p_1 <-> p_3). Therefore, the answer is no.