Consider the following premises. p_4 or ~w. p_4 <-> w. Can we infer ~(w <-> p_4) from them?
 From p_4 or ~w we can infer w -> p_4. From p_4 <-> w we can infer p_4 -> w. Finally, from w -> p_4, p_4 -> w we can infer w <-> p_4, which contradicts ~(w <-> p_4). Therefore, the answer is no.