Consider the following premises. s <-> p. s or ~q_4. Can we infer ~(q_4 -> p) from them?
 From s <-> p we can infer s -> p. From s or ~q_4 we can infer q_4 -> s. Finally, from q_4 -> s, s -> p we can infer q_4 -> p, which contradicts ~(q_4 -> p). Therefore, the answer is no.