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