Consider the following premises. t <-> s. t -> p_2. p_2 -> t. ~s. t -> p_2. Can we infer ~p_2 from them?
 From t -> p_2, p_2 -> t we can infer t <-> p_2. From t <-> p_2 we can infer p_2 -> t. From t <-> s, ~s we can infer ~t. From p_2 -> t, t -> p_2 we can infer p_2 <-> t. Finally, from p_2 <-> t, ~t we can infer ~p_2. Therefore, the answer is yes.