Consider the following premises. p_4 <-> q_22. q_22. q_2 -> ~p_4. Can we infer ~q_2 or w from them?
 From p_4 <-> q_22 we can infer q_22 -> p_4. From q_22 -> p_4, q_22 we can infer p_4. From q_2 -> ~p_4, p_4 we can infer ~q_2. Finally, from ~q_2 we can infer ~q_2 or w. Therefore, the answer is yes.