Consider the following premises. ~s_1. p_12 -> q_10. p_12 -> s_1. q_10 -> p_12. Can we infer ~q_10 or w from them?
 From p_12 -> s_1, ~s_1 we can infer ~p_12. From p_12 -> q_10, q_10 -> p_12 we can infer p_12 <-> q_10. From p_12 <-> q_10, ~p_12 we can infer ~q_10. Finally, from ~q_10 we can infer ~q_10 or w. Therefore, the answer is yes.