Consider the following premises. q -> q_4. q_2 -> ~q_10. s -> q_4. q or s. ~q_4. Can we infer ~q_2 from them?
 From q -> q_4, s -> q_4, q or s we can infer q_4. From q_4 we can infer q_4 or q_10. From q_4 or q_10, ~q_4 we can infer q_10. Finally, from q_2 -> ~q_10, q_10 we can infer ~q_2. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.