Consider the following premises. s_2 -> w. q_3 <-> w. ~r_4. q -> s_2. q_3 -> r_4. Can we infer ~q from them?
 From q_3 -> r_4, ~r_4 we can infer ~q_3. From q_3 <-> w, ~q_3 we can infer ~w. From s_2 -> w, ~w we can infer ~s_2. Finally, from q -> s_2, ~s_2 we can infer ~q. Therefore, the answer is yes.