Consider the following premises. ~w_1. q_4 -> q. w_1 or ~q. Can we infer q_4 from them?
 From w_1 or ~q we can infer q -> w_1. From q -> w_1, ~w_1 we can infer ~q. Finally, from q_4 -> q, ~q we can infer ~q_4, which contradicts q_4. Therefore, the answer is no.