Consider the following premises. q or r_1. w_3 or ~r_1. w_3 or ~r_12. ~q or r_12. Can we infer w_3 from them?
 From q or r_1, ~q or r_12 we can infer r_1 or r_12. From w_3 or ~r_1 we can infer r_1 -> w_3. From w_3 or ~r_12 we can infer r_12 -> w_3. Finally, from r_1 -> w_3, r_12 -> w_3, r_1 or r_12 we can infer w_3. Therefore, the answer is yes.