Consider the following premises. q_3 -> w_1. w_1 -> r. r -> q_3. ~w_1. Can we infer ~r from them?
 From r -> q_3, q_3 -> w_1 we can infer r -> w_1. From r -> w_1, w_1 -> r we can infer r <-> w_1. Finally, from r <-> w_1, ~w_1 we can infer ~r. Therefore, the answer is yes.