Consider the following premises. w_1 or ~q_4. w_1 -> q_4. ~w_1. Can we infer q_4 from them? If possible, name the inference rules being used at each step.
 From w_1 or ~q_4 we can infer q_4 -> w_1 via rewriting. From q_4 -> w_1, w_1 -> q_4 we can infer q_4 <-> w_1 via biconditional introduction. Finally, from q_4 <-> w_1, ~w_1 we can infer ~q_4 via biconditional elimination, which contradicts q_4. Therefore, the answer is no.