Consider the following premises. u_1 -> w_3. w_3 <-> q_1. ~u_1. w_3 -> u_1. Can we infer ~q_1 or p_4 from them? If possible, name the inference rules being used at each step.
 From u_1 -> w_3, w_3 -> u_1 we can infer u_1 <-> w_3 via biconditional introduction. From u_1 <-> w_3, ~u_1 we can infer ~w_3 via biconditional elimination. From w_3 <-> q_1, ~w_3 we can infer ~q_1 via biconditional elimination. Finally, from ~q_1 we can infer ~q_1 or p_4 via addition. Therefore, the answer is yes.