Consider the following premises. q_20 or ~u_4. u_4 <-> q_20. ~u_4. Can we infer ~q_20 or r_3 from them? If possible, name the inference rules being used at each step.
 From u_4 <-> q_20 we can infer q_20 -> u_4 via biconditional elimination. From q_20 or ~u_4 we can infer u_4 -> q_20 via rewriting. From q_20 -> u_4, u_4 -> q_20 we can infer q_20 <-> u_4 via biconditional introduction. From q_20 <-> u_4, ~u_4 we can infer ~q_20 via biconditional elimination. Finally, from ~q_20 we can infer ~q_20 or r_3 via addition. Therefore, the answer is yes.