Consider the following premises. ~q. s -> r_3. r_3 -> q. s or ~q. Can we infer r_3 from them? If possible, name the inference rules being used at each step.
 From s or ~q we can infer q -> s via rewriting. From q -> s, s -> r_3 we can infer q -> r_3 via transitivity. From r_3 -> q, q -> r_3 we can infer r_3 <-> q via biconditional introduction. Finally, from r_3 <-> q, ~q we can infer ~r_3 via biconditional elimination, which contradicts r_3. Therefore, the answer is no.