Consider the following premises. ~s. ~p_22. p_22 <-> r_4. s or q. Can we infer r_4 from them? If possible, name the inference rules being used at each step.
 From p_22 <-> r_4 we can infer r_4 -> p_22 via biconditional elimination. From s or q, ~s we can infer q via disjunctive syllogism. Finally, from r_4 -> p_22, ~p_22 we can infer ~r_4 via modus tollens, which contradicts r_4. Therefore, the answer is no.