Consider the following premises. r_4 <-> p_2. p_10 and q_10. p_2 -> ~p_10. Can we infer r_4 from them? If possible, name the inference rules being used at each step.
 From p_10 and q_10 we can infer p_10 via simplification. From p_2 -> ~p_10, p_10 we can infer ~p_2 via modus tollens. Finally, from r_4 <-> p_2, ~p_2 we can infer ~r_4 via biconditional elimination, which contradicts r_4. Therefore, the answer is no.