Consider the following premises. q <-> p_3. ~q_10. q -> q_10. p_1 -> p_3. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From q <-> p_3 we can infer p_3 -> q via biconditional elimination. From q -> q_10, ~q_10 we can infer ~q via modus tollens. From p_3 -> q, ~q we can infer ~p_3 via modus tollens. Finally, from p_1 -> p_3, ~p_3 we can infer ~p_1 via modus tollens, which contradicts p_1. Therefore, the answer is no.