Consider the following premises. p_1 <-> p_9. p_9 -> ~q_9. q_9. p_9 -> p_1. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From p_9 -> ~q_9, q_9 we can infer ~p_9 via modus tollens. From p_1 <-> p_9 we can infer p_1 -> p_9 via biconditional elimination. From p_1 -> p_9, p_9 -> p_1 we can infer p_1 <-> p_9 via biconditional introduction. Finally, from p_1 <-> p_9, ~p_9 we can infer ~p_1 via biconditional elimination, which contradicts p_1. Therefore, the answer is no.