Consider the following premises. ~q_8. p_8 <-> q_8. p_1 -> p_8. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From p_8 <-> q_8 we can infer p_8 -> q_8 via biconditional elimination. From p_1 -> p_8, p_8 -> q_8 we can infer p_1 -> q_8 via transitivity. Finally, from p_1 -> q_8, ~q_8 we can infer ~p_1 via modus tollens, which contradicts p_1. Therefore, the answer is no.