Consider the following premises. q_4. p_4 -> p_1. p_1 -> p_4. p_4 -> ~q_4. Can we infer p_1 from them? If possible, name the inference rules being used at each step.
 From p_4 -> ~q_4, q_4 we can infer ~p_4 via modus tollens. From p_1 -> p_4, p_4 -> p_1 we can infer p_1 <-> p_4 via biconditional introduction. Finally, from p_1 <-> p_4, ~p_4 we can infer ~p_1 via biconditional elimination, which contradicts p_1. Therefore, the answer is no.