Consider the following premises. p_4 <-> q. p -> q. ~s_3. p_4 -> s_3. Can we infer p from them? If possible, name the inference rules being used at each step.
 From p_4 -> s_3, ~s_3 we can infer ~p_4 via modus tollens. From p_4 <-> q, ~p_4 we can infer ~q via biconditional elimination. Finally, from p -> q, ~q we can infer ~p via modus tollens, which contradicts p. Therefore, the answer is no.