Consider the following premises. w -> t. p_8 <-> q_4. ~q_19. w. q_4 -> q_19. Can we infer p_8 from them? If possible, name the inference rules being used at each step.
 From q_4 -> q_19, ~q_19 we can infer ~q_4 via modus tollens. From w -> t, w we can infer t via modus ponens. Finally, from p_8 <-> q_4, ~q_4 we can infer ~p_8 via biconditional elimination, which contradicts p_8. Therefore, the answer is no.