Consider the following premises. q_6 -> p. p_6 -> w. p_6. w -> p. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From p_6 we can infer p_6 or q_6 via addition. From p_6 -> w, w -> p we can infer p_6 -> p via transitivity. Finally, from p_6 -> p, q_6 -> p, p_6 or q_6 we can infer p via disjunction elimination, which contradicts ~p. Therefore, the answer is no.