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