Consider the following premises. ~w. p -> p_13. p_13 or ~w. p_13 -> w. Can we infer ~p from them?
 From p_13 or ~w we can infer w -> p_13. From p_13 -> w, w -> p_13 we can infer p_13 <-> w. From p_13 <-> w, ~w we can infer ~p_13. Finally, from p -> p_13, ~p_13 we can infer ~p. Therefore, the answer is yes.