Consider the following premises. p_11 -> w. ~w. p -> p_11. p_11 -> p. Can we infer p from them? If possible, name the inference rules being used at each step.
 From p_11 -> p, p -> p_11 we can infer p_11 <-> p via biconditional introduction. From p_11 <-> p we can infer p -> p_11 via biconditional elimination. From p_11 -> w, ~w we can infer ~p_11 via modus tollens. Finally, from p -> p_11, ~p_11 we can infer ~p via modus tollens, which contradicts p. Therefore, the answer is no.