Consider the following premises. ~p_4. p_22 <-> p_4. p_11 or p_22. Can we infer ~p_11 from them? If possible, name the inference rules being used at each step.
 From p_22 <-> p_4, ~p_4 we can infer ~p_22 via biconditional elimination. From p_11 or p_22 we can infer ~p_22 -> p_11 via rewriting. Finally, from ~p_22 -> p_11, ~p_22 we can infer p_11 via modus ponens, which contradicts ~p_11. Therefore, the answer is no.