Consider the following premises. s_4 and p_2. s_4 -> p_6. p_6 -> s_4. Can we infer ~p_6 from them? If possible, name the inference rules being used at each step.
 From s_4 and p_2 we can infer s_4 via simplification. From p_6 -> s_4, s_4 -> p_6 we can infer p_6 <-> s_4 via biconditional introduction. From p_6 <-> s_4 we can infer s_4 -> p_6 via biconditional elimination. Finally, from s_4 -> p_6, s_4 we can infer p_6 via modus ponens, which contradicts ~p_6. Therefore, the answer is no.