Consider the following premises. ~p_6 -> p_2. u -> p_2. p_6 -> ~t_4. t_4 and s_4. Can we infer ~p_2 from them? If possible, name the inference rules being used at each step.
 From t_4 and s_4 we can infer t_4 via simplification. From p_6 -> ~t_4, t_4 we can infer ~p_6 via modus tollens. From ~p_6 we can infer ~p_6 or u via addition. Finally, from ~p_6 -> p_2, u -> p_2, ~p_6 or u we can infer p_2 via disjunction elimination, which contradicts ~p_2. Therefore, the answer is no.