Consider the following premises. s_1 -> s. s -> t_1. p_11 -> t_1. p_4 <-> t_1. p_11 or s_1. Can we infer ~p_4 from them? If possible, name the inference rules being used at each step.
 From s_1 -> s, s -> t_1 we can infer s_1 -> t_1 via transitivity. From p_11 -> t_1, s_1 -> t_1, p_11 or s_1 we can infer t_1 via disjunction elimination. From p_4 <-> t_1 we can infer t_1 -> p_4 via biconditional elimination. Finally, from t_1 -> p_4, t_1 we can infer p_4 via modus ponens, which contradicts ~p_4. Therefore, the answer is no.