Consider the following premises. p_13 <-> s_2. r. t -> p_13. t or s_2. Can we infer ~p_13 from them? If possible, name the inference rules being used at each step.
 From p_13 <-> s_2 we can infer s_2 -> p_13 via biconditional elimination. Finally, from t -> p_13, s_2 -> p_13, t or s_2 we can infer p_13 via disjunction elimination, which contradicts ~p_13. Therefore, the answer is no.