Consider the following premises. p -> t_4. ~r_1 -> s_3. p_15 or p. p_15 -> t_4. r_1 -> ~t_4. Can we infer s_3 from them? If possible, name the inference rules being used at each step.
 From p_15 -> t_4, p -> t_4, p_15 or p we can infer t_4 via disjunction elimination. From r_1 -> ~t_4, t_4 we can infer ~r_1 via modus tollens. Finally, from ~r_1 -> s_3, ~r_1 we can infer s_3 via modus ponens. Therefore, the answer is yes.