Consider the following premises. t -> r_10. s_2 -> ~r_10. p_10 -> r_1. r_1 -> r_10. p_10 or t. Can we infer s_2 from them? If possible, name the inference rules being used at each step.
 From p_10 -> r_1, r_1 -> r_10 we can infer p_10 -> r_10 via transitivity. From p_10 -> r_10, t -> r_10, p_10 or t we can infer r_10 via disjunction elimination. Finally, from s_2 -> ~r_10, r_10 we can infer ~s_2 via modus tollens, which contradicts s_2. Therefore, the answer is no.