Consider the following premises. ~p_3. p_3 -> q_3. q_3 -> r_3. r_3 -> p_3. Can we infer r_3 from them?
 From p_3 -> q_3, q_3 -> r_3 we can infer p_3 -> r_3. From r_3 -> p_3, p_3 -> r_3 we can infer r_3 <-> p_3. Finally, from r_3 <-> p_3, ~p_3 we can infer ~r_3, which contradicts r_3. Therefore, the answer is no.