Consider the following premises. q_1 -> r_3. u or r. u -> r_3. r -> q_1. Can we infer ~r_3 from them? If possible, name the inference rules being used at each step.
 From r -> q_1, q_1 -> r_3 we can infer r -> r_3 via transitivity. Finally, from u -> r_3, r -> r_3, u or r we can infer r_3 via disjunction elimination, which contradicts ~r_3. Therefore, the answer is no.