Consider the following premises. q -> s_3. q_1 -> s_1. s_1 -> q. s -> q_1. Can we infer ~(s -> s_3) from them? If possible, name the inference rules being used at each step.
 From s_1 -> q, q -> s_3 we can infer s_1 -> s_3 via transitivity. From s -> q_1, q_1 -> s_1 we can infer s -> s_1 via transitivity. Finally, from s -> s_1, s_1 -> s_3 we can infer s -> s_3 via transitivity, which contradicts ~(s -> s_3). Therefore, the answer is no.