Consider the following premises. p -> s_4. p. q. s_1 -> s_4. Can we infer s_4 and q from them? If possible, name the inference rules being used at each step.
 From p we can infer p or s_1 via addition. From p -> s_4, s_1 -> s_4, p or s_1 we can infer s_4 via disjunction elimination. Finally, from s_4, q we can infer s_4 and q via conjunction. Therefore, the answer is yes.