Consider the following premises. ~r_3 or s_4. p. r_3 or r. ~r. Can we infer ~s_4 from them? If possible, name the inference rules being used at each step.
 From r_3 or r, ~r_3 or s_4 we can infer r or s_4 via resolution. Finally, from r or s_4, ~r we can infer s_4 via disjunctive syllogism, which contradicts ~s_4. Therefore, the answer is no.