Consider the following premises. ~q_4 or r. p -> q_4. p. Can we infer q_1 or r from them?
 From p -> q_4, p we can infer q_4. From q_4 we can infer q_4 or q_1. Finally, from q_4 or q_1, ~q_4 or r we can infer q_1 or r. Therefore, the answer is yes.