Consider the following premises. p_7 or p. ~p. ~p_7. Can we infer r_3 from them?
 From p_7 or p, ~p_7 we can infer p. From p we can infer p or r_3. Finally, from p or r_3, ~p we can infer r_3. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.