Consider the following premises. r_1 -> p_11. ~r_1. p_11 -> r_1. p_11 or ~q_7. Can we infer q_7 from them? If possible, name the inference rules being used at each step.
 From p_11 -> r_1, r_1 -> p_11 we can infer p_11 <-> r_1 via biconditional introduction. From p_11 or ~q_7 we can infer q_7 -> p_11 via rewriting. From p_11 <-> r_1, ~r_1 we can infer ~p_11 via biconditional elimination. Finally, from q_7 -> p_11, ~p_11 we can infer ~q_7 via modus tollens, which contradicts q_7. Therefore, the answer is no.