Consider the following premises. q_11 -> s. q_2 or ~r_1. s -> q_11. ~s. q_11 <-> q_2. Can we infer ~r_1 from them? If possible, name the inference rules being used at each step.
 From q_2 or ~r_1 we can infer r_1 -> q_2 via rewriting. From s -> q_11, q_11 -> s we can infer s <-> q_11 via biconditional introduction. From s <-> q_11, ~s we can infer ~q_11 via biconditional elimination. From q_11 <-> q_2, ~q_11 we can infer ~q_2 via biconditional elimination. Finally, from r_1 -> q_2, ~q_2 we can infer ~r_1 via modus tollens. Therefore, the answer is yes.