Consider the following premises. p_12 <-> q_12. ~p_12. p <-> r. p -> q_12. Can we infer ~r from them?
 From p_12 <-> q_12, ~p_12 we can infer ~q_12. From p -> q_12, ~q_12 we can infer ~p. Finally, from p <-> r, ~p we can infer ~r. Therefore, the answer is yes.