Consider the following premises. r -> p_6. q_1 <-> p_6. ~q_1. p_6 -> r. Can we infer r from them? If possible, name the inference rules being used at each step.
 From p_6 -> r, r -> p_6 we can infer p_6 <-> r via biconditional introduction. From q_1 <-> p_6, ~q_1 we can infer ~p_6 via biconditional elimination. Finally, from p_6 <-> r, ~p_6 we can infer ~r via biconditional elimination, which contradicts r. Therefore, the answer is no.