Consider the following premises. t or r. r -> q_6. q_6 -> t. t -> q_6. Can we infer ~q_6 from them? If possible, name the inference rules being used at each step.
 From t -> q_6, q_6 -> t we can infer t <-> q_6 via biconditional introduction. From t <-> q_6 we can infer t -> q_6 via biconditional elimination. Finally, from t -> q_6, r -> q_6, t or r we can infer q_6 via disjunction elimination, which contradicts ~q_6. Therefore, the answer is no.