Consider the following premises. t_1 -> ~p. p. r -> t_1. r or ~t_1. Can we infer r from them? If possible, name the inference rules being used at each step.
 From r or ~t_1 we can infer t_1 -> r via rewriting. From t_1 -> ~p, p we can infer ~t_1 via modus tollens. From r -> t_1, t_1 -> r we can infer r <-> t_1 via biconditional introduction. Finally, from r <-> t_1, ~t_1 we can infer ~r via biconditional elimination, which contradicts r. Therefore, the answer is no.