Consider the following premises. ~p. s_4 -> t_1. t_1 -> s_4. p <-> s_4. Can we infer t_1 from them? If possible, name the inference rules being used at each step.
 From t_1 -> s_4, s_4 -> t_1 we can infer t_1 <-> s_4 via biconditional introduction. From p <-> s_4 we can infer s_4 -> p via biconditional elimination. From s_4 -> p, ~p we can infer ~s_4 via modus tollens. Finally, from t_1 <-> s_4, ~s_4 we can infer ~t_1 via biconditional elimination, which contradicts t_1. Therefore, the answer is no.