Consider the following premises. t or w_4. ~t. t_1 -> ~w_4. Can we infer t_1 from them? If possible, name the inference rules being used at each step.
 From t or w_4, ~t we can infer w_4 via disjunctive syllogism. Finally, from t_1 -> ~w_4, w_4 we can infer ~t_1 via modus tollens, which contradicts t_1. Therefore, the answer is no.