Consider the following premises. q_1 -> t_2. u_1. w -> ~u_1. ~w -> t_2. Can we infer t_2 from them? If possible, name the inference rules being used at each step.
 From w -> ~u_1, u_1 we can infer ~w via modus tollens. From ~w we can infer ~w or q_1 via addition. Finally, from ~w -> t_2, q_1 -> t_2, ~w or q_1 we can infer t_2 via disjunction elimination. Therefore, the answer is yes.