Consider the following premises. p -> t. w_4 -> q_1. p or w_4. q_1 -> t. Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From w_4 -> q_1, q_1 -> t we can infer w_4 -> t via transitivity. Finally, from p -> t, w_4 -> t, p or w_4 we can infer t via disjunction elimination, which contradicts ~t. Therefore, the answer is no.