Consider the following premises. p or ~w_1. p -> r_6. w_1 or t_4. t_4 -> s_2. r_6 -> s_2. Can we infer ~s_2 from them? If possible, name the inference rules being used at each step.
 From p or ~w_1 we can infer w_1 -> p via rewriting. From w_1 -> p, p -> r_6 we can infer w_1 -> r_6 via transitivity. From w_1 -> r_6, r_6 -> s_2 we can infer w_1 -> s_2 via transitivity. Finally, from w_1 -> s_2, t_4 -> s_2, w_1 or t_4 we can infer s_2 via disjunction elimination, which contradicts ~s_2. Therefore, the answer is no.