Consider the following premises. s_1 -> t. w or p. t <-> p. w -> s_1. Can we infer ~t from them?
 From w -> s_1, s_1 -> t we can infer w -> t. From t <-> p we can infer p -> t. Finally, from w -> t, p -> t, w or p we can infer t, which contradicts ~t. Therefore, the answer is no.