Consider the following premises. s -> t_4. r_6 -> r. t_4 -> r_6. r -> r_2. r_2 -> p. Can we infer ~(s -> p) from them? If possible, name the inference rules being used at each step.
 From r -> r_2, r_2 -> p we can infer r -> p via transitivity. From s -> t_4, t_4 -> r_6 we can infer s -> r_6 via transitivity. From s -> r_6, r_6 -> r we can infer s -> r via transitivity. Finally, from s -> r, r -> p we can infer s -> p via transitivity, which contradicts ~(s -> p). Therefore, the answer is no.