Consider the following premises. s -> p. r_1 -> p_6. p_6 -> s. p -> r_1. Can we infer ~(r_1 <-> p_6) from them? If possible, name the inference rules being used at each step.
 From p_6 -> s, s -> p we can infer p_6 -> p via transitivity. From p_6 -> p, p -> r_1 we can infer p_6 -> r_1 via transitivity. Finally, from r_1 -> p_6, p_6 -> r_1 we can infer r_1 <-> p_6 via biconditional introduction, which contradicts ~(r_1 <-> p_6). Therefore, the answer is no.