Consider the following premises. p_11 -> t_3. p -> u_1. r_11 -> p. u_1 -> p_11. t_3 -> r_11. Can we infer ~(p_11 <-> u_1) from them? If possible, name the inference rules being used at each step.
 From p_11 -> t_3, t_3 -> r_11 we can infer p_11 -> r_11 via transitivity. From p_11 -> r_11, r_11 -> p we can infer p_11 -> p via transitivity. From p_11 -> p, p -> u_1 we can infer p_11 -> u_1 via transitivity. Finally, from p_11 -> u_1, u_1 -> p_11 we can infer p_11 <-> u_1 via biconditional introduction, which contradicts ~(p_11 <-> u_1). Therefore, the answer is no.