Consider the following premises. u_2 -> S_12(a_12). p_1 -> u_2. forall x_12: R_12(x_12) <-> S_12(x_12). Can we infer ~(p_1 -> R_12(a_12)) from them? If possible, name the inference rules being used at each step.
 From forall x_12: R_12(x_12) <-> S_12(x_12) we can infer R_12(a_12) <-> S_12(a_12) via universal instantiation. From p_1 -> u_2, u_2 -> S_12(a_12) we can infer p_1 -> S_12(a_12) via transitivity. From R_12(a_12) <-> S_12(a_12) we can infer S_12(a_12) -> R_12(a_12) via biconditional elimination. Finally, from p_1 -> S_12(a_12), S_12(a_12) -> R_12(a_12) we can infer p_1 -> R_12(a_12) via transitivity, which contradicts ~(p_1 -> R_12(a_12)). Therefore, the answer is no.