Consider the following premises. u_2 -> S_7(a_7). forall x_7: R_7(x_7) <-> S_7(x_7). Can we infer ~(u_2 -> R_7(a_7)) from them? If possible, name the inference rules being used at each step.
 From forall x_7: R_7(x_7) <-> S_7(x_7) we can infer R_7(a_7) <-> S_7(a_7) via universal instantiation. From R_7(a_7) <-> S_7(a_7) we can infer S_7(a_7) -> R_7(a_7) via biconditional elimination. Finally, from u_2 -> S_7(a_7), S_7(a_7) -> R_7(a_7) we can infer u_2 -> R_7(a_7) via transitivity, which contradicts ~(u_2 -> R_7(a_7)). Therefore, the answer is no.