Consider the following premises. forall x_10: R_10(x_10) -> S_10(x_10). w -> R_10(a_10). S_10(a_10) -> w. Can we infer ~(R_10(a_10) <-> S_10(a_10)) from them? If possible, name the inference rules being used at each step.
 From forall x_10: R_10(x_10) -> S_10(x_10) we can infer R_10(a_10) -> S_10(a_10) via universal instantiation. From S_10(a_10) -> w, w -> R_10(a_10) we can infer S_10(a_10) -> R_10(a_10) via transitivity. Finally, from R_10(a_10) -> S_10(a_10), S_10(a_10) -> R_10(a_10) we can infer R_10(a_10) <-> S_10(a_10) via biconditional introduction, which contradicts ~(R_10(a_10) <-> S_10(a_10)). Therefore, the answer is no.