Consider the following premises. forall x_10: R_10(x_10) -> S_10(x_10). R_10(g_4) or ~S_10(g_4). Can we infer ~(S_10(g_4) <-> R_10(g_4)) 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(g_4) -> S_10(g_4) via universal instantiation. From R_10(g_4) or ~S_10(g_4) we can infer S_10(g_4) -> R_10(g_4) via rewriting. Finally, from S_10(g_4) -> R_10(g_4), R_10(g_4) -> S_10(g_4) we can infer S_10(g_4) <-> R_10(g_4) via biconditional introduction, which contradicts ~(S_10(g_4) <-> R_10(g_4)). Therefore, the answer is no.