Consider the following premises. forall x_10: R_10(x_10) -> S_10(x_10). r_2 -> R_10(a_10). S_10(a_10) -> r_2. Can we infer ~(S_10(a_10) <-> R_10(a_10)) from them?
 From forall x_10: R_10(x_10) -> S_10(x_10) we can infer R_10(a_10) -> S_10(a_10). From S_10(a_10) -> r_2, r_2 -> R_10(a_10) we can infer S_10(a_10) -> R_10(a_10). Finally, from S_10(a_10) -> R_10(a_10), R_10(a_10) -> S_10(a_10) we can infer S_10(a_10) <-> R_10(a_10), which contradicts ~(S_10(a_10) <-> R_10(a_10)). Therefore, the answer is no.