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