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