Consider the following premises. p_4 -> T(a_10). S_10(a_10) -> p_4. forall x_10: T(x_10) -> S_10(x_10). Can we infer ~(S_10(a_10) <-> T(a_10)) from them?
 From forall x_10: T(x_10) -> S_10(x_10) we can infer T(a_10) -> S_10(a_10). From S_10(a_10) -> p_4, p_4 -> T(a_10) we can infer S_10(a_10) -> T(a_10). Finally, from S_10(a_10) -> T(a_10), T(a_10) -> S_10(a_10) we can infer S_10(a_10) <-> T(a_10), which contradicts ~(S_10(a_10) <-> T(a_10)). Therefore, the answer is no.