Consider the following premises. S(a_12). S_12(a_12) -> S(a_12). forall x_12: S(x_12) -> S_12(x_12). Can we infer ~S_12(a_12) from them?
 From forall x_12: S(x_12) -> S_12(x_12) we can infer S(a_12) -> S_12(a_12). From S(a_12) -> S_12(a_12), S_12(a_12) -> S(a_12) we can infer S(a_12) <-> S_12(a_12). From S(a_12) <-> S_12(a_12) we can infer S(a_12) -> S_12(a_12). Finally, from S(a_12) -> S_12(a_12), S(a_12) we can infer S_12(a_12), which contradicts ~S_12(a_12). Therefore, the answer is no.