Consider the following premises. forall x_7: Q_1(x_7) -> S_7(x_7). ~Q_1(a_7). S_7(a_7) -> Q_1(a_7). Can we infer ~S_7(a_7) from them?
 From forall x_7: Q_1(x_7) -> S_7(x_7) we can infer Q_1(a_7) -> S_7(a_7). From Q_1(a_7) -> S_7(a_7), S_7(a_7) -> Q_1(a_7) we can infer Q_1(a_7) <-> S_7(a_7). Finally, from Q_1(a_7) <-> S_7(a_7), ~Q_1(a_7) we can infer ~S_7(a_7). Therefore, the answer is yes.