Consider the following premises. S_7(a_7) <-> Q_1(a_12). forall x_7: S(x_7) <-> S_7(x_7). forall x_2: ~Q_1(x_2). Can we infer ~S(a_7) from them?
 From forall x_2: ~Q_1(x_2) we can infer ~Q_1(a_12). From forall x_7: S(x_7) <-> S_7(x_7) we can infer S(a_7) <-> S_7(a_7). From S_7(a_7) <-> Q_1(a_12), ~Q_1(a_12) we can infer ~S_7(a_7). Finally, from S(a_7) <-> S_7(a_7), ~S_7(a_7) we can infer ~S(a_7). Therefore, the answer is yes.