Consider the following premises. Q_13(a_12) -> S_2(a_10). forall z: ~S_2(z). forall x_13: Q_13(x_13) -> P_13(x_13). forall x_13: P_13(x_13) -> Q_13(x_13). Can we infer ~P_13(a_12) from them?
 From forall x_13: P_13(x_13) -> Q_13(x_13), forall x_13: Q_13(x_13) -> P_13(x_13) we can infer forall x_13: P_13(x_13) <-> Q_13(x_13). From forall x_13: P_13(x_13) <-> Q_13(x_13) we can infer P_13(a_12) <-> Q_13(a_12). From forall z: ~S_2(z) we can infer ~S_2(a_10). From Q_13(a_12) -> S_2(a_10), ~S_2(a_10) we can infer ~Q_13(a_12). Finally, from P_13(a_12) <-> Q_13(a_12), ~Q_13(a_12) we can infer ~P_13(a_12). Therefore, the answer is yes.