Consider the following premises. Q_10(c) -> P_10(c). ~P_10(c). forall x_10: P_10(x_10) <-> Q_10(x_10). Can we infer ~Q_10(c) from them?
 From forall x_10: P_10(x_10) <-> Q_10(x_10) we can infer forall x_10: P_10(x_10) -> Q_10(x_10). From forall x_10: P_10(x_10) -> Q_10(x_10) we can infer P_10(c) -> Q_10(c). From P_10(c) -> Q_10(c), Q_10(c) -> P_10(c) we can infer P_10(c) <-> Q_10(c). Finally, from P_10(c) <-> Q_10(c), ~P_10(c) we can infer ~Q_10(c). Therefore, the answer is yes.