Consider the following premises. forall x_10: ~Q_10(x_10). forall x_10: P(x_10) -> Q_10(x_10). forall x_10: Q_10(x_10) -> P(x_10). P(a_5) <-> t. Can we infer ~t from them?
 From forall x_10: P(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> P(x_10) we can infer forall x_10: P(x_10) <-> Q_10(x_10). From forall x_10: P(x_10) <-> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~P(x_10). From forall x_10: ~P(x_10) we can infer ~P(a_5). Finally, from P(a_5) <-> t, ~P(a_5) we can infer ~t. Therefore, the answer is yes.