Consider the following premises. P_6(a_5) or q. forall x_12: ~P_12(x_12). forall x_12: P_12(x_12) <-> Q_12(x_12). forall x_12: P_6(x_12) -> Q_12(x_12). Can we infer ~q from them?
 From forall x_12: P_12(x_12) <-> Q_12(x_12), forall x_12: ~P_12(x_12) we can infer forall x_12: ~Q_12(x_12). From forall x_12: P_6(x_12) -> Q_12(x_12), forall x_12: ~Q_12(x_12) we can infer forall x_12: ~P_6(x_12). From forall x_12: ~P_6(x_12) we can infer ~P_6(a_5). Finally, from P_6(a_5) or q, ~P_6(a_5) we can infer q, which contradicts ~q. Therefore, the answer is no.