Consider the following premises. forall x_10: ~Q_10(x_10). P_10(c) <-> w_1. forall x_10: Q_10(x_10) -> P_10(x_10). forall x_10: P_10(x_10) -> Q_10(x_10). Can we infer w_1 from them?
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> P_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), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~P_10(x_10). From forall x_10: ~P_10(x_10) we can infer ~P_10(c). Finally, from P_10(c) <-> w_1, ~P_10(c) we can infer ~w_1, which contradicts w_1. Therefore, the answer is no.