Consider the following premises. forall x_10: P_10(x_10) <-> Q_3(x_10). exists x_10: P_10(x_10) and Q_10(x_10). Can we infer forall x_10: ~Q_3(x_10) from them? If possible, name the inference rules being used at each step.
 From exists x_10: P_10(x_10) and Q_10(x_10) we can infer exists x_10: P_10(x_10) via existential simplification. From forall x_10: P_10(x_10) <-> Q_3(x_10) we can infer forall x_10: P_10(x_10) -> Q_3(x_10) via universal biconditional elimination. Finally, from forall x_10: P_10(x_10) -> Q_3(x_10), exists x_10: P_10(x_10) we can infer exists x_10: Q_3(x_10) via existential modus ponens, which contradicts forall x_10: ~Q_3(x_10). Therefore, the answer is no.