Consider the following premises. forall x_14: P(x_14) <-> U_3(x_14). exists x_14: U_3(x_14). forall x_14: Q_3(x_14). Can we infer forall x_14: ~P(x_14) from them? If possible, name the inference rules being used at each step.
 From exists x_14: U_3(x_14), forall x_14: Q_3(x_14) we can infer exists x_14: U_3(x_14) and Q_3(x_14) via existential conjunction. From forall x_14: P(x_14) <-> U_3(x_14) we can infer forall x_14: U_3(x_14) -> P(x_14) via universal biconditional elimination. From exists x_14: U_3(x_14) and Q_3(x_14) we can infer exists x_14: U_3(x_14) via existential simplification. Finally, from forall x_14: U_3(x_14) -> P(x_14), exists x_14: U_3(x_14) we can infer exists x_14: P(x_14) via existential modus ponens, which contradicts forall x_14: ~P(x_14). Therefore, the answer is no.