Consider the following premises. forall x_16: P_16(x_16) <-> U(x_16). forall x_16: U(x_16) or W_2(x_16). exists x_16: ~Q_16(x_16). forall x_16: P_16(x_16) <-> Q_16(x_16). Can we infer forall x_16: ~W_2(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) <-> Q_16(x_16), exists x_16: ~Q_16(x_16) we can infer exists x_16: ~P_16(x_16) via existential biconditional elimination. From forall x_16: P_16(x_16) <-> U(x_16), exists x_16: ~P_16(x_16) we can infer exists x_16: ~U(x_16) via existential biconditional elimination. Finally, from forall x_16: U(x_16) or W_2(x_16), exists x_16: ~U(x_16) we can infer exists x_16: W_2(x_16) via existential disjunctive syllogism, which contradicts forall x_16: ~W_2(x_16). Therefore, the answer is no.