Consider the following premises. exists x_10: Q_10(x_10) -> W_2(x_10). forall x_10: U_3(x_10). forall x_10: P_10(x_10) -> W_2(x_10). forall x_10: P_10(x_10) or Q_10(x_10). Can we infer forall x_10: ~W_2(x_10) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> W_2(x_10), exists x_10: Q_10(x_10) -> W_2(x_10), forall x_10: P_10(x_10) or Q_10(x_10) we can infer exists x_10: W_2(x_10) via existential disjunction elimination. From exists x_10: W_2(x_10), forall x_10: U_3(x_10) we can infer exists x_10: W_2(x_10) and U_3(x_10) via existential conjunction. Finally, from exists x_10: W_2(x_10) and U_3(x_10) we can infer exists x_10: W_2(x_10) via existential simplification, which contradicts forall x_10: ~W_2(x_10). Therefore, the answer is no.