Consider the following premises. forall x_6: U(x_6). forall x_6: S_4(x_6) -> Q_6(x_6). forall x_6: S_4(x_6) or W(x_6). forall x_6: ~Q_6(x_6). Can we infer exists x_6: ~W(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: S_4(x_6) -> Q_6(x_6), forall x_6: ~Q_6(x_6) we can infer forall x_6: ~S_4(x_6) via universal modus tollens. From forall x_6: S_4(x_6) or W(x_6), forall x_6: ~S_4(x_6) we can infer forall x_6: W(x_6) via universal disjunctive syllogism. From forall x_6: U(x_6), forall x_6: W(x_6) we can infer forall x_6: U(x_6) and W(x_6) via universal conjunction. Finally, from forall x_6: U(x_6) and W(x_6) we can infer forall x_6: U(x_6) via universal simplification, which contradicts exists x_6: ~W(x_6). Therefore, the answer is no.