Consider the following premises. forall x_6: W_4(x_6) or U_4(x_6). forall x_6: ~W_4(x_6). forall x_6: U_4(x_6) <-> Q(x_6). Can we infer exists x_6: ~Q(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: W_4(x_6) or U_4(x_6), forall x_6: ~W_4(x_6) we can infer forall x_6: U_4(x_6) via universal disjunctive syllogism. From forall x_6: U_4(x_6) <-> Q(x_6) we can infer forall x_6: U_4(x_6) -> Q(x_6) via universal biconditional elimination. Finally, from forall x_6: U_4(x_6) -> Q(x_6), forall x_6: U_4(x_6) we can infer forall x_6: Q(x_6) via universal modus ponens, which contradicts exists x_6: ~Q(x_6). Therefore, the answer is no.