Consider the following premises. forall x_6: ~Q_6(x_6). forall x_6: T(x_6) <-> Q_6(x_6). forall x_6: T(x_6). Can we infer forall x_6: W(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: T(x_6) <-> Q_6(x_6), forall x_6: ~Q_6(x_6) we can infer forall x_6: ~T(x_6) via universal biconditional elimination. From forall x_6: T(x_6) we can infer forall x_6: T(x_6) or W(x_6) via universal addition. Finally, from forall x_6: T(x_6) or W(x_6), forall x_6: ~T(x_6) we can infer forall x_6: W(x_6) via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.