Consider the following premises. forall x_9: W(x_9). exists x_9: P_5(x_9) <-> W(x_9). forall x_9: ~P_5(x_9). Can we infer exists x_9: T_1(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: W(x_9) we can infer forall x_9: W(x_9) or T_1(x_9) via universal addition. From exists x_9: P_5(x_9) <-> W(x_9), forall x_9: ~P_5(x_9) we can infer exists x_9: ~W(x_9) via existential biconditional elimination. Finally, from forall x_9: W(x_9) or T_1(x_9), exists x_9: ~W(x_9) we can infer exists x_9: T_1(x_9) via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.