Consider the following premises. U(c_1). forall x_3: T(x_3) <-> W_1(x_3). forall x_3: W_1(x_3) -> ~U(x_3). Can we infer exists x_3: ~T(x_3) from them? If possible, name the inference rules being used at each step.
 From U(c_1) we can infer exists x_3: U(x_3) via existential generalization. From forall x_3: W_1(x_3) -> ~U(x_3), exists x_3: U(x_3) we can infer exists x_3: ~W_1(x_3) via existential modus tollens. Finally, from forall x_3: T(x_3) <-> W_1(x_3), exists x_3: ~W_1(x_3) we can infer exists x_3: ~T(x_3) via existential biconditional elimination. Therefore, the answer is yes.