Consider the following premises. forall x_3: ~U_1(x_3). exists x_3: T(x_3) -> P(x_3). forall x_3: P(x_3) <-> U_1(x_3). Can we infer forall x_3: T(x_3) from them? If possible, name the inference rules being used at each step.
 From forall x_3: P(x_3) <-> U_1(x_3) we can infer forall x_3: P(x_3) -> U_1(x_3) via universal biconditional elimination. From exists x_3: T(x_3) -> P(x_3), forall x_3: P(x_3) -> U_1(x_3) we can infer exists x_3: T(x_3) -> U_1(x_3) via existential transitivity. Finally, from exists x_3: T(x_3) -> U_1(x_3), forall x_3: ~U_1(x_3) we can infer exists x_3: ~T(x_3) via existential modus tollens, which contradicts forall x_3: T(x_3). Therefore, the answer is no.