Consider the following premises. exists x_15: P_15(x_15) <-> U(x_15). forall x_15: U(x_15) or ~T(x_15). forall x_15: U(x_15) -> T(x_15). forall x_15: Q_15(x_15). forall x_15: P_15(x_15) -> ~Q_15(x_15). Can we infer forall x_15: T(x_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) -> ~Q_15(x_15), forall x_15: Q_15(x_15) we can infer forall x_15: ~P_15(x_15) via universal modus tollens. From forall x_15: U(x_15) or ~T(x_15) we can infer forall x_15: T(x_15) -> U(x_15) via universal rewriting. From forall x_15: T(x_15) -> U(x_15), forall x_15: U(x_15) -> T(x_15) we can infer forall x_15: T(x_15) <-> U(x_15) via universal biconditional introduction. From exists x_15: P_15(x_15) <-> U(x_15), forall x_15: ~P_15(x_15) we can infer exists x_15: ~U(x_15) via existential biconditional elimination. Finally, from forall x_15: T(x_15) <-> U(x_15), exists x_15: ~U(x_15) we can infer exists x_15: ~T(x_15) via existential biconditional elimination, which contradicts forall x_15: T(x_15). Therefore, the answer is no.