Consider the following premises. forall x_7: ~P_7(x_7). forall x_7: Q_7(x_7) <-> U(x_7). forall x_7: P_7(x_7) <-> Q_7(x_7). exists x_7: T(x_7) -> U(x_7). Can we infer forall x_7: T(x_7) from them? If possible, name the inference rules being used at each step.
 From forall x_7: P_7(x_7) <-> Q_7(x_7), forall x_7: ~P_7(x_7) we can infer forall x_7: ~Q_7(x_7) via universal biconditional elimination. From forall x_7: Q_7(x_7) <-> U(x_7), forall x_7: ~Q_7(x_7) we can infer forall x_7: ~U(x_7) via universal biconditional elimination. Finally, from exists x_7: T(x_7) -> U(x_7), forall x_7: ~U(x_7) we can infer exists x_7: ~T(x_7) via existential modus tollens, which contradicts forall x_7: T(x_7). Therefore, the answer is no.