Consider the following premises. forall x_13: Q_13(x_13) -> U_3(x_13). exists x_13: U_1(x_13). forall x_13: P_13(x_13) or Q_13(x_13). forall x_13: U_1(x_13) -> T(x_13). forall x_13: P_13(x_13) -> U_3(x_13). Can we infer forall x_13: ~(T(x_13) and U_3(x_13)) from them? If possible, name the inference rules being used at each step.
 From forall x_13: P_13(x_13) -> U_3(x_13), forall x_13: Q_13(x_13) -> U_3(x_13), forall x_13: P_13(x_13) or Q_13(x_13) we can infer forall x_13: U_3(x_13) via universal disjunction elimination. From forall x_13: U_1(x_13) -> T(x_13), exists x_13: U_1(x_13) we can infer exists x_13: T(x_13) via existential modus ponens. Finally, from exists x_13: T(x_13), forall x_13: U_3(x_13) we can infer exists x_13: T(x_13) and U_3(x_13) via existential conjunction, which contradicts forall x_13: ~(T(x_13) and U_3(x_13)). Therefore, the answer is no.