Consider the following premises. exists x_13: U_4(x_13). forall x_13: T(x_13) <-> U_4(x_13). forall x_13: U(x_13). Can we infer forall x_13: ~(U(x_13) and T(x_13)) from them? If possible, name the inference rules being used at each step.
 From forall x_13: T(x_13) <-> U_4(x_13) we can infer forall x_13: U_4(x_13) -> T(x_13) via universal biconditional elimination. From forall x_13: U_4(x_13) -> T(x_13), exists x_13: U_4(x_13) we can infer exists x_13: T(x_13) via existential modus ponens. Finally, from forall x_13: U(x_13), exists x_13: T(x_13) we can infer exists x_13: U(x_13) and T(x_13) via existential conjunction, which contradicts forall x_13: ~(U(x_13) and T(x_13)). Therefore, the answer is no.