Consider the following premises. exists x: U(x). forall x: T(x). forall x: U(x) <-> R_2(x). Can we infer forall x: ~(R_2(x) and T(x)) from them? If possible, name the inference rules being used at each step.
 From forall x: U(x) <-> R_2(x) we can infer forall x: U(x) -> R_2(x) via universal biconditional elimination. From forall x: U(x) -> R_2(x), exists x: U(x) we can infer exists x: R_2(x) via existential modus ponens. Finally, from exists x: R_2(x), forall x: T(x) we can infer exists x: R_2(x) and T(x) via existential conjunction, which contradicts forall x: ~(R_2(x) and T(x)). Therefore, the answer is no.