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