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