Proof that the calculus of constructions extended with recursive types isn't strongly normalizing?
With general recursive types you can define the type

type T = T -&gt; T


With that type you can type self-application -- and in fact, every term of the untyped lambda calculus, including any of the well-known fixed-point operators. For example, the Y operator:

Y = \f:T. (\x:T. f (x x)) (\x:T. f (x x))