Are there intractable problems? Obviously, there is no problem in NP which can be shown to be intractable (by which I mean: not in P).
Is there a problem (outside of NP) which can be shown to be intractable (not lying in P)?

NP-hard / NP. A problem is in NP-hard when every problem L in NP can be reduced in polynomial time to H. Under the assumption of $P \neq NP $ ,NP-hard is intractable. Therefore NP-hard / NP is intractable. 
https://en.wikipedia.org/wiki/NP-hardness
