This is a 4 node graph with 5 edges of edge lengths 40, 30, 20, 10, and 5. The edge of length 5 is between edges 4 and 3. The edge of weight 10 will be a part of the MST only if it is not the heaviest edge of all cycles that it is a part of. But it is the heaviest edge in the cycle 4 to 3 to 4. So it is not a part of some MST.

       40
  1-----------2
  |           |
30|           | 20
  |           |
  |    10     |
  4-----------3
  |           |
  |-----------|
        5