vector - QGIS: "Invalid geometry" even after using validity checker and v.clean

I'm trying to intersect two layers in QGIS, similar to this unanswered question. I've performed Vector > Geometry Tools > Check Geometry Validity and I've run GRASS's v.clean, per these questions.

I'm still getting this response:

GEOS geoprocessing error: One or more input features have invalid geometry.

• Is there a better way to check geometry?


• Is there a way QGIS can tell me where the problem in the geometry is?


• Can anyone see what I'm doing wrong using my files?

Here is a link to the underlying set of Voronoi polygons I want to intersect: https://www.dropbox.com/s/edev53n7nn7b6wy/Voronoi1.zip?dl=0

Here is a link to the problematic outline of Liberia that's giving me an "invalid geometry" error when I try intersecting it with the above (already run through Check Validity and v.clean): https://www.dropbox.com/s/4oa7ln7rk2n6e23/Liberia%20Outline%20Valid%20Cleaned.zip?dl=0

Answer

I ran the Check validity from the dropdown

Used the default settings

The result was an Invalid Output

I then copied and pasted the co-ordinated into the QGIS project window screen (Centre bottom) and zoomed in until I found an intersection...

I deleted three nodes to remove the spike intersecting and ran the Intersection to get the result.