Odd, that would imply that the 7z bundled with Vortex is broken - except it seems to work for everyone else.
Please try this:
a) Open "Command Prompt" from the start menu (you can type into the search field to find it)
cd "c:\Program Files\Black Tree Gaming Ltd\Vortex\"
This should now show usage instructions for running 7z from the command line. If it shows an error message instead, please post a screenshot of that error, otherwise go on.
resources\app.asar.unpacked\node_modules\7z-bin\win\7z.exe t "<full path to one of the mod archives>" -bb3
(you have to put in the path of one of the mod files!)
This should verify the file and print some diagnostics.
Please make a screenshot of the output of this command and post it.