How to reinstall OS X when Recovery isn't working? [closed]

My wife has a MacBook Pro that she bought new in 2012. In 2013/14 it had an issue with the system files and when she took it into the Genius bar at Apple they reinstalled the OS (wiping all personal data in the process). At this point they also upgraded her to the latest OS X at the time. I'm not sure what version this was but I assume Mavericks or Yosemite for reasons that will become clear.

At the weekend the laptop seemed to grind to a halt and lockup while we were browsing the web. After waiting for several minutes to regain any kind of response, we did a hard reboot using the power button. On restarting the system showed a grey screen and a flashing directory symbol with a '?', then switched to the Prohibitory symbol. Unfortunately the warranty has no expired so any trip to the Apple Store will be quite expensive.

I've been reading various articles and posts for the last few days to try and work out how to fix this, as follows:

1. Apple Hardware Test comes back OK.
2. Booting from the local Recovery partition (Command-R) does not work. Every time I try this it boots Internet Recovery instead. This means that I cannot reinstall the version of Mac OS X currently on the disk. Running diskutil list in Internet Recovery I can see that the Recovery partition exists on disk0 but I assume it is corrupt in some way.
3. I have ran 'First Aid' in Disk Utility a number of times in a Verify/Fix cycle. It says that it has fixed the disk but there still seem to be issues in the fix log (checksum errors, etc.). Another strange note here is that it shows the 500GB disk as having all space used except 37.5MB. This wasn't the case when the laptop was working.
4. Finally, when I run the Internet Recovery and select Reinstall OS X it tries to install Mountain Lion and gives me an error saying that the laptop cannot be 'upgraded' as it is running a newer OS (presumably Mavericks or Yosemite)

So my question is: What is the best course of action to get out of this bind? My thoughts are:

• Is there a way to get the local recovery partition working?
• Is there a way to determine the version of OS X installed on the system from the recovery tool?
• Is there a way to obtain a disc copy (without paying as we already have it installed) of Mavericks or Yosemite so that I can reinstall from media?
• Finally, is my only option now to do an Erase and then Install OS X from the Internet Recovery tool?

Any help much appreciated.

My recommendation would be to completely wipe the existing OS so that the OS X installer does not give you any errors about "upgrades".

As mentioned by Apple, I would boot the Mac while holding Command (⌘)-R. Once you are in OS X Utilities, select the Disk Utility option. In Disk Utility, select the drive containing the existing Macintosh HD partition, and then click the Erase button. Format the drive as OS X Extended (Journaled) with the GUID Partition Map. Once the drive has been erased and reformatted, exit Disk Utility.

Back in OS X Utilities, you should now be able to select Reinstall OS X which will guide you through reinstalling OS X Mountain Lion on the freshly reformatted disk without giving an error about any existing OS.

Try Option-Command-R, this will install the latest version of macOS compatible with that machine.