We are sorry about the inconvenience.
Which OS X do you have on your Mac?
First make a backup of your songs in iReal Pro under File/Backup. After that delete other versions of the app completely.

Use Spotlight to find other copies of iReal b/Pro that you might have installed in folders other than Applications.
You can Command click from the Spotlight results to find the location of eventual other copies of app showing up in Spotlight and delete them.
Then delete any related files using the Go to Folder command from the Go menu in the Finder:
Go to:
~/Library/Application Support/
and delete the folder called iReal b/Pro

Then open the Terminal app (type terminal in the Spotlight search window or find it in the Applications/Utilities/ folder)
- type "defaults delete com.massimobiolcati.irealbookmac"

After this clean up, restart your computer and download iReal Pro from the Mac App Store.
Let us know if it solved the problem.