This isn't my first time rooting an S III, but this is the first time that I ran into this problem.
What I did:
1) Factory Reset the phone.
2) Rooted using Odin and CF-Auto-Root. Odin says Pass!
3) SuperSU is not installed.
4) Installed Root Checker and it says that the device is not rooted.
5) Install SuperSU through the Play Store and states that there is not a SU binary installed.
I have tried to push it through multiple times, with and without USB Debugging, and still the same issue. Also when I try to enter the Boot Recovery Menu I get CF-Auto-Root going through again.
Thank you in advance.