Read through the blue paper you got at your 2:1 layoff meeting. Outcome #2: Statutory appeals will be forwarded to HR Legal for ODI. Why HR Legal, and not just plain old HR, you ask? So they can uphold the ISP decision without getting sued. In other words, to cover their asses.
I have been through 2 ODIs in the last 8 years. One was successful (because it involved indisputable, publicly known data that affected many people, not just me), and the other was a complete sham (because it was my word vs. my manager's, and the HR rep protected the manager at all costs).
If you do keep fighting, I recommend you have rock solid data to back you up.