Ok so everyone's talking about what would happen if an immovable object met an unstoppable force, but the actual question is "What would happen if an immovable object met an immovable object mover". Immovable Objects, by definition cannot be moved, NO exceptions are mentioned in the definition. but the Immovable object mover (IOM) is, also by definition, a force specifically to move the immovable object
So what would happen if an IOM met an Immovable Object
1. The IOM successfully moves the Immovable Object, but this doesn't make logical sense. If the Immovable Object is moved, it isn't an immovable object, it's just a regular object that just so happens to be extremely difficult to move
2. The IOM fails to move the Immovable Object. This means the Immovable Object remains Immovable, but this still isn't logical. if an IOM fails to do the very reason to exist, that means it doesn't even exist.
No matter the outcome, it will always end up illogical. You cannot be both moving and unmoving at the same time, and you can never be none. What would really happen...