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Let's see: An immovable object has infinite inertia, so it has an infinite mass. An unstoppable force is probably infinite as well. Were we in the finite domain, we could use
Newton's second law that says: F=ma, or a = F/m.
Therefore the body would be accelerated by the quotient of the force and mass.
Here we go into the speculative domain - if the infinities are equivalent,
I will divide them and get a constant, therefore there is a constant acceleration and the unstoppable force wins (the object moves).
The part where I cheated was when dividing infinities, which is not a well-defined mathematical operation.
I believe we could say this: an unstoppable force would win over an equally immovable object.

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