Good question. You need to carefully read your written purchase agreement to determine if the water softener was to remain in the unit or not. From what you have written, the water softener would be readily removable from the home that you bought and would not be considered a fixture.However, if the purchase contract did not state that the seller was keeping the water softener, then you have a very good argument that the water softener was included in the purchase of the home that you acquired. I recommend that you consult with a real estate attorney further about your situation and the course to take against the seller.