This is more of a question of real estate law and so I've changed the area of practice to that. I hope that helps.
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You should really speak to a local attorney about this in person. There is not enough information in the question, and there really isn't any "abandonment law on real estate with no children," in Washington. Although this question got moved to the real estate category, it sounds like your question is about who gets the house in the divorce, if I am understanding correctly. If you both own the home together ("split equally between the two of us") it is an asset that will be before the court for division, regardless of any alleged abandonment.
The real property will be divided equitably by the court and the title is held as a community asset to be settled by the court.
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