Quetion about 买房协议.

我们签了一买房协议。有一条：
4. Fixtures & Personal Property
(A) Included in this sale are all existing items permanently installed in the property, free of liens, including plumbing;......
...
(C)Excluded fixtures and items:
Refrigerator, Washer, Dryer, Speakers in family room, all window treatments.

现在是他们有一个小小的 playground set 在后院. For some reason our agent forgot to add it to the list of the item A specifically. But it is also not in the excluded (C). We always think it should be included because it is anchored to the ground. Our agent also told me several time it should be included. So we didn't pay much attention. Now the seller ask us to buy it or otherwise they are going to remove it. And our agent turns out very weak. Because the seller's agent is his boss who owns the company.

Here is the question. Can the term "Included in this sale are all existing items permanently installed in the property," support us arguing that playground set should be in the sale of this property?