How do I get rid of vines that are taking over the entire yard?

I recently moved into a beautiful home that has tons of yard space, trees and well established Iris beds but in the past few months I have been over run by vines that seem to come from nowhere. They are climbing up the trees, have almost over run the Iris bed and nothing seems to help. I have been weeding and pulling them out, everything looks good and then after the rain, they are right back and it seems like more are there.


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