You say that like itsuh bad thing...
I'm not trying to refute the logic. I'm trying to see why it's relevant. I don't think it is.
The logic proves that libertarian free will does not and cannot exist. Since Arminianism is the theological implication of libertarian free will, if the logic is true, Arminianism must be false.
In fact, I recall from Marsden's biography that Edwards said that if the Bible taught Arminianism, that would be enough to discredit Scripture. I'm inclined to agree. Soft determinism is the only position in philosophy of the mind that makes any sense, and this is just what we find Scripture teaching. If you don't like extended examinations of why libertarian free will can't work, listen to Jesus describing how bad trees bring bad fruit and good trees bring good fruit.