"Double reprobation," also known as double predestination,
There is no such doctrine as double reprobation.
John Calvin called it a "horrible decree" but held it (Calvin, Institutes, book 3, chapter 9, section 7). This is in opposition to the view that God actively saves the elect but does nothing for the sinful. The results are the same, but God is not an active agent in damning them to hell.
Again,this is reprobation instead of preterition.
And "horrible decree" means awesome or awe-inspiring.
John Wesley and other Arminians have gotten a lot of mileage out of "horrible decree".