Okay, the ball is in your court. Prove that what you call reprobation (see your definition above) is "all over the bible" and "cannot be missed".
I would suggest pulling out around 10 to 12 passages scattered across the Old Testament, and about an equal number likewise scattered across the New. Prove that it is "all over" and "cannot be missed".
I am not sure if I can give you 12 verses. The bible is full of truths that you and I both probably believe that we could not support with 12 verse.
Jude speaks of some persons “who long ago were designated for the condemnation, ungodly persons who pervert the grace of our God into licentiousness and deny our only Master and Lord, Jesus Christ (Jude 4).
Paul has he spoke in Jude 4 also speaks in the same way in Rom. 9:17-22
“I have raise you up for the very purpose of showing my power in you, so that my name may be proclaimed in all the earth” So then he has mercy upon whomever he wills, and he hardnes the heart of whomever he wills… What if God, desiring to show his wrath and to make known his power, has endured with much patience the vessels of wrath made for destruction (Rom. 9:17:22)
Some people would say God failed to choose all for salvation but they should be careful.
Paul says,
“The elect obtained it, but the rest were hardened” Rom. 11:7. And Peter says of those who reject the gospel, “they stumble because they disobey the word, as they were destined to do” 1 Peter 2:8
It also appears Jesus can thank God both for hiding the knowledge of salvation from some and for revealing it to others. “Jesus declared, I thank you, Father, Lord of heaven and earth, that you have hidden these things from the wise and understanding and revealed them to babes’ yea, Father, for such was your gracious will” Matt. 11:25-26
We also must not forget, God’s justice results in HIS Glory. Paul says. “ What if God, desiring to show his wrath and to make known his power, has endured with much patience the vessels of wrath and to make known his power, has endured with much patience the vessels of wrath made for destruction (Rom.9:22) Paul also points to the fact of such punishment on the vessels of wrath” serves to show the greatness of Gods mercy toward us” God does this “In order to make known riches of his Glory for the vessels of mercy (Rom.9:23)
Remember
Election to salvation is as a cause for rejoicing and praise to God, who is worthy of praise and receives all the credit for our salvation (Eph. 1:3-6; 1 Peter 1:1-3)
Reprobation brings God sorrow, not delight (Ezek 33:11) The blame for condemnation of sinnes is always put on the people or angels who rebel, NEVER on God himself (John 3:18-19;5:40) Reprobation lies in the sinner.
Another way to look at it is election = Gods grace Vs. reprobation is Gods justice.
Ezek.33:11, Rom.9:1-4
Credit:
The Bible
Systematic Theology By Wayne Grudem