I uphold Single Predestination - so yes, I too believe only the elect actually obtain salvation. I too believe that on Judgement Day, all the non-elect will end up being condemned. It's just the process and the 'when' that we may disagree on.
Calvinists believe God chose to condemn the non-elect at the same time He chose to promise salvation to the elect, before any man's good or evil. That very well could've been so if only God hadn't further revealed His desire for all, non-elect included, to repent and live. This desire is in direct internal contradiction with a predestined decree of God Himself.
Consequently, single predestination holds God as conditionally desiring and providing the means of salvation to the non-elect too without any predestined decree of a promise nor of condemnation. And the non-elect reject and fall away from such an offer of love, filling up their measure of iniquity - after which God decrees condemnation over them, possibly through hardening of their hearts unto His glory.
The non-elect cant respond positively to the gospel and can not bear good fruit to God.
Refer to the parable of the sower sowing the seed. Only one type fell on the good ground and bore much fruit. none of the other bore any fruit to maturity. That good soil was the prepared heart of the new birth, a work that God did in their life, so that caused them to be fruitful and multiply.
If you do not bear good fruit to God, you are cut down and cast into the fire where is wailing and gnashing of teeth.
Jesus tells his disciples that they will bear much fruit to the glory of God, by their bearing much fruit, the Father is glorified.
Romans 8 tells us about the carnal mind, how it can not be submitted to God's laws, it is at enmity with God.
And contrast that with the spiritually minded which does please God, they are in Christ. The carnal mind, who are the non-elect, are at war with God will never submit to following Christ, it is why you must be born again first.
5 For those who live according to the flesh set their minds on the things of the flesh, but those who live according to the Spirit, the things of the Spirit. 6 For to be carnally minded is death, but to be spiritually minded is life and peace.
7 Because the carnal mind is enmity against God; for it is not subject to the law of God, nor indeed can be. 8 So then, those who are in the flesh cannot please God.
9 But you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. Now if anyone does not have the Spirit of Christ, he is not His. 10 And if Christ is in you, the body is dead because of sin, but the Spirit is life because of righteousness.