Will everyone be saved?
Short answer: No!
There are some who think that because Christ is called “the Savior of THE WORLD” (John 4:42; 1 John 4:14), and ”Savior of all men” ( Timothy 4:10) that indicates EVERYONE will be saved. See the comments here and here. The idea is that everyone is destined to be saved, so if you believe in predestination, you must believe that everyone is destined to be saved.
Personally, I think its easy to reconcile “savior of the world’ with predestination – There is ONLY one savior for the people of this world, the Son of God, Jesus of Nazareth. But this does not mean He is the savior of EVERYONE one in this world. Because he is the only savior for the people of this world, then He is the savior of the world. This does not mean everyone WILL be or even COULD be saved, in fact it does not speak to the issue of predestination at all – merely that He is the only savior available.
But that is a different thing than the idea that everyone will be saved. People must repent and turn to God (Acts 26:20). Godly sorrow leads to repentance which leads to salvation (2 Corinthians 7:10). Not everyone will repent (Revelation 9:20-21, 16:8-11).
Its obvious at least SOME people are predestined to destruction (John 17:12). They are destined to disobey the message of Christ (1 Peter 2:8). God made everything for its purpose – even the wicked for destruction (Proverbs 16:4). No one can come to Christ unless God draws and enables them (John 6:44, 6:65). The work of God is that we believe in Christ (John 6:29). Jesus is the author of salvation (Hebrews 2:9-10) and the author & perfecter of faith (Hebrews 12:2). It is God who grants repentance (2 Timothy 2:25). ALL that God the Father gives to Christ WILL come to Him (John 6:37). Its obvious that not all will be saved as not every one will believe in the Son of God so God’s wrath is still upon them (John 3:36), and their “names have not been written in the book of life from the creation of the world” (Revelation 13:8, 17:8). In fact, we know there are some destined for the lake of fire – the second death (Revelation 21:8).
So no, not everyone will be saved.