Proposition 1: If God promises that all things are worked together for the good of those who believe
– This is seen in Romans 8:28
P1A: going to Hell is not good
P2: and someone who truly believes apostatizes forever from the faith
Then: P3; a promise of God has failed (which is in contradiction with His nature)
P3A: if God is all knowing so he knows everything that will happen and all powerful so that he can make things happen.
P3B: and a promise then fails
Then: P3C; God would be a liar for he would know that what he says will not come to pass.
P3Ci: if God is truthful and therefore cannot lie
P3Cii: and a worldview/argument leads to the conclusion that God lied
Then: P3Ciii: that worldview is false or a proposition in the argument is false.
If this all holds true, then proposition 2 must be false (for P1 is an exegetical truth of Scripture [see here] (presupposing the evangelical understanding of the inerrancy and authority of Scripture)) and this person has to either have temporarily backslidden or was in fact never truly a believer (and perseverance of the saints is proven to be true; see here for the an outline of the doctrine).
CP1: if it is impossible for someone who is a true believer to fall away
CP1A: an inability to choose to walk away means that a believer is only able to in the end choose A and not B. A (persevering to glorification) is ensured by God’s persevering power making B (apostatizing forever from the faith) impossible.
CP2: and libertarian free will requires freedom of contrary choice (ability to choose A or B)
Then: CP3; libertarian free will is necessarily false according to God’s infallible word (Romans 8:28) and the universe is partially determined; because Scripture teaches that humans are responsible for their actions Compatibilism is true (soft determinism is the reality of our world.)