John 8:23 states:
But he continued, "You are from below; I am from above. You are of
this world; I am not of this world.
Oh wait, what's right before that:
This made the Jews ask, "Will he kill himself? Is that why he says,
'Where I go, you cannot come'?"
So let's grammatically simplify that:
"The Jews are from below..."
Even Earlier (verse 13) we get:
The Pharisees challenged him, “Here you are, appearing as your own
witness; your testimony is not valid.”
So then
"The Pharisees are from below..."
So what this is saying is that the Pharisees are from below.
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1 John 4:5-6 states:
They are from the world and therefore speak from the viewpoint of the
world, and the world listens to them. We are from God, and whoever
knows God listens to us; but whoever is not from God does not listen
to us. This is how we recognize the Spirit of truth and the spirit of
falsehood.
Earlier we have:
You, dear children, are from God and have overcome them, because the
one who is in you is greater than the one who is in the world.
So this simplifies to:
You, dear children, and I are from God...
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So the two statements are taken to be:
You, dear children, and I are from God...
"The Pharisees are from below..."
So that would be a contradiction iff either the author was a Pharisee (known false) or the audience of 1 John are both Pharisees and "dear children."
So I would say that's probably not a contradiction.
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From this follows following. Does the born again experience happens by the Holy Spirit or by both the word of God/Gospel and Holy Spirit?
That actually is a contradiction, that doesn't follow at all.
And to it I would answer (since I'm fairly confident that's beyond the scope of the response you were looking for) (1 Peter 1:12):
...when they spoke of the things that have now been told you by those
who have preached the gospel to you by the Holy Spirit sent from
heaven. Even angels long to look into these things.