Yes, it can be proven. Any atheists remaining would violate at least one of your premises.
Those are not separate premises; they have to be taken together as one premise, all of them being the case.
You cannot prove that as the premise states
if God wants everyone to believe in him, and if God were to do what would be within his omnipotent power in order to prove to everyone that he exists, there would be no atheists.
If there are any atheists at all, then either:
- God didn't have the power to convince them that he exists, or
- God didn't know how to convince them, or
- God doesn't want to convince them.
Part of the hypothetical premise is that
God is omniscient (meaning he would know how to get everyone to believe in him) and God wants everyone to believe in him, but nowhere was it stated that God was trying to convince atheists to believe in Him.
From the stated premise, we know that the omnipotent has the power to convince atheists, and we know that the omniscient God has the knowledge to convince atheists, so that leaves only one possibility -- God doesn't want to convince atheists.
This violates your premises.
You said that God "would know how to get everyone to believe in him." The implication of what you're saying now is that he doesn't actually know how to do this.
The implication of what you're saying now is that he doesn't actually know how to do this.
That God "would know how to get everyone to believe in him" does not mean God would be
able to convince everyone to believe in Him, and it does not mean that God
wants to convince everyone to believe in Him….. God just knows how because God is omniscient.
Right... so how is any of this relevant?
You say that free will is "the will/ability to make choices based upon their desires and preferences." Well, if God decides what those "desires and preferences" are, then God can control what you do, regardless of you being free to choose between the desires that God has given you.
That is true; God could override our desires and preferences and make us believe in Him against our free will. But that was not included in my premise that God would do that: The premise states:
God wants everyone to believe in him, and if God were to do what would be within his omnipotent power in order to prove to everyone that he exists.
IOW, free will as you've described it wouldn't stop God from being able to choose any outcome he wants.
No, it would not stop God from doing anything He wanted to do.
And if it did stop him, you'd be violating your own premises again: you said that "God wants everyone to believe in him." If God doesn't want everyone to believe in him because it would violate their free will, then the premise that God wants everyone to believe in him would be false.
No, it would not be false because the premise does not state that God wants everyone to believe in Him even if it violates their free will. It simply states that
God wants everyone to believe in Him.
The premise does not state that God wants everyone to believe in Him by overriding their free will and forcing everyone to believe in Him.
The premise states that
God would know how to get everyone to believe in him and God wants everyone to believe in him, and God would do what would be within his omnipotent power in order to prove to everyone that he exists. The premise does not say that God would be successful on getting everyone to believe in him.
Free will is the fly in the ointment.