> God is greater than the greatest imaginable thing, so must exist (this one is proven to be logically valid with computational theorem prover)
Logical validity is a very weak thing to demonstrate (it is trivial to construct a logically valid argument for any position), to be a proof you'd need to show soundness. https://iep.utm.edu/val-snd/#:~:text=A%20deductive%20argumen....
Sure, if I give an axiom that “The greatest imaginable thing must exist”, “God is an imaginable thing”, and “God is greater than any other imaginable thing”, a computational theorem prover will validate “God must exist”.
This doesn’t prove God exists. It just proves either God exists or one of your axioms are wrong.
> the world is intelligently designed
That’s not a proof, or even proven, just an unprovable conjecture.
> there must be a first cause, and that must be God
Those are two unproven claims, (“There must be a First Cause” and “If there is a First Cause, it must be God”), not a proof.
> nothing in this world is perfect so there must be a transcendently perfect being
That’s just a non-sequitur. Even taking the premise to be true, it does not (at all) lead to the conclusion.
> we can only be satisfied be an infinite being, so the object of our desire lies beyond this world
The “we can only be satisfied” part is unproven (and unprovable), and the other part doesn’t follow from it. That there must exist something that fulfills are desire to be satisfied is wishful thinking, not some kind of logical necessity, so even an infinite being was necessary for that that doesn’t mean such a being must exist.
> moral laws exist and require a law giver
All “moral laws” which provably exist are attributable to a huan lawgiver. Any other “moral laws” are speculative, as is any other lawgiver.
> our mind is not reducible to our body, and must have been created by an even greater being
The premise is not true, and isn’t even related to the conclusion. If it were true it would require a mind to have some nonphysical component, not “an even greater being” as a creator.
> jesus existed, claimed to be God, and rose from the dead according to reliable historical documentation
None of that is true based on “reliable historical documentation”