You're perfectly reasonable to reject both ATI1 and FTI1. Rejecting a premise does not require you to have a counterproof, as the truth table response offered implies.
To invoke truth tables when discussing premises is mixing up logical theory with logical semantics.
Truth tables tell us about the
semantic model we are considering, which in this case is the actual world we live in.
Whereas premises relate to a proof, which is an object of theory, not semantics.
In the context of reasoning about the actual world, rejecting a premise is essentially saying "I do not believe this is necessarily true in our actual world", which is a long way short of stating belief in a semantic counterexample.
So rejecting FTI1 denotes a belief: "It seems possible to me that this world has a God and that that God is not the same as Jesus".
Rejecting ATI1 denotes a belief: "It seems possible to me that this world contains a man Jesus but no God". Actually it denotes no belief at all since it collapses to a tautology, which I explain at the end of this post.
I would expect most agnostics to reject both FTI1 and ATI1, which is essentially just saying that they don't know whether this world has a God or not.
I think the trouble started with casual talk of "denying premises" or premises being "False".
Premises, being part of Theory, are not True or False. Consider Euclid's parallel postulate (postulate being a synonym of premise). By accepting it, we get one sort of geometry, by rejecting it, we allow a range of alternative geometries.
Strictly speaking one does not deny premises.
One either accepts them or rejects them, that's all.
When reasoning about the world, accepting a premise means we think it's necessarily true in this world. Rejecting it means we don't think it's necessarily true. A sceptic will reject most premises they come across not because they believe them to be correspond to a false state of affairs in the actual world, but because they don't believe them to
necessarily correspond to a true state of affairs in the actual world.
We need to always bear in mind that there's much more that we don't know about the world than we do know, so any statement that something is Necessarily the case is a very bold claim. Unless it's a tautology, it may be safest to reject it. But that will depend on context, eg whether we are discussing philosophy or crossing a road.
Lastly, let's come back to why ATI1 is a tautology.
Let OM3C denote the unary predicate: "is a mind that is omniscient, omnipotent and omnibenevolent, and created the world, and there is no other object in the world that satisfies those conditions", and let J denote Jesus of Nazareth whom we will assume to have actually lived in Palestine at some time in the reign of Augustus, and to have preached and gained a significant following, hence sidestepping the distracting Historical Jesus debate. So we take as True that the world (the semantic "model" for our logical "theory") contains object J.
Then we can write FTI1 as
(exists x: OM3C(x) ) -> OM3C(J)
and we can write ATI1 as
(for all x: not OM3C(x) ) -> not OM3C(J)
We see from this version that ATI1 is a tautology because if any predicate at all, call it P, is True for every object in the actual world, then it is True for any particular object in the actual world, such as J.
So we can replace ATI1 by any Tautology such as J=J.
This muddle shows the advisability of following Kant's advice that "existence is not a predicate" (although I don't think he ever said it in exactly those terms).
There is no predicate for "exists" so we need to use predicates about attributes, like OM3C, instead.
In conclusion, my dear Moliere, I uphold your right to reject both premises but, having now discovered that ATI1 is a tautology, humbly suggest that there's no harm in accepting that one (which leads nowhere).