Atheism

If you don't have a definition of God, I doubt that you will ever be able to explain what does 'no-God' is supposed to mean.

What Frank is telling you is correct, as a strict matter of logic

It is nothing of the kind

You simply repeat, and continue to insist on the correctness of, the same fundamental mistake

You confuse logic with "linguistic truth" or something along that nature.

The laws of logic do NOT depend on meaning.

If you are trying to deny the validity of logic itself

In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica

As is true of all axioms of logic, the law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the grounds that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act which would essentially be self-defeating.

Since the early 20th century, certain logicians have proposed logics that deny the validity of the law. Collectively, these logics are known as "paraconsistent" or "inconsistency-tolerant" logics. Graham Priest advances the strongest thesis of this sort, which he calls "dialetheism". Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true. Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic.

[An] objection that is that "negation" in paraconsistent logic is not really negation; it is merely a subcontrary-forming operator. Some, such as David Lewis, have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true.

In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica

As is true of all axioms of logic, the law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the grounds that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act which would essentially be self-defeating.
Since the early 20th century, certain logicians have proposed logics that deny the validity of the law. Collectively, these logics are known as "paraconsistent" or "inconsistency-tolerant" logics.

I was asking how do you apply the law for conservation of energy at time zero of the Big Bang 'theory', and the state of Infinite Temperature (without heat carrier), and the LNC simultaneously to the formal model of that theory?

Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic

The futility arises from circularity because nobody can adequately define "existence" without resorting to an absolutist axiom which itself constitutes an " ultimate belief".

It does not matter what you postulate as "existing" if you think "existence" is independent of the contextual requirements of observers. That is a notion defined as "naive realism".

The argument will be circular since "independence" by definition is an absolutist starting axiom.

But "independent existence" of anything at all is unprovable because it requires at least one observer...The involvement of "an observer" (thinger) is antithetical to "independence".

Who, I wonder, is the observer who gives existence to the observer who then, in turn, deprives all material objects of any "real" or "true" existence?

Good thing Berkeley had an answer for that, too. It's GOD, doncha know?

And finally get over your assumption that humans, of necessity, are the determinant of REALITY.

They may be...but even you should be intelligent enough to recognize that they may not be!