The domain of discourse is a reality with one god.
Explanation. The above term is a logical disjunction. The above term omnipotence notably excludes maximal omnipotence.
Explanation. Some might argue that Axiom 2 god's unlimited ability to do or undergo something can be limited to a singular or few things. An example is that god may create the universe and then lose omnipotence. However, if that is true, then god can be limited. According to Axiom 1, if every god can be limited, then no god is omnipotent. Is someone with one wish, without loopholes of getting more wishes, omnipotent?
Proposition 1. IF EVERY GOD IS A GOD WITH OMNIPOTENCE, THEN EVERY GOD IS A GOD WITH UNLIMITED ABILITY TO DO OR UNDERGO SOMETHING.
Proof. Every god is a god with omnipotence, then every god is a god with unlimited power [Def. 1]. If every god is a god with unlimited power, then every god is a god with unlimited ability to do or undergo something [Def. 2].
Proposition 2. IF EVERY GOD IS A GOD WITH OMNIPOTENCE, THEN EVERY GOD IS GOD WITH UNLIMITED ABILITY TO UNDERGO LIMITED POWER.
Proof. If every god is a god with omnipotence, then every god is a god with unlimited ability to do or undergo something [1]. If every god is a god with unlimited ability to do or undergo something, then every god is a god with unlimited ability to undergo limited power [Axiom 2].
Proposition 3. IF EVERY GOD IS A GOD WITH OMNIPOTENCE, THEN EVERY GOD IS A GOD THAT CAN BE LIMITED.
Proof. If every god is a god with omnipotence, then every god is god with unlimited ability to undergo limited power [2]. If every god is a god with unlimited ability to undergo limited power, then every god is a god that can be limited [Axiom 3].
Proposition 4. IF EVERY GOD IS A GOD WITH OMNIPOTENCE, THEN NO GOD IS A GOD WITH OMNIPOTENCE.
Proof. If every god is a god with omnipotence, then every god is a god that can be limited [3]. If every god is a god that can be limited, then no god is a god with omnipotence [Axiom 1].
Proposition 5. NO GOD IS A GOD WITH OMNIPOTENCE.
Proof. If every god is a god with omnipotence, then no god is a god with omnipotence [4].
Remark. Proof by contradiction.