My deductive argument against orthodox (no capital O) trinitarianism

Deductive argument against the trinity
AXIOMS
1. A = YHWH
2. X = The Father
3. Y = The son
4. X = A ∨ X ≠ A
5. Y = A ∨ Y ≠ A

PREMISES
1. X = A
2. Y = A
3. Y ≠ X
∴ ⊥

Into simple words

AXIOMS/Truths presupposed for the argument
1. Let A be YHWH/God
2. Let X be God The Father
3. Let Y be God the Son
4. X either is A or isn't A
5. Y either is A or isn't A

Premises/Argument
1. X is A
2. Y is A
3. Y is not X

Therefore, this is a contradiction. Because X and Y are both A, but not eachother.
Further explination: If the Father and Son are fully God, they must be identical to eachother. Why? Because they are both God. Since something is or is-not God, something that is-God is fully God with no distinction. If one of them are "identical/alike" to God, then they are not God. But since, according to orthodox trinitarianism, they are numerically distinct, this posits a contradiction under their own logic and semantics.

AXIOMS
1. A = YHWH/God/Divine essence
2. X = The Father
3. Y = The son
4. (X = A) ∨ (X ≠ A)
5. (Y = A) ∨ (Y ≠ A)
6: T = Trinity
7. M = Modalism
8. (M = T) → ⊥
9. (M ≠ T) → ¬⊥

(X = A) ∧ (Y = A) → (X=Y)

Simplified:
X is A, and Y is A, therefore, X is Y.

In Trinitarianism: X (The Father) and Y (The Son) are not identical, therefore,

(X = A) ∧ (Y = A) ∧ (X ≠ Y) → ⊥

Simplified: X is A, and Y is A. X is not Y. Therefore, contradiction.

Trinitarian counterargument: "The persons are numerically distinct from eachother, and count as something different apart of divine essence."

Reductio ad absurdum with 2 possibilities:

(1) "The persons and the essence are equal and that is no distinction, aka the essence is the persons.":

(a) (X = A) ∧ (Y = A) ∧ (X=Y) → ¬⊥M.
(b) (X = A) ∧ (Y = A) ∧ (X=Y) → ⊥T.

Simplified:
(a) X is A, and Y is A, and X is Y. Therefore, no contradiction to modalism.
(b) X is A, and Y is A, and X is Y. Therefore, contradiction to Trinitarianism. (The person isnt the divine essence)
∴ This collapses into modalism and contradicts Trinitarianism, because the persons are identical. Therefore, Trinitarianism is false.

(2) "The persons are distinct from the divine essence aka the essence is-not the persons."

Then the argument stands, because:
(a) (X = A) ∨ (X ≠ A)
(b) (X ∼ A) → (X ≠ A)
∴(X ≠ A) → ⊥T

Simplified:

(a) Law of non-contradiction (X is either A, or Not-A)
(b) If X is not fully identical/only alike to A, then, X is not-A. (The person isnt the divine essence)
∴ X is not A, therefore the trinity is contradictory