My discovery about mathematics

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I indicate defect of the logic treating =.

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Let X be a countable axiom system of the standard mathematics. Set up that (a≠b) ∈X and ∀x(x=x) ∈X.
In the logic treating =, ∀x∀y((x=x)∧((x=y)⇒(P(x)⇔P(y))) is true for every propositional function P(z).
Theorem 1. X isn't consistent if the logic treating = is consistent.
Proof. Assume that X is consistent. Let d be an individual symbol which X doesn't include.
Put Y=X∪{d=a}. If Y isn't consistent, X |- d≠a. X doesn't include d.
X |- ∀x(x≠a). X |- a≠a. X isn't consistent. (Y |- a≠a ⇒ X |- a≠a) is true.
In the logic treating =, (d=b)⇒((Y |- a≠a) ⇔(X∪{b=a} |- a≠a)) is true. (d=b)⇒(Y |- a≠a) is true then for
X∪{b=a} |- a≠a is true. So ((d=b) ⇒ (X |- a≠a)) is true in the logic treating =.
If X |- d≠b, X |- ∀x(x≠b). X |- b≠b. So X∪{d=b} is consistent and has a model.
You can set up that d=b and the elements of X are true. X |- a≠a is true then in the logic treating =.
a≠a is true in it. The logic treating = isn't consistent.♦
The logic treating = isn't consistent and can prove any conjectures. Let's prove Riemann hypothesis.
Let s₁, s₂,… be the zero points of ζ(s). Define G(s_i)=2ⁱ and G(0)=3 and G(ζ(s_i))=5ⁱ.
Let t₁,t₂,… be the other terms. Define G(t_i)=7ⁱ. G(t)=G(u) ⇒ t=u.
Put R(z)=(G(z)=G(0))∨∀x((G(ζ(x))=G(z))→(Re(x)=1/2)∨(Im(x)=0)).
Like Gödel number, G(t) isn't a term. R(z) is a propositional function which isn't a logical formula.
In the logic treating = , (ζ(s_i)=0) ⇒ (R(ζ(s_i)) ⇔ R(0)). ζ(s_i)=0 and R(0) are true.
R(ζ(s_i)) ⇒ (Re(s_i)=1/2) ∨(Im(s_i)=0).

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Conjectures of the standard mathematics are solved as nonsense in the logic treating =.
Mathematicians must surmount this paradox.