A counterexample to a six-variable polynomial inequality

Proved

WorkbookSource.plus_12728

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Find a counterexample for the inequality: $4(a^{2}+x^{2})(b^{2}+y^{2})(c^{2}+z^{2})\geq 3(abx+bcy+caz)^{2}$ for real numbers $a, b, c, x, y, z$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_12728 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_12728 : ∃ a b c x y z : ℝ, ¬(4 * (a ^ 2 + x ^ 2) * (b ^ 2 + y ^ 2) * (c ^ 2 + z ^ 2) ≥ 3 * (a * b * x + b * c * y + c * a * z) ^ 2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_12728; Apache-2.0

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