lean_workbook_plus_12527

Disproved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove the inequality\n\n $x^3+2xy^2+y^3+2yz^2+z^3+2zx^2\geq 3(x^2y+y^2z+z^2x)$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_12527 : ∀ x y z : ℝ, x^3 + 2 * x * y^2 + y^3 + 2 * y * z^2 + z^3 + 2 * z * x^2 ≥ 3 * (x^2 * y + y^2 * z + z^2 * x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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