lean_workbook_plus_48748

Disproved

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

We reduce again and finally we obtain the inequality: $(a^4b^2+1)+(a^2b^4+1)+(a^4c^2+1)+(a^2c^4+1)+(b^4c^2+1)+(b^2c^4+1)+(a^3b^3+a^3c^3)+(b^3a^3+b^3c^3)+(c^3a^3+c^3b^3) \ge 2a^2b+2ab^2+2a^2c+2ac^2+2b^2c+2bc^2+2a^3+2b^3+2c^3$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48748 : ∀ a b c : ℝ, (a^4 * b^2 + 1) + (a^2 * b^4 + 1) + (a^4 * c^2 + 1) + (a^2 * c^4 + 1) + (b^4 * c^2 + 1) + (b^2 * c^4 + 1) + (a^3 * b^3 + a^3 * c^3) + (b^3 * a^3 + b^3 * c^3) + (c^3 * a^3 + c^3 * b^3) ≥ 2 * a^2 * b + 2 * a * b^2 + 2 * a^2 * c + 2 * a * c^2 + 2 * b^2 * c + 2 * b * c^2 + 2 * a^3 + 2 * b^3 + 2 * c^3   :=  by sorry

Source

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

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