FI-MO 2011 Problem 2

Find all integers $x$ and $y$ satisfying the inequality $x^4-12x^2+x^2y^2+30\leq 0.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.