Epicurus proposed the logical problem of evil, it uses deductive reasoning to show that God is not both benevolent and omnipotent.

If God is willing to prevent evil, but cannot, then God is not omnipotent.

If God is able to prevent evil, but isn't willing, then God is malevolent.

If God is neither omnipotent, or benevolent, then we cannot call him God.

This is similar to J. L. Mackie's inconsistent triad.