Complex sentence: For example, there are models of Peano arithmetic in which Goodstein's theorem fails; because it can be proved in ZFC that Goodstein's theorem holds in the standard model, a model where Goodstein's theorem fails must be nonstandard.
Split into simpler sentences: For example, there are models of Peano arithmetic in which Goodstein's theorem fails. It can be proved in ZFC that Goodstein's theorem holds in the standard model, so a model where Goodstein's theorem fails must be nonstandard.