We derive a phenomenological "no-lose theorem" for naturalness up to the TeV scale, which applies when quantum corrections to the Higgs mass are canceled by perturbative BSM particles (top partners) due to to some symmetry. In particular we focus on neutral top partner scenarios, including but not limited to the Twin Higgs model. We classify all perturbative neutral top partner structures in order to compute their irreducible low-energy signatures at proposed future lepton and hadron colliders, as well as the irreducible tunings suffered in each scenario. Central to our theorem is the assumption that SM-charged BSM states appear in the UV completion of neutral naturalness, which is the case in all known examples. We find that proposed future colliders probe any such scenario of naturalness with tuning of 10% or better unless the top partner multiplicity is very high. This provides strong model-independent motivation for both new lepton and hadron colliders, which in tandem act as discovery machines for general naturalness. Realizing a concrete scenario which avoids our arguments while still lacking experimental signatures remains an open model-building challenge.