∀ {R : Type u_3} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R],
  (∀ (x y : R), x ≤ y ↔ ∃ p ∈ AddSubmonoid.closure (Set.range fun s => star s * s), y = x + p) → StarOrderedRing R