import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12_2000_p20
  (x y z : ℝ)
  (h₀ : 0 < x ∧ 0 < y ∧ 0 < z)
  (h₁ : x + 1/y = 4)
  (h₂ : y + 1/z = 1)
  (h₃ : z + 1/x = 7/3) :
  x*y*z = 1 := by sorry