Shadow of Io Theorem

(all (time-voyager-2-c)
 (find (shadow-point-c)
  (exists
   (time-sun sun-spacetime-loc time-io io-spacetime-loc 
    time-jupiter jupiter-spacetime-loc time-voyager-2 
    voyager-2-spacetime-loc shadow-point jupiter-ellipsoid 
    ray-sun-to-io)
  (and
   (= ray-sun-to-io
      (two-points-to-ray
        (event-to-position sun-spacetime-loc) 
        (event-to-position io-spacetime-loc)))
   (= jupiter-ellipsoid
      (body-and-time-to-ellipsoid jupiter time-jupiter))
   (= shadow-point
      (intersect-ray-ellipsoid ray-sun-to-io jupiter-ellipsoid)) 
   (lightlike? jupiter-spacetime-loc voyager-2-spacetime-loc) 
   (lightlike? io-spacetime-loc jupiter-spacetime-loc) 
   (lightlike? sun-spacetime-loc io-spacetime-loc) 
   (= voyager-2-spacetime-loc
      (ephemeris-object-and-time-to-event voyager-2 time-voyager-2)) 
   (= jupiter-spacetime-loc
      (ephemeris-object-and-time-to-event jupiter time-jupiter)) 
   (= io-spacetime-loc
      (ephemeris-object-and-time-to-event io time-io)) 
   (= sun-spacetime-loc
      (ephemeris-object-and-time-to-event sun time-sun))
   (= shadow-point (abs (coords-to-point j2000) shadow-point-c)) 
   (= time-voyager-2
      (abs ephemeris-time-to-time time-voyager-2-c))))))