PA-28T INSTRUCTOR PLT AND STUDENT LANDED GEAR UP AFTER OVERRIDING THE AUTOMATIC GEAR EXTENSION SYS.

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I WAS A VOLUNTEER FLT INSTRUCTOR FOR A WINGS WEEKEND AT GREENWOOD ARPT (HFY). THE PLT WAS A PVT PLT LICENSE HOLDER. WE HAD DEPARTED HFY AND PERFORMED THE AIRWORK PORTION; STALLS; STEEP TURNS; ETC. THEN WE CALLED HULMAN APCH FOR A VECTOR TO BMG. OUR FIRST LNDG WAS A NORMAL LNDG; FULL STOP. THEN WE DID A SOFT FIELD TKOF AND RETURNED FOR A SOFT FIELD LNDG TO A FULL STOP. THEN WE DID A SHORT FIELD TKOF. WE WERE THEN PERFORMING A NO FLAP LNDG. I OBSERVED THE PLT REVIEWING HIS CHKLIST THAT WAS PRINTED ON THE PANEL. I THOUGHT WE HAD LOWERED THE GEAR. THE INDICATOR LIGHTS WERE BLOCKED BY THE THROTTLE QUADRANT; SO THERE WAS NOT A DIRECT VIEW OF THE INDICATOR LIGHTS. THE PLANE LANDED FLAT ON THE RWY AND THE ENG CAME TO A STOP. THE PLANE THEN SKIDDED TO THE L OFF THE RWY AND THE L WING HIT A RWY LIGHT. THE PLANE CAME TO A STOP IN THE GRASS WITH THE R WING HALFWAY OVER THE RWY. WE THEN EXITED THE PLANE AFTER INSURING EVERYTHING WAS SHUT OFF. THE ARPT CREW LIFTED THE PLANE BY THE ENG MOUNT AND THE WHEELS WERE LOWERED. THE PLANE WAS THEN TOWED BACK TO THE APRON. THE DAMAGE TO THE PLANE APPEARED TO BE THE PROP WHICH WAS A 3 BLADE PROP; AND A DENT IN THE L WING. THE STEP TO GET UP ON THE WING WAS ALSO BENT. THERE WERE NO INJURIES. THE FAA WAS CONTACTED AND THE PLT IS GOING BACK TO BLOOMINGTON TO MEET WITH THEM. THE PLT IS THE OWNER OF THE PLANE AND HAS OWNED IT FOR ABOUT 3 YRS. AFTERWARDS; THE PLT INDICATED THAT HE HAD SET THE GEAR ACTUATION LEVER TO OVERRIDE SO THAT IT WOULD NOT AUTOMATICALLY LOWER.