Odd play

[rbmartin]

I saw this happen yesterday in an NFHS Girls softball game (I was just a fan) but I don't think any rulings would be different than baseball so here it is. I am also 99% certain that one or both umpires kicked this royally.

Bases loaded. No outs. batter hits weakly down 3rd baseline on fair territory. F5 (playing kinda shallow) attempts to catch ball in air but clearly short-hops the ball. Field ump, who was positioned pretty deep for "C" position IMO, calls "OUT!" HP umpire shouts "no catch !" and points to the ground. R3 (view was shielded by F5) dives headfirst back onto 3rd. Pitcher throws back to F6 (who came over to cover 3rd) who was clearly standing on 3rd, who catches the ball and then tags R3, who was clearly already touching the bag.

Field ump was an seasoned umpire and plate ump has worked state finals games in the past.

Before I tell you what the ruling was, how would you guys sort this out?