No rulebook to refer to with me today, but here is my take under ASA rules.
Once F3 slips on or is hindered by the equipment left on the ground, the ball is dead, interference is called and the runner closest to home at that time is declared out. All other runners are returned to the base they last legally touched.
This ruling assumes that the bats left on the ground near the dugout are warmup or extra bats. If F3 trips over the bat that was used by the batter, play continues. This piece of equipment is where it was supposed to be, discarded on the ground after use by the batter.
If I am incorrect, I'm sure that my compatriots on the board will let me know!
