Once we get past all the other impossibilities in the Futurama movie Bender's Big Score, Tuxedo Bender, who began our story by traveling from the end to the beginning to carry the time code back to place on Fry, makes the same trip again. This time as he waits in the cave, he knows who all those other Benders are, because this time he remembers having been each of them already. This time, though, he changes history in a drastic way: he persuades each of his temporal duplicates not to emerge from the cave on schedule, but to wait until the end and emerge together after the Scammers have been defeated, depriving the Scammer aliens of their treasures.
Thus we have Mona Lisa Bender stealing the Mona Lisa, then meeting Tuxedo Bender in the cave, and being persuaded not to exit. If he does not, though, then Egypt Tomb Bender can never depart to steal the Egyptian relics. Since he cannot depart, he cannot return, and no other Bender will ever leave to steal artifacts in the past.
It is unclear what will happen from that. If the Scammer Aliens come looking in the cave for their missing robot, they will find both Mona Lisa Bender and Tuxedo Bender. The latter is not under their control--they erased the control code. However, unless the latter erases the control code from the former (and we do not know if he can do that), the former will obey the Scammers and bring the artifact out of the caves. If asked why he did not come sooner, he will explain that the other Bender told him to wait, and that will lead to trouble.
It seems likely that the Scammers would send Mona Lisa Bender back to destroy Tuxedo Bender. If he succeeds, Tuxedo Bender is no longer in the cave when future Benders arrive, and does not emerge at the end (nor do all the other Benders), but time is preserved. If he fails, he will probably be destroyed himself. That will undo the existence of all other Benders, including Tuxedo Bender, and the code will never be delivered to Fry's tattoo, and we have a complicated infinity loop.
This same problem applies to all other Benders, but it also means that Fry will not flee to the past, Terminator Bender will not pursue him, they will not duplicate themselves, and Lars will never exist.
The film suggests that this is the same temporal duplicate problem it has had all along, and perhaps in a sense it is: each Bender in the cave represents another that did not make a time trip. Yet here it puts the doppelganger problem in stark relief. As we observed early in our analysis, a time traveler who duplicates himself by not making a time trip he already made creates an infinity loop; it is the time traveling version that cannot exist. Yet here it is difficult to grasp. The problem is that Mona Lisa Bender never becomes Egypt Bender, yet Egypt Bender already exists. Thus all the Benders in the cave are duplicates of each other, and under Futurama rules doom will take them all.
--which is what happens as the film is ending and all the duplicate Benders with their art treasures begin meeting their fates.
Hopefully we have now examined all the anomalies in this film, and next time can provide a summary of the disasters as well as the interesting points.
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