But that code also returns just the one match if you ask it whether the minute hand and hour hand ever coincide (ignoring the second hand). So it falls a bit short of proving that the three-way event never happens, because it only considers events which happen at an integer number of seconds. The numbers involved are not irrational, but nor are they integers (elevenths of a 12-hour period).

It occurs to me that if your clock doesn't have a sweep second hand, then that's a whole different calculation.

Peter