Modern solvers have also built-in facilities to detect and do something about symmetry. E.g. Gurobi has the option Symmetry which can be set to 2 (aggressive). I never had much luck with this. Indeed the results are:
Cplex shows very similar behavior:
Note that Cplex provides a large number of settings for the symmetry option:
That is probably just an educational tool to teach the user a lesson about combinatorial explosion: finding the right settings for your model.
Often solver suppliers say this is a solved problem:
This is an example that shows the fixes are at least insufficient. The algorithms do not handle this problem always in a satisfactory way.