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Maximum likelihood and maximum parsimony are two key methods for phylogenetic tree reconstruction. Under certain conditions, each of these two methods can perform more or less efficiently, resulting in unresolved or disputed phylogenies. We show that a neural network can distinguish between four-taxon alignments that were evolved under conditions susceptible to either long-branch attraction or long-branch repulsion. When likelihood and parsimony methods are discordant, the neural network can provide insight as to which tree reconstruction method is best suited to the alignment. When applied to the contentious case of Strepsiptera evolution, our method shows robust support for the current scientific view, that is, it places Strepsiptera with beetles, distant from flies., (© The Author(s) 2020. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.)