About everytime cataphracts have gotten into prolonged melee with infantry, its gone not very well. Aurelian, during the last major battle against the Alamanni charged a mix formation of horse and infantry with his Cataphracts and heavy horse which was repulsed with relatively high casualties as the horses were killed from beneath the cataphracts. They then routed and crashed into his right flank which only managed to be reformed due to the discipline of his troops.
Additionally the Sassanids never really managed to successfully invade against Romans because the Romans were reliably able to defeat heavy horse (unless you are a fat rich guy) and the Romans were only usually defeated on campaign by the inability to hold Armenia and Mesopotamia because they had to spread themselves so thin in the cases of Anthony and Trajan.
Funny enough Aurelian made the members of the cataphract units that did not rally back to him dress up as women after he won the battle.
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