Dating from 1960 ("the systems are about 56 years old"), and especially given that the system in question is likely an IBM mainframe, Fortran would be my guess.

Dating from 1960 ("the systems are about 56 years old"), and especially given that the system in question is likely an IBM mainframe, Fortran would be my guess. Fortran can actually be surprisingly pleasant, at least as pleasant as C, but I'm guessing their particular code is not.