  The separation of a filament and sigmoid is observed during an X1.4 flare on
July 12, 2012 in solar active region 11520, but the corresponding magnetic
field change is not clear. We construct a data-constrained magnetohydrodynamic
simulation of the filament-sigmoid system with the flux rope insertion method
and magnetic flux eruption code, which produces the magnetic field evolution
that may explain the separation of the low-lying filament and high-lying hot
channel (sigmoid). The initial state of the magnetic model contains a magnetic
flux rope with a hyperbolic flux tube, a null point structure and overlying
confining magnetic fields. We find that the magnetic reconnections at the null
point make the right footpoint of the sigmoid move from one positive magnetic
polarity (P1) to another (P3). The tether-cutting reconnection at the
hyperbolic flux tube occurs and quickly cuts off the connection of the
low-lying filament and high-lying sigmoid. In the end, the high-lying sigmoid
erupts and grows into a coronal mass ejection, while the low-lying filament
stays stable. The observed double J-shaped flare ribbons, semi-circular ribbon,
and brightenings of several loops are reproduced in the simulation, where the
eruption of the magnetic flux rope includes the impulsive acceleration and
propagation phases.
