Almost invariably cable supplied with inverters is insufficient to carry heavy loads for max inverter rating. As already shown by SamG to reach the 2000w inverter rating the cables would be pulling upwards of 190a.I believe they are 6 awg-- they came with the inverter
6 awg is only good to carry around 85a at best for a load of ~1000 w.
Simply put when you get the replacement inverter go out and buy the right size cable.