The flight instructor and the pilot were conducting an instructional flight when the airplane had a total loss of engine power due to fuel exhaustion. The airplane fuselage sustained substantial damage during the forced landing in rough terrain. The flight instructor reported that there were no preimpact mechanical malfunctions or failures that would have precluded normal operation. The airplane operator reported that the fuel tanks remained intact after the accident, were void of usable fuel, and both fuel tank quantity gauges indicated empty. Before the flight, the flight instructor asked another flight instructor to request the fixed based operator (FBO) to refuel the airplane. However, despite the fuel request being relayed to the FBO front desk personnel, the airplane was not fueled before it departed on the flight. The flight instructor and the pilot both admitted that they did not visually confirm the fuel quantity during their preflight inspection. Additionally, believing that the fuel tanks were topped-off as requested, the pilots erroneously reset the airplane’s electronic fuel totalizer to reflect a full fuel load before takeoff.