Be advised, National Park Service Superintendent's Compendium - https://www.nps.gov/prwi/learn/management/park-superintendent-compendium-revised.htm

Subsection 1.5 General Access Entering and exiting the park by other than established park maintained roads and trails which appear on the park's visitor map is prohibited without a permit. - These trails are NOT on the park's visitor map
Subsection 2.23 - Recreation Fees Fee Areas at Prince William Forest Park
Under Title 36 C.F.R. Part 71, recreation fees are established for the following entrance fee areas, and/or for the use of the following specialized sites, facilities, equipment or services, or for participation in the following group activity, recreation events or specialized recreation.

In addition, these trails are NOT maintained by the park, and are NOT patrolled by NPS personnel, except for potential enforcement of park rules and regulations

The trails are an illegal access to the park and are not maintained. The trails shown in the NE corner of the park are along a natural gas pipeline, are not maintained for foot access, have steep slopes, and are highly susceptible to erosion, and are not sustainable. The powerlines in the SW corner of the park are not trails, and should not be used as such. If users are hurt, it would be difficult to find them and evacuate them.