Is Liverpool to Knaresborough via York the shortest route or within 3 miles of the shortest route? No.
NRT mileages (as required by the Routeing Guide):
Table 90 & 39 - Leeds to Liverpool 74 3/4 miles (via Newton-le-Willows and Manchester Victoria)
Table 39 - Leeds to Liverpool 77 1/2 miles (via Warrington Central and Manchester Piccadilly)
Table 39 - York to Liverpool 103 miles
Table 35 - Leeds to Knaresborough 22 miles
Table 35 - York to Knaresborough 16 3/4 miles
Distance via Newton-le-Willows and Leeds (shortest route): 94 3/4 miles
Distance via Warrington Central and Leeds (direct Liverpool - Leeds TPE): 99 1/2 miles
Distance via York: 119 3/4 miles
Is Liverpool to Knaresborough via York possible on a direct train? No.
Is Liverpool to Knaresborough via York a mapped route? No - York is an Routeing Point for Knaresborough but fails the fares check so is not appropriate for Liverpool.
Is the route reasonable (
http://www.nationalrail.co.uk/terms/guidance.html - no legal basis for this though)? - Yes, in terms of distance and journey time, no in terms of fares.
Is the route sold by Trainline and WebTIS powered booking engines? - No.