Check (AB,CD)==0 (orthogonality).
Check (AB, CD, DA) ==0 (planarity).
Check AD>AC>AB,  AC>BC,  BD>BC (order).
Check whether the projections to XY,  YZ,  XZ craddle each other continuations.
It is sufficient to check only the projections to XY plane to get Accepted verdict.

Sounds too complex.
If we replace C, D with their orthogonal projection on AB, then all steps except first collapse to only one step (check D = C*a, a > 1).

Still too complex, though. Over 20 lines in Python. There should be more simple solution...

Edited by author 26.12.2017 04:30

No lengths or projections XY, etc. Using scalar product (sp) and triple product (tp) it is at most five conditions:

  sp(ab,cd) == 0 and tp(ab,bc,cd) == 0 and # ⟂ and planar
  sp(ab,bc) >= 0 and # C after B
  sp(cd,bc) >= 0 and # BC goes in direction of CD
  sp(cd,bd) >= sp(cd,bc) # D after C