  We consider 32 homotopy classifications of knot projections (images of
generic immersions from a circle into a 2-sphere). These 32 equivalence
relations are obtained based on which moves are forbidden among the five type
of Reidemeister moves. We show that 32 cases contain 20 non-trivial cases that
are mutually different. To complete the proof, we obtain new tools, i.e., new
invariants.
