Proof with Geometry.
intros.
cut (Col C D B).
Geometry.
assert (parallel C D A B).
Geometry.
eapply par_col_col_1;eauto...
Qed.

Theorem common_point_not_par :
forall A B C D Y : Point,
Col Y A B ->
Col Y C D ->
A <> B ->
C <> D ->
~ Col Y A C ->
~ parallel A B C D.