Proof with Geometry.
unfold parallelogram,parallel, S4 in |- *.
intros.
DecompAndAll.
assert (S A C D = S A C B + S A B D + S B C D)...
RewriteVar (S A C B) H0.
RewriteVar (S B C D) H2.
NormalizeRing H.
rewrite H.
replace (S B A C) with (- S A B C)...
ring_simplify (S A B C + - - S A B C)...
Qed.

Theorem para_not_col_1 :
forall A B C D : Point,
parallelogram A B C D ->
~ Col A B D.