Proof with Geometry.
unfold parallel in |- *.
intros.
assert (S4 A C B D = - S4 C A D B)...
rewrite H0 in H...
Qed.
Hint Resolve par_2: Geom.

(* Specifications: *)
Theorem not_parallel_not_eq_1 : forall A B C D,
~ parallel A B C D -> A<>B.