Proof with Col.
intros.
apply NNPP.
unfold not;intro.
assert (P<>Q);auto;clear H5.
(* *)
assert (Col D P Q).
eapply col_transitivity_2...
(* *)
assert (B<>A).
unfold not;intro.
treat_equalities.
unfold Col in H.
intuition.
(* *)
assert (Col A P Q).
eapply col_transitivity_2...
(* *)
assert (Col C P Q).
eapply col_transitivity_2...
(* *)
assert (Col Q A C).
eapply col_transitivity_2...
(* *)
cases_equality Q A.
treat_equalities.
(* *)
assert (Col Q B C).
eapply (col_transitivity_2 P Q B C)...
auto.
(* *)
assert (Col A C B).
eapply col_transitivity_2...
assert (Col A B C)...
(* *)
Qed.

(* Specifications: *)
Lemma l6_25 : forall A B, A<>B -> exists C, ~ Col A B C.
Proof with Tarski.