Hint Resolve para_4: Geom.

(* Specifications: *)
Theorem not_para_eq_1 : forall A B C, ~ parallelogram A A B C.
Theorem not_para_eq_2 : forall A B C, ~ parallelogram A B C C.
Theorem not_para_eq_3 : forall A B C, ~ parallelogram A B C A.
Theorem not_para_eq_4 : forall A B C, ~ parallelogram A B B C.
Theorem not_para_eq_5 : forall A B C, ~ parallelogram A B A C.
Theorem not_para_eq_6 : forall A B C, ~ parallelogram A B C B.
Hint Resolve not_para_eq_1 not_para_eq_2 not_para_eq_3
not_para_eq_4 not_para_eq_5 not_para_eq_6 : Geom.
Theorem para_not_eq_1 : forall A B C D,
parallelogram A B C D -> A<>B.
Theorem para_not_eq_2 : forall A B C D,
parallelogram A B C D -> A<>C.
Theorem para_not_eq_3 : forall A B C D,
parallelogram A B C D -> A<>D.
Theorem para_not_eq_4 : forall A B C D,
parallelogram A B C D -> B<>C.
Theorem para_not_eq_5 : forall A B C D,
parallelogram A B C D -> B<>D.
Theorem para_not_eq_6 : forall A B C D,
parallelogram A B C D -> C<>D.