(* Lemma test17 : forall A B C D E F G H I J K L : Point, S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S D E F + S E D F + S G H I + S I G H + S A J K + S K J A + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S A B C + S B B C + S A B C + S B A C + S J K L + S K L J + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C + S A B C + S B A C =0 -> 0=0. *)

Lemma test174 : forall A B C P,
S B C P <> 0 ->
S A B P <> 0 ->
S C A P <> 0 ->
False ->
- (S A C P / S B C P * (S B A P / S C A P * (S C B P / S A B P))) = 1.