Definition BetT A B C := IBet A B C \/ A=B \/ B=C.

Lemma lower_dim : ~ (BetT beeson_s_axioms.PA beeson_s_axioms.PB beeson_s_axioms.PC \/ BetT beeson_s_axioms.PB beeson_s_axioms.PC beeson_s_axioms.PA \/ BetT beeson_s_axioms.PC beeson_s_axioms.PA beeson_s_axioms.PB).