!A:Prop.!B:Prop.!C:Prop.(and (sumbool A False) (and (or True B) (or B False))) -> True

!A:Prop.!B:Prop.!C:Prop.(and (sumbool A C) (and (or A B) !D:Prop.(or B D))) -> True

!A:Prop.!B:Prop.!C:Prop.(and (and A C) (and (and A B) (and B C))) -> True

(and True True) -> True
(and True False) -> True