formulas(sos). all x all y (Sum(x,y) = Sum(y,x)). all x (Sum(x,x) = x). all x all y all z (Sum(Sum(x,y),z) = Sum(x,Sum(y,z))). all x all y (IsIn(x,y) <-> (exists z (Sum(x,z) = y))). end_of_list. formulas(goals). all x all y all z ((IsIn(x,y) & IsIn(y,z)) -> IsIn(x,z)). end_of_list.