LAB § 2292
An employment, having no specified term, may be terminated at the will of either party on notice to the other.  Employment for a specified term means an employment for a period greater than one month.
UIC § 1256
An individual is presumed to have been discharged for reasons other than misconduct in connection with his or her work and not to have voluntarily left his or her work without good cause unless his or her employer has given written notice to the contrary to the department as provided in Section 1327, setting forth facts sufficient to overcome the presumption.  The presumption provided by this section is rebuttable.
Where's the contradiction between those two statutes? I don't see it.