All leases shall provide that if oil, gas or other hydrocarbon substances are not encountered on or before the end of the initial term, the lease shall not terminate if the lessee is then prosecuting drilling operations on the leased lands with due diligence, in which event the same shall remain in force so long as lessee shall keep one string of tools in operation on the leased lands, allowing not to exceed ninety days between the completion of one well and the commencement of the next until such substances are encountered in quantities deemed paying quantities by lessee. All leases shall further provide that if oil, gas or other hydrocarbon substances in paying quantities shall have been discovered on the leased lands prior to the expiration of the initial term, then in the event at any time after the expiration of the initial term production on the leased land shall cease from any cause, the lease shall not terminate provided lessee resumes operations for the drilling of a well or the restoration of production within ninety days from such cessation. The lease shall remain in force during the prosecution of such operations, and if production results therefrom, then so long as production continues.