Usually, it is best to lease two different sections on two different leases. The company may have only leased on one of the sections.
The inheritance documents should have had a more complete description of each of the sections with lots or something like SW4 NE4, etc. You would not have inherited the entire sections, but only a portion of them. The description in the lease is reflecting that the lease covers lots 1 & 2 of section 31. There is a similar description for section 30.
Have you tried looking in www.okcountyrecords.com to see if you can find a better description from an old lease or probate documents?
Cimarex had a well planned in 30 back in 2009. Do you have a lease from that time frame? Or give me a name to look up and I can look on a subscription service to see if it gives a better description in a lease.
The images below show the original plats from the time of patent back at statehood. You can see where Lots 1 and 2 are from section 31. Essentially the west half of the NW4 of the section. The Lots are not 40 acres because there is an adjustment for the curvature of the earth. The lease will state the gross acres, but not the net acres (in most cases). You would have to figure out the net from a title search or back calculating from a division order.