SemiBase

A certified basis of 18 identities

This list of identities is a basis, proved in Lean, of [6, 13560], which generates the variety V[13560]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-e09f4490e4b053c5 in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. xyx ≈ xyx²
  3. xyx ≈ xy²x
  4. xyx² ≈ xyxy
  5. xyxy ≈ xy²x
  6. xyzx ≈ xyzyx
  7. xyzx ≈ xyz²x
  8. xyxzx ≈ xyxzy
  9. xyzx² ≈ xyzxy
  10. xyzx² ≈ xyzxz
  11. xyzxy ≈ xyzyx
  12. xyzxz ≈ xyz²x
  13. xyztx ≈ xyztzx
  14. xyzxtx ≈ xyzxty
  15. xyzxtx ≈ xyzxtz
  16. xyztx² ≈ xyztxz
  17. xyztxz ≈ xyztzx
  18. xyztxux ≈ xyztxuz