SemiBase

A certified basis of 22 identities

This list of identities is a basis, proved in Lean, of [6, 5636], which generates the variety V[5636]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-589f4da7b42fe805 in the data of the bases-min seal.

Certified for

The identities

  1. x³ ≈ x⁴
  2. x³y ≈ xyx
  3. x²y ≈ x²y²
  4. xyx ≈ xyx²
  5. xy² ≈ xy³
  6. x²yxy ≈ xyx
  7. xyx ≈ xyxyx
  8. xyx ≈ xy²xy
  9. xyz ≈ xyz²
  10. x²yxz ≈ xyxz
  11. x²yz ≈ x²yzy
  12. x²yzx ≈ xyxz
  13. xyxyz ≈ xyxz
  14. xyxz ≈ xyxzx
  15. xyxz ≈ xyxzy
  16. xyxz ≈ xy²xz
  17. xyxz ≈ xy²zx
  18. xyxz ≈ xyzxy
  19. xyxz ≈ xyzxz
  20. xyxz ≈ xyzyx
  21. xy²z ≈ xy²zy
  22. xy²z ≈ xyzyz