SemiBase

A certified basis of 22 identities

This list of identities is a basis, proved in Lean, of [6, 3841], which generates the variety V[3841]. Removing the identities that follow from the others leaves 6 identities (Vampire); the variety page shows the shortest known basis.

Identifier sb-fc6999e5ad4d3f47 in the data of the bases-min seal.

Certified for

The identities

  1. x² ≈ x³
  2. x²yx ≈ xyx
  3. xyx ≈ xyx²
  4. x²y² ≈ y²x²
  5. xyxy ≈ xyxyx
  6. xyxy ≈ yxyxy
  7. xyxzx ≈ xzxyx
  8. xy²zx ≈ xzy²x
  9. xyxyzx ≈ yxyzx
  10. xyxzy ≈ xyxzyx
  11. xyxzyx ≈ yxzyx
  12. xyzxy ≈ xyzxyx
  13. xyzxyx ≈ yzxyx
  14. xyzxz ≈ xyzxzx
  15. xyxzytx ≈ yxzytx
  16. xyzxytx ≈ yzxytx
  17. xyzxty ≈ xyzxtyx
  18. xyzxtyx ≈ yzxtyx
  19. xyzxtz ≈ xyzxtzx
  20. xyztxz ≈ xyztxzx
  21. xyzxtyux ≈ yzxtyux
  22. xyztxuz ≈ xyztxuzx