Here's a derivation of Syl, Simp, and Hilbert from HI-11:

 
 








 
 

          1. CpCCCqrsCCsCstCrt                                                    [HI-11]
D1.1   =  2. CCCpqrCCrCrsCqs
D2.2   =  3. CCCCpCpqCrqCCCpCpqCrqsCps
D2.3   =  4. CCCpqCCpqrCCCCpCpsCtsqr
D3.1   =  5. CpCCCqrCCqrsCCprs
D4.1   =  6. CCCCCpqCCpqrCsrtCCtCtuCqu
D4.5   =  7. CCCCCpqCCpqrCsrCCpqtCCCCpqCCpqtqt
D5.1   =  8. CCCpqCCpqrCCCsCCCtuvCCvCvwCuwqr
D6.3   =  9. CCCpqCCpqrCCpqr
D7.6   = 10. CCCCCpqCCpqqCCCpqCCpqqCqqCCpqqCqq
D8.1   = 11. CCCpCCCqrsCCsCstCrtuCCuCuvCwv
D6.9   = 12. CCCCCpqCCpqrrCCCCpqCCpqrrsCqs
D2.10  = 13. CCCppCCppqCCCrppq
D12.1  = 14. CpCCqCqrCCCspqr
D13.1  = 15. CCCpCqrCqrCCCqrCCqrsCrs
D14.14 = 16. CCpCpqCCCrCsCCtCtuCCCvstupq
D14.2  = 17. CCpCpqCCCrCCCstuCCuCuvCtvpq
D15.9  = 18. CCCCpqrCCCpqrsCrs
D16.14 = 19. CCCpCqCCrCrsCCCtqrsCuCuvCCCwCuCuvuv
D17.1  = 20. CCCpCCCqrsCCsCstCrtCCuvwCCwCwxCvx
D11.18 = 21. CCCpCCpCpqCrqCCpCCpCpqCrqsCts
D2.19  = 22. CCCCCpCqCqrqrCCCCpCqCqrqrsCCqCqrs
D20.18 = 23. CCCCCpqCCpqrCsrCCCCpqCCpqrCsrtCqt
D18.21 = 24. CCCpCCpCpqCrqss
D21.1  = 25. CpCCCCCqrCCqrsCtsCCCCqrCCqrsCtsuCru
D20.22 = 26. CCCCpCpqCrqCCCpCpqCrqsCCrps
D2.24  = 27. CCpCpqCpq                                                                   [Hilbert]
D23.25 = 28. CCCpqrCqr
D28.28 = 29. CpCqp                                                                              [Simp]
D28.26 = 30. CCCCpCpqCrqsCCrps
D30.228 =31. CCpqCCqrCpr                                                               [Syl]

 
Dolph Ulrich, 2007