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# [Pyth], 15 bytes

    !f.A-VtTsM._T.p

[Try it online!][TIO-ltadqqft]

Outputs True if no valid recipe exists, False if one does. If truthy/falsy outputs are allowed, the `!` can be removed, to just output all valid permutations. Takes input as lists, not sets.

    !f.A-VtTsM._T.p
                 .p  All permutations of parts
     f               Filter permutations
              ._T    All prefixes of parts
            sM       Sum prefixes
        -VtT         Filter each part for ingredients
                     not contained in previous part
      .A             Check all parts had something new
    !                Check whether no permutations remain

[Pyth]: https://github.com/isaacg1/pyth
[TIO-ltadqqft]: https://tio.run/##K6gsyfj/XzFNz1E3rCSk2FcvPkSv4P//aEMdIx3jWJ1oIDLSMQGSIAEQbRwLAA "Pyth – Try It Online"