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# [Brachylog], 8 bytes

    pᵐ≠{b|}ᵛ

[Try it online!][TIO-klyo3k5f]

[Brachylog]: https://github.com/JCumin/Brachylog
[TIO-klyo3k5f]: https://tio.run/##SypKTM6ozMlPN/pfXa6koGunoFRuX/2obcOjpuZHHcuVSopKU/WUakDMtMScYiC79uGuztqHWyf8LwASjzoXVCfVALmz//@PjlaKUNIB4lgdICsSznR0cgaynR2dUHguSDxHZxdnCNfF38kVJODk7@IKFgkJDfABiYSE@ngGwLS4gERcHF2cILqcHIOAfCDpB@P6QfhBrkCRWAA "Brachylog – Try It Online"

Since it takes $5!*5! = 14400$ tries to determine that the first test case gives false, I've added some shorter ones...

```
pᵐ          Permute each element of the input.
  ≠         The permuted elements are not equal,
   {  }ᵛ    but yield the same result if
     |      maybe
    b       their first elements are removed.