Impossible values of allunique() and allequal()

[Eldriitch]

With the following struct, allunique and allequal are giving incompatible (and mathematically impossible!) results.
MWE:

module MWE
struct Problem
    position::Array{Float64}
    value::Float64
end
Base.:(==)(a::Problem, b::Problem) = a.position == b.position && a.value == b.value
end

and then in the REPL

julia> X = [MWE.Problem([0.0,0.0,0.0], 4*pi) for i in 1:32];

julia> allunique(X)
true
julia> allequal(X)
true

And even more confusingly

julia> allunique(X[1:31])
false
julia> allequal(X[1:31])
true

So not only are we getting incompatible values of allunique and allequal, we also fail to have allunique(X) => allunique(X[1:end]).
Clearly allunique is behaving both contrary to the documentation and any reasonable expectation, for iterators with at least 32 entries.
Julia versioninfo:

julia> versioninfo()
Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × AMD Ryzen 9 7940HS w/ Radeon 780M Graphics
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)

[mbauman]

When you change how a struct defines equality, you must also symmetrically change how it hashes. Check out AutoHashEquals.jl.

Closing as a duplicate of #12198.

[Eldriitch]

I see -- that makes sense. Not great that the documentation is just... literally wrong then.

[mbauman]

The biggest issue that I see is that the == docstring could be worded more strongly in what it means to implement. See my suggested improvement in #55135.