= Solution
In the ordered <computational basis> $00,01,10,11$, the first two <qubits> of $|\psi_{0000}\rangle$ have amplitudes $(1,1,1,1)/2$, while those of $|\psi_{1111}\rangle$ have amplitudes $(-1,1,1,1)/2$. Both have the same normalized answer <qubit> $|-\rangle$. Their <inner product> is therefore
$$
\boxed{\langle\psi_{0000}|\psi_{1111}\rangle=\frac{-1+1+1+1}{4}=\frac12.}
$$
A common <unitary operator> $U\otimes I$ preserves this nonzero <inner product>. To distinguish the alternatives with certainty using the prescribed <quantum measurement in the computational basis>, their first-register outcome supports would have to be disjoint: every outcome possible under one alternative must be impossible under the other. Vectors with disjoint <computational basis> supports have zero <inner product>, contradicting its preservation. Thus \b[no such $U$ exists]. This is also an instance of <perfect discrimination of pure states requires orthogonality>; allowing a more general <quantum measurement> would not rescue this pair of states. The obstruction concerns these prepared oracle-output states, rather than every conceivable oracle-query procedure.
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