In 1978, Durfee conjectured that the signature of the Milnor fiber of smoothings
of a normal surface singularity is always non-positive.
Although counterexamples of this conjecture were found for non-complete intersection case,
the conjecture had been open for complete intersection surface singularities.
In this talk, I will explain that Durfee's conjecture is true for complete intersection surface singularities
as an application of a slope inequality of certain fibered surfaces.