A thought thread:

We might not be able to "disprove" the after life but we can very well say it is very much unlikely.
The soul or spirit (dependent on how your theology perceives it) is a major component of the afterlife claim and as such evidence for the unlikelihood of the...

existence of the soul would act as evidence for the unlikelihood of an afterlife as well.(or the lack of positive evidence in both cases)

As far as I know there is nothing that acts as evidence to show that all features attributed to the soul aren't just the brain operating as it usually does.

If that is the case there is nothing that suggests that there is an extra state of being contained within us that would qualify us for entry into an afterlife.

Basically, the lack of positive evidence for the existence of the soul is a good enough indicator for whether or not there is an afterlife.