The liquidazione part means, here, payment or settlement. Autoliquidazione is basically where you work out yourself how much you have to pay and submit the calculation along with the payment -a bit like our self assessment tax returns in the UK, tho with those I’m not sure you always have to pay the amount you owe at the same time as you submit the form – there are other ways, hence I think you need to include the payment bit too.

The clause says that F must provide XX with documentation re its duties regarding contributivi, retributivi, assicurativi e previdenziali. These docs include those relating to the assicurativi bit, one example being the bit with your term in - they have to produce the cert. saying they have calculated and paid the INAIL insurance premium.

The links provided give an indication of the meaning of the term (with regard to income tax). Also if you look on the INAIL site at their stuff about autoliq. it seems clear that this is what it is.