Produces ATP from ADP in the presence of a proton gradient across the membrane. The archaeal alpha chain is a catalytic subunit. ATP + 4 H(+)(in) + H2O = ADP + 5 H(+)(out) + phosphate This protein undergoes a protein self splicing that involves a post-translational excision of the VDE intervening region (intein) followed by peptide ligation. The intein interrupts the ATP-binding site. Belongs to the ATPase alpha/beta chains family.