Abstract Mutex groups are defined in the context of STRIPS planning as sets of facts out of which, maximally, one can be true in any state reachable from the initial state. This work provides a complexity analysis showing that inference of mutex groups is as hard as planning itself (PSPACE-Complete) and it also shows a tight relationship between mutex groups and graph cliques. Furthermore, we propose a new type of mutex group called a fact-alternating mutex group (fam-group) of which inference is NPComplete. We introduce an algorithm for the inference of fam-groups based on integer linear programming that is complete with respect to the maximal fam-groups and we demonstrate that famgroups can be beneficial in the translation of planning tasks into finite domain representation, for the detection of dead-end state and for the pruning of spurious operators. The experimental evaluation of the pruning algorithm shows a substantial increase in a number of solved tasks in domains from the optimal deterministic track of the last two planning competitions (IPC 2011 and 2014).