(=> (Common-Goal-Of ?A ?B) (And (Cardinality (Setofall ?H (_Social ?B ?H)) 1) (Exists (?G) (And (Mereological-Member ?B ?G) (Person ?G))) (Cardinality (Setofall ?F (_Distributed ?B ?F)) 1))) (<=> (Common-Goal-Of ?A ?B) (And (Goal-Of ?A ?B) (Temporalized-Entity ?A) (*Agent ?B) (Group ?B) (Cardinality (Setofall ?C (_Distributed ?B ?C)) 1) (Exists (?D) (And (Mereological-Member ?B ?D) (Person ?D))) (Cardinality (Setofall ?E (_Social ?B ?E)) 1)))