(define-relation Do (?a ?s1 ?s2)
((Arity 3)      (nth-domain 1 action)
                (nth-domain 2 situation)
                (nth-domain 3 situation))
:axiom
(forall (?a)    
        (exists (?Phi)
                (complex_action_def ?a ?Phi)))

(define-relation subaction (?a1 ?a2)
((Arity 2)      (nth-domain 1 action)
                (nth-domain 2 action))
:axioms
(forall (?a)
        (subaction ?a ?a))
(forall (?a1 ?a2 ?a3)
        (=>     (and    (subaction ?a1 ?a2)
                        (subaction ?a2 ?a3))
                (subaction ?a1 ?a3)))
(forall (?a1 ?a2 ?a3)
        (=>     (and    (subaction ?a2 ?a1)
                        (subaction ?a3 ?a1))
                (exists (?a)
                        (and    (subaction ?a2 ?a)
                                (subaction ?a3 ?a)
                                (subaction ?a ?a1)))))

(define-relation primitive (?a)
((Arity 1)      (nth-domain 1 action))
:axioms
(forall (?a)    
        (<=>    (primitive ?a)
                (not (exists (?a1)
                        (subaction ?a1 ?a))))
(forall (?a ?s1 ?s2)
        (=>     (primitive ?a)
                (<=>    (Do ?a ?s1 ?s2)
                        (and    (Poss ?a ?s)
                                (= ?s2 (do ?a ?s1))))))

(define-relation DoT (?a ?t1 ?t2)
((Arity 3)      (nth-domain 1 action)
                (nth-domain 2 time)
                (nth-domain 3 time))
:def
(exists (?s1 ?s2)
        (and    (Do ?a ?s1 ?s2)
                (= (start ?s1) ?t1)
                (= (start ?s2) ?t2)))

(define-relation duration (?a ?t)
((Arity 2)      (nth-domain 1 action)
                (nth-domain 2 time))
:def
(=>     (DoT ?a ?t1 ?t2)
        (= ?t (- ?t2 ?t1)))

(define-relation Occurs (?a ?s1 ?s2)
((Arity 3)      (nth-domain 1 action)
                (nth-domain 2 situation)
                (nth-domain 3 situation))
:def
(and    (Do ?a ?s1 ?s2)
        (actual ?s2))

(define-relation OccursT (?a ?t1 ?t2)
((Arity 3)      (nth-domain 1 action)
                (nth-domain 2 time)
                (nth-domain 3 time))
:def
(exists (?s1 ?s2)
        (and    (Occurs ?a ?s1 ?s2)
                (= (start ?s1) ?t1)
                (= (start ?s2) ?t2)))

(define-relation Occurs^B (?a ?s1 ?s2 ?b)
((Arity 4)      (nth-domain 1 action)
                (nth-domain 2 situation)
                (nth-domain 3 situation)
                (nth-domain 4 branch))
:def
(and    (Do ?a ?s1 ?s2)
        (branch ?s2 ?b)
        (feasible_branch ?b))