in mcs -- (I) Base case open INV . -- fresh constants ops p q z : -> Pid . -- check red inv11(init,p,q,z) . close -- ------------------------------1.1: pc(s,r) = rs, p != r, q != r ---------------------- -- ----------------------------------1.1a. ----------------- -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq z = r . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l3 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l4 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l5 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l6 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.1.1-(1) pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- ------------------------------1.2: pc(s,r) = rs, p = r, q = r---------------------- -- 1.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq q = r . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- 1.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq q = r . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- -- 1.2 pc(s,r) = rs, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq q = r . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- ------------------------------1.3: pc(s,r) = rs, p = r, q != r---------------------- -- -- 1.3-(1) pc(s,r) = rs, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (q = r) = false . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.3-(1) pc(s,r) = rs, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (q = r) = false . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.3-(1) pc(s,r) = rs, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (q = r) = false . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . -- check red (inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- ----------------------------1.4: pc(s,r) = rs, p != r, q = r -------------------------- -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l3 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l4 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l5 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l6 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- -- 1.4-(1) pc(s,r) = rs, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = rs . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(want(s,r),p,q,z) . close -- ------------------------------2.1: pc(s,r) = l1, p != r, q != r ---------------------- -- ----------------------------------2.1a. ----------------- -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq z = r . -- red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l3 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l4 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l5 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,p) = l6 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- ------------------------------2.2: pc(s,r) = l1, p = r, q = r---------------------- -- 2.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq q = r . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- 2.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq q = r . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- -- 2.2 pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq q = r . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- ------------------------------2.3: pc(s,r) = l1, p = r, q != r---------------------- -- -- 2.3-(1) pc(s,r) = l1, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (q = r) = false . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.3-(1) pc(s,r) = l1, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.3-(1) pc(s,r) = l1, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . -- check red (inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- ----------------------------2.4: pc(s,r) = l1, p != r, q = r -------------------------- -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l3 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l4 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l5 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l6 . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- -- 2.4-(1) pc(s,r) = l1, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l1 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stnxt(s,r),p,q,z) . close -- ------------------------------3.1: pc(s,r) = l2, p != r, q != r ---------------------- -- ----------------------------------3.1a. ----------------- -- -- 3.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq z = r . eq glock(s) = nop . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . red (inv4(s,p) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq z = r . eq glock(s) = nop . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l1, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq z = r . eq (glock(s) = nop) = false . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq next(s,q) = r . eq pc(s,q) = l6 . eq pc(s,z) = l11 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv10(s,q,z) and inv10(s,r,q) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq next(s,q) = r . eq (pc(s,q) = l6) = false . eq pc(s,z) = l11 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv10(s,q,z) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq (next(s,q) = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.1.1-(1) pc(s,r) = l2, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- ------------------------------3.2: pc(s,r) = l2, p = r, q = r---------------------- -- -- 3.2-1 pc(s,r) = l2, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq q = r . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.2-1 pc(s,r) = l2, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq q = r . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.2-1 pc(s,r) = l2, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq q = r . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- ------------------------------3.3: pc(s,r) = l2, p = r, q != r---------------------- -- -- 3.3-(1) pc(s,r) = l2, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (q = r) = false . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.3-(1) pc(s,r) = l2, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.3-(1) pc(s,r) = l2, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . -- check red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- ----------------------------3.4: pc(s,r) = l2, p != r, q = r -------------------------- -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq z = r . eq glock(s) = nop . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq z = r . eq glock(s) = nop . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . red (inv4(s,p) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq z = r . eq (glock(s) = nop) = false . red (inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l3 . eq pc(s,z) = l11 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l4 . eq pc(s,z) = l11 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l5 . eq pc(s,z) = l11 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,p) = l6 . eq pc(s,z) = l11 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv18(s,r) and inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- -- 3.4-(1) pc(s,r) = l2, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l2 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stprd(s,r),p,q,z) . close -- ------------------------------4.1: pc(s,r) = l3, p != r, q != r ---------------------- -- ----------------------------------4.1a. z = r , p != z ----------------- -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq pred(s,r) = nop . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq pred(s,r) = nop . eq q = r . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq pred(s,r) = nop . eq (q = r) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq pred(s,r) = nop . eq q = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq pred(s,r) = nop . eq (q = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq (pred(s,r) = nop) = false . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq z = r . eq (pred(s,r) = nop) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l3 . eq q = r . eq pred(s,r) = nop . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l3 . eq q = r . eq (pred(s,r) = nop) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l4 . eq q = r . eq pred(s,r) = nop . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l4 . eq q = r . eq (pred(s,r) = nop) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l5 . eq q = r . eq pred(s,r) = nop . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l5 . eq q = r . eq (pred(s,r) = nop) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l6 . eq q = r . eq pred(s,r) = nop . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l6 . eq q = r . eq (pred(s,r) = nop) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l3 . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l4 . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l5 . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq pc(s,p) = l6 . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq q = r . eq pred(s,r) = nop . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq q = r . eq (pred(s,r) = nop) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.1.1-(1) pc(s,r) = l3, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l3 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- ------------------------------4.2: pc(s,r) = l3, p = r, q = r---------------------- -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq z = r . eq pred(s,r) = nop . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq z = r . eq (pred(s,r) = nop) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq pred(s,r) = nop . eq q = r . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq pred(s,r) = nop . eq (q = r) = false . eq pc(s,z) = l11 . red (inv1(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv1(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv1(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv1(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red (inv1(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv5(s,z,r) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . eq lock(s,z) = false . red (inv2(s,r,z) and inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq lock(s,z) = true . red (inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq pred(s,r) = nop . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq (pred(s,r) = nop) = false . eq q = r . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq (pred(s,r) = nop) = false . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- -- 4.2-1 pc(s,r) = l3, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l3 . eq p = r . eq (z = r) = false . eq (pred(s,r) = nop) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(chprd(s,r),p,q,z) . close -- ------------------------------5.1: pc(s,r) = l4, p != r, q != r ---------------------- -- ----------------------------------5.1a. ----------------- -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq z = r . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq (q = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- ------------------------------5.2: pc(s,r) = l4, p = r, q = r---------------------- -- 5.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq q = r . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- 5.2 open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq q = r . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- -- 5.2 pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq q = r . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- ------------------------------5.3: pc(s,r) = l4, p = r, q != r---------------------- -- -- 5.3-(1) pc(s,r) = l4, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq (q = r) = false . eq p = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.3-(1) pc(s,r) = l4, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.3-(1) pc(s,r) = l4, p = r, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l4 . eq (q = r) = false . eq p = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . -- check red (inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- ----------------------------5.4: pc(s,r) = l4, p != r, q = r -------------------------- -- -- 5.4-(1) pc(s,r) = l4, p != r, q = r open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq z = r . -- check red (inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- -- 5.1.1-(1) pc(s,r) = l4, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l4 . eq (p = r) = false . eq q = r . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(stlck(s,r),p,q,z) . close -- ------------------------------6.1: pc(s,r) = l5, p != r, q != r ---------------------- -- ----------------------------------6.1a. z = r , p != z ----------------- -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq z = r . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq q = r . eq lock(s,r) = false . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq lock(s,r) = true . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (q = r) = false . eq lock(s,r) = false . eq pc(s,p) = l3 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (q = r) = false . eq lock(s,r) = true . eq pc(s,p) = l3 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq z = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (q = r) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq lock(s,r) = false . red (inv6(s,r) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq lock(s,r) = true . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l11 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l11 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l11 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l11 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l11 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------- z = l10 -------- -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l11 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l10 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l10 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l10 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l10 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l11 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l8 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l8 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l8 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l8 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------- z = l7 -------- -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l11 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l7 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l7 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l7 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l7 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l11 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv3(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = cs . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = cs . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = cs . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = cs . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------- z = l6 -------- -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq lock(s,z) = false . eq pc(s,p) = l11 . red (inv2(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv2(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv2(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv2(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv2(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l6 . eq lock(s,z) = true . eq pc(s,p) = l11 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l6 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l6 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l6 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l6 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------- z = l3 -------- -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pred(s,z) = nop . eq pc(s,p) = l11 . red (inv1(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv1(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv1(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv1(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv1(s,p,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq pc(s,z) = l3 . eq (pred(s,z) = nop) = false . eq pc(s,p) = l11 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = cs . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l8 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l7 . red (inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pred(s,r) = z . eq pc(s,z) = l3 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq (pred(s,r) = z) = false . eq pc(s,z) = l3 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l3 . eq pc(s,p) = l3 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l3 . eq pc(s,p) = l3 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red (inv6(s,r) and inv10(s,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . -- check eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.1.1-(1) pc(s,r) = l5, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l6) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------------------------------6.2: pc(s,r) = l5, p = r, q = r---------------------- -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq z = r . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq (z = r) = false . eq q = r . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq (z = r) = false . eq q = r . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq pred(s,r) = z . eq pc(s,z) = l11 . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = cs . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv19(s,p,r,z) and inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq (pred(s,r) = z) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- -- 6.2-1 pc(s,r) = l5, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l5 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(stnpr(s,r),p,q,z) . close -- ------------------------------7.1: pc(s,r) = l6, p != r, q != r ---------------------- -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq z = r . eq lock(s,r) = false . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq q = r . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq z = r . eq lock(s,r) = false . eq (q = r) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq z = r . eq lock(s,r) = true . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq z = r . eq q = r . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq lock(s,r) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq lock(s,r) = true . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq z = r . eq (q = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq lock(s,r) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq lock(s,r) = true . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq q = r . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l11 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l10 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = cs . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l8 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l7 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l6 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (q = r) = false . eq pc(s,z) = l3 . eq pc(s,p) = l1 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l2 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = rs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l9 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l12 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq q = r . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,p) = l1) = false . eq (pc(s,p) = l2) = false . eq (pc(s,p) = rs) = false . eq (pc(s,p) = l9) = false . eq (pc(s,p) = l12) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . eq (q = r) = false . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq q = r . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq q = r . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (q = r) = false . eq pc(s,p) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l4 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l5 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,p) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.1.1-(1) pc(s,r) = l6, (p = r) = false, (q = r) = false open INV . op s : -> Sys . ops p q r z : -> Pid . eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . eq pc(s,r) = l6 . eq (p = r) = false . eq (z = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq (q = r) = false . eq (pc(s,p) = l3) = false . eq (pc(s,p) = l4) = false . eq (pc(s,p) = l5) = false . eq (pc(s,p) = l6) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- ------------------------------7.2: pc(s,r) = l6, p = r, ---------------------- -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq z = r . eq lock(s,r) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq lock(s,r) = true . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq (z = r) = false . eq q = r . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq (z = r) = false . eq q = r . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq lock(s,r) = false . eq pc(s,z) = l11 . red ( inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l10 . red (inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l8 . red (inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l7 . red (inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = cs . red (inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l6 . red (inv7(s,r,z) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l3 . red (inv2(s,z,r) and inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq lock(s,r) = true . eq pc(s,z) = l11 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l10 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l8 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l7 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = cs . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l6 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq pc(s,z) = l3 . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close -- -- 7.2-1 pc(s,r) = l6, p = r, q = r open INV . -- fresh constants op s : -> Sys . ops p q r z : -> Pid . -- induction hypothesis eq [:nonexec] : inv11(s,P:Pid,Q:Pid,Z:Pid) = true . -- assumptions eq pc(s,r) = l6 . eq p = r . eq (z = r) = false . eq (q = r) = false . eq (pc(s,z) = l11) = false . eq (pc(s,z) = l10) = false . eq (pc(s,z) = l8) = false . eq (pc(s,z) = l7) = false . eq (pc(s,z) = cs) = false . eq (pc(s,z) = l6) = false . eq (pc(s,z) = l3) = false . eq lock(s,r) = true . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . eq lock(s,r) = false . red ( inv11(s,p,q,z)) implies inv11(chlck(s,r),p,q,z) . close