## German_pfs

### Safety properties

Below are the safety properties we want to verify, in negated form.

∃ z1,z2. z1≠z2 ∧ ( Cache[z1] = Exclusive ∧ Cache[z2] ≠ Invalid )

### Options used

-brab 2

### Inferred invariants

All invariants are shown in their negated form, where
#1 and #2
are distinct existentially quantified variables.

Curcmd = Empty1 && Flag = True Cache[#1] = Exclusive && Shrset[#2] = True Chan2[#1] = Gnte && Shrset[#2] = True Cache[#1] = Exclusive && Invset[#2] = True Chan2[#1] = Gnte && Invset[#2] = True Exgntd = True && Chan2[#1] = Gnts Cache[#1] = Exclusive && Chan2[#2] = Inv Chan2[#1] = Gnte && Chan2[#2] = Inv Cache[#1] = Exclusive && Chan3[#2] = Invack Chan2[#1] = Gnte && Chan3[#2] = Invack Flag = True && Chan2[#1] = Inv Chan2[#1] = Inv && Invset[#1] = True Flag = True && Chan3[#1] = Invack Chan3[#1] = Invack && Invset[#1] = True Curcmd = Empty1 && Chan2[#1] = Inv Chan2[#1] = Inv && Chan3[#1] = Invack Shrset[#1] = False && Invset[#1] = True Exgntd = False && Curcmd = Reqs && Chan2[#1] = Inv Curcmd = Empty1 && Chan3[#1] = Invack Chan2[#1] = Inv && Shrset[#1] = False Exgntd = False && Curcmd = Reqs && Chan3[#1] = Invack Chan3[#1] = Invack && Shrset[#1] = False Chan2[#1] = Gnts && Chan3[#1] = Invack Chan2[#1] = Gnte && Chan3[#1] = Invack Chan2[#1] = Gnte && Shrset[#1] = False Cache[#1] <> Invalid && Chan3[#1] = Invack Chan2[#1] = Gnts && Shrset[#1] = False Exgntd = False && Chan2[#1] = Gnte Cache[#1] = Exclusive && Chan3[#1] = Invack Chan2[#1] = Gnte && Chan2[#2] = Gnte Cache[#1] <> Invalid && Shrset[#1] = False Chan2[#1] = Gnte && Chan2[#2] = Gnts Exgntd = False && Cache[#1] = Exclusive Cache[#2] <> Invalid && Chan2[#1] = Gnte Cache[#1] = Exclusive && Chan2[#2] = Gnts

You can find the list of all invariants that can be extracted from BRAB here (also in negated form), this collection being inductive.

### Search graph

The algorithm starts from the formula located at the bottom,
inside a red
octagon. Variables #1, #2,
… that appear
in the nodes are distinct skolem variables so we show a formula
φ(#1, #2) as equivalent to ∃
z_{1}, z_{2}.
z_{1} ≠ z_{2} ∧ φ(z_{1},
z_{2}). Plain black edges represent
pre-image relations and are annotated by the transition instance that
was considered. Black circles denote nodes that were obtained by
pre-image computation and were not covered by already visited
nodes. The nodes circled in gray are the one that were not
useful because they were subsumed by formulas pointed by the
gray dashed
arrows. Approximations are shown
in blue rectangles. Each approximation originates from the node that
connects its rectangle with a bold dashed blue edge.