## German.CTC

### Safety properties

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

Control properties:

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

Data properties:

Exgntd = False ∧ MemData ≠ AuxData

∃ z. ( CacheState[z] ≠ Invalid ∧ CacheData[z] ≠ AuxData )

### Options used

-brab 2

### Inferred invariants

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

CacheState[#1] = Exclusive && Shrset[#2] = True Chan2Cmd[#1] = Gnte && Shrset[#2] = True CacheState[#1] = Exclusive && Invset[#2] = True Chan2Cmd[#1] = Gnte && Invset[#2] = True Exgntd = True && Chan2Cmd[#1] = Gnts Chan2Cmd[#2] = Inv && CacheState[#1] = Exclusive Chan2Cmd[#1] = Gnte && Chan2Cmd[#2] = Inv Chan3Cmd[#2] = Invack && CacheState[#1] = Exclusive Chan2Cmd[#1] = Gnte && Chan3Cmd[#2] = Invack Chan2Cmd[#1] = Inv && Invset[#1] = True Chan3Cmd[#1] = Invack && Invset[#1] = True Curcmd = Empty && Chan2Cmd[#1] = Inv Chan2Cmd[#1] = Inv && Chan3Cmd[#1] = Invack Invset[#1] = True && Shrset[#1] = False Exgntd = False && Curcmd = Reqs && Chan2Cmd[#1] = Inv Curcmd = Empty && Chan3Cmd[#1] = Invack Chan2Cmd[#1] = Inv && Shrset[#1] = False Exgntd = False && Curcmd = Reqs && Chan3Cmd[#1] = Invack Chan3Cmd[#1] = Invack && Shrset[#1] = False Chan2Cmd[#1] = Gnts && Chan3Cmd[#1] = Invack Chan3Cmd[#1] = Invack && CacheState[#1] <> Invalid Chan2Cmd[#1] = Gnts && Shrset[#1] = False Chan3Cmd[#1] = Invack && CacheState[#1] = Exclusive Chan2Cmd[#1] = Gnte && CacheState[#1] = Exclusive Chan2Cmd[#1] = Gnts && CacheState[#1] = Exclusive CacheState[#1] <> Invalid && Shrset[#1] = False Exgntd = False && CacheState[#1] = Exclusive

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.