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1
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2
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node Sofar( X : bool ) returns ( Sofar : bool );
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let
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Sofar = X -> X and pre Sofar;
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5
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tel
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6
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node excludes8( X1, X2, X3, X4, X5, X6, X7, X8 : bool ) returns ( excludes : bool );
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8
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let
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9
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excludes = not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 or
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10
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X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 or
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not X1 and X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 or
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12
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not X1 and not X2 and X3 and not X4 and not X5 and not X6 and not X7 and not X8 or
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13
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not X1 and not X2 and not X3 and X4 and not X5 and not X6 and not X7 and not X8 or
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14
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not X1 and not X2 and not X3 and not X4 and X5 and not X6 and not X7 and not X8 or
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15
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not X1 and not X2 and not X3 and not X4 and not X5 and X6 and not X7 and not X8 or
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16
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not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and X7 and not X8 or
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17
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not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and X8;
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18
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tel
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19
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node firefly(e1, e2, e3, e4, e5, e6, e7, e8 : bool; i_invalid : int)
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returns(invalid, dirty, exclusive, shared : int);
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var
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23
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garde1, garde2, garde3, garde4, garde5, garde6, garde7, garde8 : bool;
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25
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mem_invalid : int;
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26
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let
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28
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mem_invalid = i_invalid -> pre mem_invalid;
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30
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garde1 = pre invalid>=1 and pre dirty=0 and pre shared=0 and pre exclusive=0 ;
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32
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garde2 = pre invalid>=1 and pre dirty>=1;
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33
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garde3 = pre invalid>=1 and pre shared+pre exclusive>=1;
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34
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garde4 = pre exclusive>=1;
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35
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garde5 = pre shared=1;
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36
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garde6 = pre invalid>=1 and pre dirty=0 and pre shared=0 and pre exclusive=0;
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37
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garde7 = pre invalid>=1 and pre dirty>=1;
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38
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garde8 = pre invalid>=1 and pre shared+pre exclusive>=1;
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39
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40
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invalid = mem_invalid ->
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41
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if(e1) then if(garde1) then pre invalid-1 else pre invalid else
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if(e2) then if(garde2) then pre invalid-1 else pre invalid else
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if(e3) then if(garde3) then pre invalid-1 else pre invalid else
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if(e6) then if(garde6) then pre invalid-1 else pre invalid else
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45
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if(e7) then if(garde7) then pre invalid-1 else pre invalid else
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46
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if(e8) then if(garde8) then pre invalid-1 else pre invalid else
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47
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pre invalid;
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48
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49
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50
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dirty = 0 ->
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51
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if(e2) then if(garde2) then pre dirty-1 else pre dirty else
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52
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if(e4) then if(garde4) then pre dirty+1 else pre dirty else
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53
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if(e6) then if(garde6) then 1 else pre dirty else
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54
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if(e7) then if(garde7) then pre dirty-1 else pre dirty else
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55
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pre dirty;
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56
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exclusive = 0 ->
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58
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if(e1) then if(garde1) then pre exclusive+1 else pre exclusive else
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59
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if(e3) then if(garde3) then 0 else pre exclusive else
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60
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if(e4) then if(garde4) then pre exclusive-1 else pre exclusive else
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if(e5) then if(garde5) then pre exclusive+1 else pre exclusive else
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if(e8) then if(garde8) then 0 else pre exclusive else
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63
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pre exclusive;
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64
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shared = 0 ->
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if(e2) then if(garde2) then pre shared+2 else pre shared else
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if(e3) then if(garde3) then pre shared + pre exclusive + 1 else pre shared else
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if(e5) then if(garde5) then pre 0 else pre shared else
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if(e7) then if(garde7) then pre shared+2 else pre shared else
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if(e8) then if(garde8) then pre shared + pre exclusive + 1 else pre shared else
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pre shared;
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72
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73
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tel
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74
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75
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-- Not provable in luke-bitvec
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76
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node top(e1, e2, e3, e4, e5, e6, e7, e8 : bool; i_invalid : int)
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77
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returns( OK : bool );
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78
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--@ contract guarantees OK;
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79
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var invalid, dirty, exclusive, shared : int;
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80
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env : bool;
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81
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let
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82
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( invalid, dirty, exclusive, shared ) =
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83
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firefly( e1, e2, e3, e4, e5, e6, e7, e8, i_invalid );
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84
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85
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env = Sofar( excludes8( e1, e2, e3, e4, e5, e6, e7, e8 ) and
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86
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i_invalid >= 0 and i_invalid < 5 );
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87
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OK = env => exclusive >= 0;
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88
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--%PROPERTY OK=true;
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89
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--%MAIN;
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90
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tel
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