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 1 ```node Sofar( X : bool ) returns ( Sofar : bool ); ``` ```let ``` ``` Sofar = X -> X and pre Sofar; ``` ```tel ``` ```node excludes9( X1, X2, X3, X4, X5, X6, X7, X8, X9 : bool ) returns ( excludes : bool ); ``` ```let ``` ``` excludes = not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and X4 and not X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and not X4 and X5 and not X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and not X4 and not X5 and X6 and not X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and X7 and not X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and X8 and not X9 or ``` ``` not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and X9; ``` ```tel ``` ```node ticket3i(e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool; ``` ```init_a1, init_a2, init_a3, init_t : int) returns ( ``` ```p1, p2, p3, t, s, a1, a2, a3 : int; erreur_ticket3i : bool); ``` ```var ``` ``` g1, g2, g3, g4, g5, g6, g7, g8, g9 : bool; ``` ```let ``` ``` erreur_ticket3i = if((p1>=3) or (p2>=3) or (p3>=3)) then true else false; ``` ``` g1 = pre p1 = 0; ``` ``` g2 = pre p1 = 1 and pre s >= a1; ``` ``` g3 = pre p1 = 2; ``` ``` g4 = pre p2 = 0; ``` ``` g5 = pre p2 = 1 and pre s >= a2; ``` ``` g6 = pre p2 = 2; ``` ``` g7 = pre p3 = 0; ``` ``` g8 = pre p3 = 1 and pre s >= a3; ``` ``` g9 = pre p3 = 2; ``` ``` p1 = 0 -> ``` ``` if(e1) then if(g1) then 1 else pre p1 else ``` ``` if(e2) then if(g2) then 2 else pre p1 else ``` ``` if(e3) then if(g3) then 0 else pre p1 else ``` ``` pre p1; ``` ``` p2 = 0 -> ``` ``` if(e4) then if(g4) then 1 else pre p2 else ``` ``` if(e5) then if(g5) then 2 else pre p2 else ``` ``` if(e6) then if(g6) then 0 else pre p2 else ``` ``` pre p2; ``` ``` p3 = 0 -> ``` ``` if(e7) then if(g7) then 1 else pre p3 else ``` ``` if(e8) then if(g8) then 2 else pre p3 else ``` ``` if(e9) then if(g9) then 0 else pre p3 else ``` ``` pre p3; ``` ``` t = init_t -> ``` ``` if(e1) then if(g1) then pre t+1 else pre t else ``` ``` if(e4) then if(g4) then pre t+1 else pre t else ``` ``` if(e7) then if(g7) then pre t+1 else pre t else ``` ``` pre t; ``` ``` s = t -> ``` ``` if(e3) then if(g3) then pre s+1 else pre s else ``` ``` if(e6) then if(g6) then pre s+1 else pre s else ``` ``` if(e9) then if(g9) then pre s+1 else pre s else ``` ``` pre s; ``` ``` a1 = init_a1 -> ``` ``` if(e1) then if(g1) then pre t else pre a1 else ``` ``` pre a1; ``` ``` a2 = init_a2 -> ``` ``` if(e4) then if(g4) then pre t else pre a2 else ``` ``` pre a2; ``` ``` a3 = init_a3 -> ``` ``` if(e7) then if(g7) then pre t else pre a3 else ``` ``` pre a3; ``` ```tel ``` ```--@ ensures OK; ``` ```node top( e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool; ``` ``` init_a1, init_a2, init_a3, init_t : int ) ``` ```returns ( OK : bool ); ``` ``` var p1, p2, p3, t, s, a1, a2, a3 : int; ``` ``` erreur_ticket3i : bool; ``` ``` env : bool; ``` ```let ``` ``` ( p1, p2, p3, t, s, a1, a2, a3 , erreur_ticket3i ) = ``` ``` ticket3i( e1, e2, e3, e4, e5, e6, e7, e8, e9, ``` ``` init_a1, init_a2, init_a3, init_t ); ``` ``` env = Sofar( excludes9( e1, e2, e3, e4, e5, e6, e7, e8, e9 ) and ``` ``` init_a1 >= 0 and ``` ``` init_a2 >= 0 and ``` ``` init_a3 >= 0 and ``` ``` init_t >= 0 ); ``` ``` OK = env => t >= 0; ``` ``` --%MAIN; ``` ```--!k:2; ``` ```--!PROPERTY: OK=true; ``` ```tel ```
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