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# TrainSwitchingPuzzle

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This model was developed to solve Puzzle Nr 40 from the book "My best mathematical and logical puzzles" by Martin Gardner. Using breadth-first, ProB takes about 5 seconds to find the shortest solution leading to a state satisfying the GOAL predicate. The trace consists of 22 steps. A visualisation of this trace can be found on YouTube.

```MACHINE GardnerSwitchingPuzzle_v2
/* v2 without a special PassThroughTunnel operation */
/* Puzzle Nr 40 from My best mathematical and logical puzzles, Martin Gardner */
/* written by Michael Leuschel, 2010 */
/*
We have ENGINE + two wagons A, B
Only ENGINE can go through tunnel
Layout:
==ENGINE ======+======A======\
/              |
|             TUN
|             NEL
|              |
\             /
======================B======
Task: move A to B's position and vice versa and return ENGINE to original position
*/
SETS
TRAINS={engine,A,B};
DEFINITIONS
GOAL == occ(topleft) = [engine] & occ(top_middle)=[B] & occ(bot_middle)=[A]
CONSTANTS
PROPERTIES
top_middle |-> bot_middle, /* Tunnel */
bot_middle|-> bot_left, bot_middle |-> leftlink} &
{ (top_middle|->bot_middle) |-> {A,B} } /* A,B are not allowed to take the tunnel */
VARIABLES occ
INVARIANT
occ: TRACKS --> iseq(TRAINS) &
!(t1,t2).(t1:TRACKS & t1/=t2 => ran(occ(t1)) /\ ran(occ(t2)) = {} ) &
UNION(t).(t:TRACKS|ran(occ(t))) = TRAINS
/*
Sequence Order on Track Sections:
====1=2=3======+====1=2=3====\
/              |
3             TUN
2             NEL
1              |
\             /
====3=2=1===========3=2=1====
*/
INITIALISATION occ := {topleft |-> [engine], top_middle |-> [A], bot_middle |->[B],
leftlink |-> <>, bot_left |-> <> }
OPERATIONS
Move(Seq,T1,T2,Rest) = PRE Seq : iseq1(TRAINS) & Rest : iseq(TRAINS) &
occ(T1)= Rest^Seq & engine:ran(Seq) & T1|->T2 : link &
restrict((T1,T2)) /\ ran(Seq) = {} THEN
occ := occ <+ {T1 |-> Rest, T2 |-> (Seq^occ(T2))}
END;
MoveRev(Seq,T1,T2,Rest) = PRE Seq : iseq1(TRAINS) & Rest : iseq(TRAINS) &
occ(T1)= Seq^Rest & engine:ran(Seq) & T2|->T1 : link &
restrict((T2,T1)) /\ ran(Seq) = {}  THEN
occ := occ <+ {T1 |-> Rest, T2 |-> (occ(T2)^Seq)}
END
END
```