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// mutual exclusion
(!((p1=2) & (p2=2))) &
(!((p1=2) & (p3=2))) &
(!((p2=2) & (p3=2)))
// liveness
// if a process is trying then eventually a process enters the critical section
((p1=1) | (p2=1) | (p3=1)) =>
P>=1 [ true U (p1=2) | (p2=2) | (p3=2) ]
// if all processes are trying process 1 enters the critical section first
(p1=1) & (p2=1) & (p3=1) =>
P>=0.5 [ !(p2=2) & !(p3=2) U (p1=2) ]