[tlaplus] Why does this liveness property not work?

[Andrew Helwer <andrew.helwer@xxxxxxxxx>]

Here's a simple spec with a variable x that counts from 1 to 5 then stutters at 5 forever:

---- MODULE Test ----
EXTENDS Naturals
VARIABLE x
Init ≜ x = 1
Next ≜
  IF x = 5 THEN UNCHANGED x
  ELSE x' = x + 1
Spec ≜ Init ∧ □[Next]_x ∧ WF_x(Next)
Liveness ≜ (x = 1) ⇒ ◇□(x = 5)
====

However, when I try to check property Liveness with TLC I get this error:

Starting... (2024-10-03 10:15:19)
Implied-temporal checking--satisfiability problem has 1 branches.
Computing initial states...
Finished computing initial states: 1 distinct state generated at 2024-10-03 10:15:19.
Error: Temporal properties were violated.

Error: The following behavior constitutes a counter-example:

State 1: <Initial predicate>
x = 1

2 states generated, 2 distinct states found, 1 states left on queue.
The depth of the complete state graph search is 2.
Finished in 00s at (2024-10-03 10:15:19)

Why is this?

Andrew

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