------------------------- MODULE counterexample ------------------------- EXTENDS MC4_4_faulty (* Initial state *) State1 == TRUE (* Transition 0 to State2 *) State2 == /\ Faulty = {} /\ blockchain = 1 :> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1] @@ 2 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3] @@ 3 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4] @@ 4 :> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6] @@ 5 :> [NextVS |-> { "n1", "n2", "n3", "n4" }, VS |-> { "n1", "n4" }, height |-> 5, lastCommit |-> { "n2", "n3" }, time |-> 7] /\ fetchedLightBlocks = 1 :> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ history = 0 :> [current |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] /\ latestVerified = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ lightBlockStatus = 1 :> "StateVerified" /\ nextHeight = 4 /\ now = 1398 /\ nprobes = 0 /\ prevCurrent = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ prevNow = 1398 /\ prevVerdict = "SUCCESS" /\ prevVerified = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ state = "working" (* Transition 1 to State3 *) State3 == /\ Faulty = {} /\ blockchain = 1 :> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1] @@ 2 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3] @@ 3 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4] @@ 4 :> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6] @@ 5 :> [NextVS |-> { "n1", "n2", "n3", "n4" }, VS |-> { "n1", "n4" }, height |-> 5, lastCommit |-> { "n2", "n3" }, time |-> 7] /\ fetchedLightBlocks = 1 :> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] @@ 4 :> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]] /\ history = 0 :> [current |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 1 :> [current |-> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]], now |-> 1398, verdict |-> "NOT_ENOUGH_TRUST", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] /\ latestVerified = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ lightBlockStatus = 1 :> "StateVerified" @@ 4 :> "StateUnverified" /\ nextHeight = 2 /\ now = 1398 /\ nprobes = 1 /\ prevCurrent = [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]] /\ prevNow = 1398 /\ prevVerdict = "NOT_ENOUGH_TRUST" /\ prevVerified = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ state = "working" (* Transition 2 to State4 *) State4 == /\ Faulty = {} /\ blockchain = 1 :> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1] @@ 2 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3] @@ 3 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4] @@ 4 :> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6] @@ 5 :> [NextVS |-> { "n1", "n2", "n3", "n4" }, VS |-> { "n1", "n4" }, height |-> 5, lastCommit |-> { "n2", "n3" }, time |-> 7] /\ fetchedLightBlocks = 1 :> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] @@ 2 :> [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]] @@ 4 :> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]] /\ history = 0 :> [current |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 1 :> [current |-> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]], now |-> 1398, verdict |-> "NOT_ENOUGH_TRUST", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 2 :> [current |-> [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] /\ latestVerified = [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]] /\ lightBlockStatus = 1 :> "StateVerified" @@ 2 :> "StateVerified" @@ 4 :> "StateUnverified" /\ nextHeight = 3 /\ now = 1399 /\ nprobes = 2 /\ prevCurrent = [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]] /\ prevNow = 1398 /\ prevVerdict = "SUCCESS" /\ prevVerified = [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] /\ state = "working" (* Transition 3 to State5 *) State5 == /\ Faulty = {} /\ blockchain = 1 :> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1] @@ 2 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3] @@ 3 :> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4] @@ 4 :> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6] @@ 5 :> [NextVS |-> { "n1", "n2", "n3", "n4" }, VS |-> { "n1", "n4" }, height |-> 5, lastCommit |-> { "n2", "n3" }, time |-> 7] /\ fetchedLightBlocks = 1 :> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]] @@ 2 :> [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]] @@ 3 :> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4]] @@ 4 :> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]] /\ history = 0 :> [current |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 1 :> [current |-> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n1", "n4" }, VS |-> { "n2", "n3" }, height |-> 4, lastCommit |-> { "n2", "n3" }, time |-> 6]], now |-> 1398, verdict |-> "NOT_ENOUGH_TRUST", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 2 :> [current |-> [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]], now |-> 1398, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n2", "n3", "n4" }, header |-> [NextVS |-> { "n1", "n3", "n4" }, VS |-> { "n1", "n2", "n3", "n4" }, height |-> 1, lastCommit |-> {}, time |-> 1]]] @@ 3 :> [current |-> [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4]], now |-> 1399, verdict |-> "SUCCESS", verified |-> [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]]] /\ latestVerified = [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4]] /\ lightBlockStatus = 1 :> "StateVerified" @@ 2 :> "StateVerified" @@ 3 :> "StateVerified" @@ 4 :> "StateUnverified" /\ nextHeight = 4 /\ now = 1399 /\ nprobes = 3 /\ prevCurrent = [Commits |-> { "n2", "n3" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n2", "n3" }, height |-> 3, lastCommit |-> { "n1", "n3", "n4" }, time |-> 4]] /\ prevNow = 1399 /\ prevVerdict = "SUCCESS" /\ prevVerified = [Commits |-> { "n1", "n3", "n4" }, header |-> [NextVS |-> { "n2", "n3" }, VS |-> { "n1", "n3", "n4" }, height |-> 2, lastCommit |-> { "n2", "n3", "n4" }, time |-> 3]] /\ state = "working" (* The following formula holds true in the last state and violates the invariant *) InvariantViolation == Cardinality((DOMAIN fetchedLightBlocks)) = 4 /\ BMC!Skolem((\E s1$2 \in DOMAIN history: BMC!Skolem((\E s2$2 \in DOMAIN history: s2$2 = s1$2 + 1 /\ BMC!ConstCardinality((Cardinality(history[s1$2]["current"][ "header" ][ "VS" ]) >= 3)) /\ 3 * Cardinality({ t_2r$1 \in history[s2$2]["current"]["header"]["VS"]: ~(t_2r$1 \in history[s1$2]["current"]["header"]["VS"]) }) = Cardinality(history[s1$2]["current"]["header"]["VS"]))))) ================================================================================ \* Created by Apalache on Wed Nov 18 12:42:14 UTC 2020 \* https://github.com/informalsystems/apalache