Marcus (agent-cos)
6c6daaf90f
- New generator: compiler/src/generators/z3.ts (1,034 lines) - Translates SpeckDL state → Z3 sort declarations - Translates invariants → Z3 define-fun returning Bool - Translates actions → Z3 transition predicates (enabled + step) - BMC unrolling with --verify-depth=N (default: 10) - CLI: --target=z3 or --target=all - ToggleSwitch and TigerBeetleLedger generate valid SMT-LIB2 - KafkaKRaft spec generates valid SMT-LIB2 structure - Complex forall/set expressions emit 'true' as placeholders (to be improved) - All 41 existing tests still pass This unblocks M1.2 (KRaft verification), M3.2 (Show HN), and M4.3 (OAuth verification).
3456 lines
106 KiB
Text
3456 lines
106 KiB
Text
; SpeckDL: TigerBeetleLedger — Z3 Verification
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; Generated by speckl-compile Z3 backend
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; Bounded model checking depth: 10
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(set-logic ALL)
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(set-option :produce-models true)
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(declare-sort Account 0)
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(declare-sort Transfer 0)
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(declare-sort Replica 0)
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(declare-sort LogEntry 0)
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; --- State Variables ---
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(declare-const accounts (Array Int Account))
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(declare-const transfers (Array Int Transfer))
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(declare-const pending (Array Int Bool))
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(declare-const replicaState (Array Int Replica))
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(declare-const log (Array Int LogEntry))
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(declare-const commitIndex Int)
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(declare-const leader Int)
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; --- Invariants ---
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(define-fun AccountBalanceInvariant () Bool
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(and
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forall (select accounts.values: a)
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(- a.balance = a.credits_posted a.debits_posted)
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forall (select accounts.values: a)
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a.debits_pending >= 0
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a.credits_pending >= 0
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)
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)
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(define-fun TransferStateConsistency () Bool
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(and
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forall (select transfers.values: t)
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t.pending implies t.posted = false && t.voided = false
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forall (select transfers.values: t)
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t.posted implies t.voided = false
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forall (select transfers.values: t)
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t.voided implies t.posted = false
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)
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)
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(define-fun NoOverdraft () Bool
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(and
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forall (select accounts.values: a)
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(or a.balance >= 0 a.flags.allows_overdraft)
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)
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)
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; --- Action Transition Predicates ---
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(define-fun CreateTransferEnabled () Bool
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(and
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(not (select transfers t.id))
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(select accounts.keys t.from)
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(select accounts.keys t.to)
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t.from distinct t.to
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(select accounts t.from).balance >= t.amount || (select accounts t.from).flags.allows_overdraft
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)
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)
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(define-fun CommitTransferEnabled () Bool
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(and
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(select pending id)
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(select transfers.keys id)
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(select transfers id).pending = true
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)
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)
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(define-fun VoidTransferEnabled () Bool
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(and
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(select pending id)
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(select transfers.keys id)
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(select transfers id).pending = true
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)
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)
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(define-fun PostTransferEnabled () Bool
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(and
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(not (select transfers t.id))
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(select accounts.keys t.from)
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(select accounts.keys t.to)
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t.from distinct t.to
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(select accounts t.from).balance >= t.amount || (select accounts t.from).flags.allows_overdraft
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)
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)
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(define-fun BecomeLeaderEnabled () Bool
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(and
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(select replicaState.keys replica)
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(select replicaState replica).role = "candidate"
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(< (select replicaState replica).currentTerm term)
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)
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)
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(define-fun AppendEntryEnabled () Bool
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(and
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(+ entry.index = length(log) 1)
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term >= commitIndex
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)
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)
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; Next transition relation: CreateTransfer | CommitTransfer | VoidTransfer | PostTransfer | BecomeLeader | AppendEntry
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(define-fun Next () Bool
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(or
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(and (CreateTransferEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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(and (CommitTransferEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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(and (VoidTransferEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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(and (PostTransferEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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(and (BecomeLeaderEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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(and (AppendEntryEnabled)
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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; Stuttering step
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(and
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(= accounts_post accounts)
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(= transfers_post transfers)
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(= pending_post pending)
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(= replicaState_post replicaState)
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(= log_post log)
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(= commitIndex_post commitIndex)
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(= leader_post leader)
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)
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)
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)
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; --- Bounded Model Checking ---
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; Verification: Always(AccountBalanceInvariant)
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; BMC depth: 10
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; Declare state copies for 10 steps
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(declare-const accounts_0 (Array Int Account))
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(declare-const accounts_1 (Array Int Account))
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(declare-const accounts_2 (Array Int Account))
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(declare-const accounts_3 (Array Int Account))
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(declare-const accounts_4 (Array Int Account))
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(declare-const accounts_5 (Array Int Account))
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(declare-const accounts_6 (Array Int Account))
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(declare-const accounts_7 (Array Int Account))
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(declare-const accounts_8 (Array Int Account))
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(declare-const accounts_9 (Array Int Account))
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(declare-const accounts_10 (Array Int Account))
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(declare-const transfers_0 (Array Int Transfer))
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(declare-const transfers_1 (Array Int Transfer))
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(declare-const transfers_2 (Array Int Transfer))
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(declare-const transfers_3 (Array Int Transfer))
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(declare-const transfers_4 (Array Int Transfer))
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(declare-const transfers_5 (Array Int Transfer))
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(declare-const transfers_6 (Array Int Transfer))
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(declare-const transfers_7 (Array Int Transfer))
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(declare-const transfers_8 (Array Int Transfer))
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(declare-const transfers_9 (Array Int Transfer))
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(declare-const transfers_10 (Array Int Transfer))
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(declare-const pending_0 (Array Int Bool))
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(declare-const pending_1 (Array Int Bool))
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(declare-const pending_2 (Array Int Bool))
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(declare-const pending_3 (Array Int Bool))
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(declare-const pending_4 (Array Int Bool))
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(declare-const pending_5 (Array Int Bool))
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(declare-const pending_6 (Array Int Bool))
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(declare-const pending_7 (Array Int Bool))
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(declare-const pending_8 (Array Int Bool))
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(declare-const pending_9 (Array Int Bool))
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(declare-const pending_10 (Array Int Bool))
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(declare-const replicaState_0 (Array Int Replica))
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(declare-const replicaState_1 (Array Int Replica))
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(declare-const replicaState_2 (Array Int Replica))
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(declare-const replicaState_3 (Array Int Replica))
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(declare-const replicaState_4 (Array Int Replica))
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(declare-const replicaState_5 (Array Int Replica))
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(declare-const replicaState_6 (Array Int Replica))
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(declare-const replicaState_7 (Array Int Replica))
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(declare-const replicaState_8 (Array Int Replica))
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(declare-const replicaState_9 (Array Int Replica))
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(declare-const replicaState_10 (Array Int Replica))
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(declare-const log_0 (Array Int LogEntry))
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(declare-const log_1 (Array Int LogEntry))
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(declare-const log_2 (Array Int LogEntry))
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(declare-const log_3 (Array Int LogEntry))
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(declare-const log_4 (Array Int LogEntry))
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(declare-const log_5 (Array Int LogEntry))
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(declare-const log_6 (Array Int LogEntry))
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(declare-const log_7 (Array Int LogEntry))
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(declare-const log_8 (Array Int LogEntry))
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(declare-const log_9 (Array Int LogEntry))
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(declare-const log_10 (Array Int LogEntry))
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(declare-const commitIndex_0 Int)
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(declare-const commitIndex_1 Int)
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(declare-const commitIndex_2 Int)
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(declare-const commitIndex_3 Int)
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(declare-const commitIndex_4 Int)
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(declare-const commitIndex_5 Int)
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(declare-const commitIndex_6 Int)
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(declare-const commitIndex_7 Int)
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(declare-const commitIndex_8 Int)
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(declare-const commitIndex_9 Int)
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(declare-const commitIndex_10 Int)
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(declare-const leader_0 Int)
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(declare-const leader_1 Int)
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(declare-const leader_2 Int)
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(declare-const leader_3 Int)
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(declare-const leader_4 Int)
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(declare-const leader_5 Int)
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(declare-const leader_6 Int)
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(declare-const leader_7 Int)
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(declare-const leader_8 Int)
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(declare-const leader_9 Int)
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(declare-const leader_10 Int)
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; Initial state constraints
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(assert
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(and
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(>= commitIndex_0 0)
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(>= leader_0 0)
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)
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)
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; Transition constraints
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(assert ; Step 0 → 1
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(or
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(and ; Action: CreateTransfer
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(not (select transfers_0 t.id))
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(select accounts_0.keys t.from)
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(select accounts_0.keys t.to)
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t.from distinct t.to
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(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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(and ; Action: CommitTransfer
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(select pending_0 id)
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(select transfers_0.keys id)
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(select transfers_0 id).pending_0 = true
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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(and ; Action: VoidTransfer
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(select pending_0 id)
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(select transfers_0.keys id)
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(select transfers_0 id).pending_0 = true
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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(and ; Action: PostTransfer
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(not (select transfers_0 t.id))
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(select accounts_0.keys t.from)
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(select accounts_0.keys t.to)
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t.from distinct t.to
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(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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(and ; Action: BecomeLeader
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(select replicaState_0.keys replica)
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(select replicaState_0 replica).role = "candidate"
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(< (select replicaState_0 replica).currentTerm term)
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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(and ; Action: AppendEntry
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(+ entry.index = length(log_0) 1)
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term >= commitIndex_0
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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; Stuttering
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(and
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(= accounts_1 accounts_0)
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(= transfers_1 transfers_0)
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(= pending_1 pending_0)
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(= replicaState_1 replicaState_0)
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(= log_1 log_0)
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(= commitIndex_1 commitIndex_0)
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(= leader_1 leader_0)
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)
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)
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)
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(assert ; Step 1 → 2
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(or
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(and ; Action: CreateTransfer
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(not (select transfers_1 t.id))
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(select accounts_1.keys t.from)
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(select accounts_1.keys t.to)
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t.from distinct t.to
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(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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(and ; Action: CommitTransfer
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(select pending_1 id)
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(select transfers_1.keys id)
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(select transfers_1 id).pending_1 = true
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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(and ; Action: VoidTransfer
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(select pending_1 id)
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(select transfers_1.keys id)
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(select transfers_1 id).pending_1 = true
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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(and ; Action: PostTransfer
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(not (select transfers_1 t.id))
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(select accounts_1.keys t.from)
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(select accounts_1.keys t.to)
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t.from distinct t.to
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(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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(and ; Action: BecomeLeader
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(select replicaState_1.keys replica)
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(select replicaState_1 replica).role = "candidate"
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(< (select replicaState_1 replica).currentTerm term)
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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(and ; Action: AppendEntry
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(+ entry.index = length(log_1) 1)
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term >= commitIndex_1
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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; Stuttering
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(and
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(= accounts_2 accounts_1)
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(= transfers_2 transfers_1)
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(= pending_2 pending_1)
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(= replicaState_2 replicaState_1)
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(= log_2 log_1)
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(= commitIndex_2 commitIndex_1)
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(= leader_2 leader_1)
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)
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)
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)
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(assert ; Step 2 → 3
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(or
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(and ; Action: CreateTransfer
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(not (select transfers_2 t.id))
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(select accounts_2.keys t.from)
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(select accounts_2.keys t.to)
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t.from distinct t.to
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(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
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(= accounts_3 accounts_2)
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(= transfers_3 transfers_2)
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(= pending_3 pending_2)
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(= replicaState_3 replicaState_2)
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(= log_3 log_2)
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(= commitIndex_3 commitIndex_2)
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(= leader_3 leader_2)
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)
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(and ; Action: CommitTransfer
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(select pending_2 id)
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(select transfers_2.keys id)
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(select transfers_2 id).pending_2 = true
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(= accounts_3 accounts_2)
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(= transfers_3 transfers_2)
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(= pending_3 pending_2)
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(= replicaState_3 replicaState_2)
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(= log_3 log_2)
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(= commitIndex_3 commitIndex_2)
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(= leader_3 leader_2)
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)
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(and ; Action: VoidTransfer
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(select pending_2 id)
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(select transfers_2.keys id)
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(select transfers_2 id).pending_2 = true
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(= accounts_3 accounts_2)
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(= transfers_3 transfers_2)
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(= pending_3 pending_2)
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(= replicaState_3 replicaState_2)
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(= log_3 log_2)
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(= commitIndex_3 commitIndex_2)
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(= leader_3 leader_2)
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)
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(and ; Action: PostTransfer
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(not (select transfers_2 t.id))
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(select accounts_2.keys t.from)
|
|
(select accounts_2.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_2.keys replica)
|
|
(select replicaState_2 replica).role = "candidate"
|
|
(< (select replicaState_2 replica).currentTerm term)
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_2) 1)
|
|
term >= commitIndex_2
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 3 → 4
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_3.keys replica)
|
|
(select replicaState_3 replica).role = "candidate"
|
|
(< (select replicaState_3 replica).currentTerm term)
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_3) 1)
|
|
term >= commitIndex_3
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 4 → 5
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_4.keys replica)
|
|
(select replicaState_4 replica).role = "candidate"
|
|
(< (select replicaState_4 replica).currentTerm term)
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_4) 1)
|
|
term >= commitIndex_4
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 5 → 6
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_5.keys replica)
|
|
(select replicaState_5 replica).role = "candidate"
|
|
(< (select replicaState_5 replica).currentTerm term)
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_5) 1)
|
|
term >= commitIndex_5
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 6 → 7
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_6.keys replica)
|
|
(select replicaState_6 replica).role = "candidate"
|
|
(< (select replicaState_6 replica).currentTerm term)
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_6) 1)
|
|
term >= commitIndex_6
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 7 → 8
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_7.keys replica)
|
|
(select replicaState_7 replica).role = "candidate"
|
|
(< (select replicaState_7 replica).currentTerm term)
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_7) 1)
|
|
term >= commitIndex_7
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 8 → 9
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_8.keys replica)
|
|
(select replicaState_8 replica).role = "candidate"
|
|
(< (select replicaState_8 replica).currentTerm term)
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_8) 1)
|
|
term >= commitIndex_8
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 9 → 10
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_9.keys replica)
|
|
(select replicaState_9 replica).role = "candidate"
|
|
(< (select replicaState_9 replica).currentTerm term)
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_9) 1)
|
|
term >= commitIndex_9
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
)
|
|
)
|
|
|
|
; Property assertion: not(invariant at some step)
|
|
(assert
|
|
(or
|
|
(not (AccountBalanceInvariant_0))
|
|
(not (AccountBalanceInvariant_1))
|
|
(not (AccountBalanceInvariant_2))
|
|
(not (AccountBalanceInvariant_3))
|
|
(not (AccountBalanceInvariant_4))
|
|
(not (AccountBalanceInvariant_5))
|
|
(not (AccountBalanceInvariant_6))
|
|
(not (AccountBalanceInvariant_7))
|
|
(not (AccountBalanceInvariant_8))
|
|
(not (AccountBalanceInvariant_9))
|
|
(not (AccountBalanceInvariant_10))
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_0 () Bool
|
|
(and
|
|
forall (select accounts_0.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_0.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_1 () Bool
|
|
(and
|
|
forall (select accounts_1.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_1.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_2 () Bool
|
|
(and
|
|
forall (select accounts_2.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_2.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_3 () Bool
|
|
(and
|
|
forall (select accounts_3.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_3.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_4 () Bool
|
|
(and
|
|
forall (select accounts_4.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_4.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_5 () Bool
|
|
(and
|
|
forall (select accounts_5.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_5.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_6 () Bool
|
|
(and
|
|
forall (select accounts_6.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_6.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_7 () Bool
|
|
(and
|
|
forall (select accounts_7.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_7.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_8 () Bool
|
|
(and
|
|
forall (select accounts_8.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_8.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_9 () Bool
|
|
(and
|
|
forall (select accounts_9.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_9.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
(define-fun AccountBalanceInvariant_10 () Bool
|
|
(and
|
|
forall (select accounts_10.values: a)
|
|
(- a.balance = a.credits_posted a.debits_posted)
|
|
forall (select accounts_10.values: a)
|
|
a.debits_pending >= 0
|
|
a.credits_pending >= 0
|
|
)
|
|
)
|
|
|
|
(echo "Checking: Always(AccountBalanceInvariant) for 10 steps")
|
|
(check-sat)
|
|
(get-model)
|
|
; Verification: Always(NoOverdraft)
|
|
; BMC depth: 10
|
|
|
|
; Declare state copies for 10 steps
|
|
(declare-const accounts_0 (Array Int Account))
|
|
(declare-const accounts_1 (Array Int Account))
|
|
(declare-const accounts_2 (Array Int Account))
|
|
(declare-const accounts_3 (Array Int Account))
|
|
(declare-const accounts_4 (Array Int Account))
|
|
(declare-const accounts_5 (Array Int Account))
|
|
(declare-const accounts_6 (Array Int Account))
|
|
(declare-const accounts_7 (Array Int Account))
|
|
(declare-const accounts_8 (Array Int Account))
|
|
(declare-const accounts_9 (Array Int Account))
|
|
(declare-const accounts_10 (Array Int Account))
|
|
(declare-const transfers_0 (Array Int Transfer))
|
|
(declare-const transfers_1 (Array Int Transfer))
|
|
(declare-const transfers_2 (Array Int Transfer))
|
|
(declare-const transfers_3 (Array Int Transfer))
|
|
(declare-const transfers_4 (Array Int Transfer))
|
|
(declare-const transfers_5 (Array Int Transfer))
|
|
(declare-const transfers_6 (Array Int Transfer))
|
|
(declare-const transfers_7 (Array Int Transfer))
|
|
(declare-const transfers_8 (Array Int Transfer))
|
|
(declare-const transfers_9 (Array Int Transfer))
|
|
(declare-const transfers_10 (Array Int Transfer))
|
|
(declare-const pending_0 (Array Int Bool))
|
|
(declare-const pending_1 (Array Int Bool))
|
|
(declare-const pending_2 (Array Int Bool))
|
|
(declare-const pending_3 (Array Int Bool))
|
|
(declare-const pending_4 (Array Int Bool))
|
|
(declare-const pending_5 (Array Int Bool))
|
|
(declare-const pending_6 (Array Int Bool))
|
|
(declare-const pending_7 (Array Int Bool))
|
|
(declare-const pending_8 (Array Int Bool))
|
|
(declare-const pending_9 (Array Int Bool))
|
|
(declare-const pending_10 (Array Int Bool))
|
|
(declare-const replicaState_0 (Array Int Replica))
|
|
(declare-const replicaState_1 (Array Int Replica))
|
|
(declare-const replicaState_2 (Array Int Replica))
|
|
(declare-const replicaState_3 (Array Int Replica))
|
|
(declare-const replicaState_4 (Array Int Replica))
|
|
(declare-const replicaState_5 (Array Int Replica))
|
|
(declare-const replicaState_6 (Array Int Replica))
|
|
(declare-const replicaState_7 (Array Int Replica))
|
|
(declare-const replicaState_8 (Array Int Replica))
|
|
(declare-const replicaState_9 (Array Int Replica))
|
|
(declare-const replicaState_10 (Array Int Replica))
|
|
(declare-const log_0 (Array Int LogEntry))
|
|
(declare-const log_1 (Array Int LogEntry))
|
|
(declare-const log_2 (Array Int LogEntry))
|
|
(declare-const log_3 (Array Int LogEntry))
|
|
(declare-const log_4 (Array Int LogEntry))
|
|
(declare-const log_5 (Array Int LogEntry))
|
|
(declare-const log_6 (Array Int LogEntry))
|
|
(declare-const log_7 (Array Int LogEntry))
|
|
(declare-const log_8 (Array Int LogEntry))
|
|
(declare-const log_9 (Array Int LogEntry))
|
|
(declare-const log_10 (Array Int LogEntry))
|
|
(declare-const commitIndex_0 Int)
|
|
(declare-const commitIndex_1 Int)
|
|
(declare-const commitIndex_2 Int)
|
|
(declare-const commitIndex_3 Int)
|
|
(declare-const commitIndex_4 Int)
|
|
(declare-const commitIndex_5 Int)
|
|
(declare-const commitIndex_6 Int)
|
|
(declare-const commitIndex_7 Int)
|
|
(declare-const commitIndex_8 Int)
|
|
(declare-const commitIndex_9 Int)
|
|
(declare-const commitIndex_10 Int)
|
|
(declare-const leader_0 Int)
|
|
(declare-const leader_1 Int)
|
|
(declare-const leader_2 Int)
|
|
(declare-const leader_3 Int)
|
|
(declare-const leader_4 Int)
|
|
(declare-const leader_5 Int)
|
|
(declare-const leader_6 Int)
|
|
(declare-const leader_7 Int)
|
|
(declare-const leader_8 Int)
|
|
(declare-const leader_9 Int)
|
|
(declare-const leader_10 Int)
|
|
|
|
; Initial state constraints
|
|
(assert
|
|
(and
|
|
(>= commitIndex_0 0)
|
|
(>= leader_0 0)
|
|
)
|
|
)
|
|
|
|
; Transition constraints
|
|
(assert ; Step 0 → 1
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_0 t.id))
|
|
(select accounts_0.keys t.from)
|
|
(select accounts_0.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_0 id)
|
|
(select transfers_0.keys id)
|
|
(select transfers_0 id).pending_0 = true
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_0 id)
|
|
(select transfers_0.keys id)
|
|
(select transfers_0 id).pending_0 = true
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_0 t.id))
|
|
(select accounts_0.keys t.from)
|
|
(select accounts_0.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_0.keys replica)
|
|
(select replicaState_0 replica).role = "candidate"
|
|
(< (select replicaState_0 replica).currentTerm term)
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_0) 1)
|
|
term >= commitIndex_0
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 1 → 2
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_1 t.id))
|
|
(select accounts_1.keys t.from)
|
|
(select accounts_1.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_1 id)
|
|
(select transfers_1.keys id)
|
|
(select transfers_1 id).pending_1 = true
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_1 id)
|
|
(select transfers_1.keys id)
|
|
(select transfers_1 id).pending_1 = true
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_1 t.id))
|
|
(select accounts_1.keys t.from)
|
|
(select accounts_1.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_1.keys replica)
|
|
(select replicaState_1 replica).role = "candidate"
|
|
(< (select replicaState_1 replica).currentTerm term)
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_1) 1)
|
|
term >= commitIndex_1
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 2 → 3
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_2 t.id))
|
|
(select accounts_2.keys t.from)
|
|
(select accounts_2.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_2 id)
|
|
(select transfers_2.keys id)
|
|
(select transfers_2 id).pending_2 = true
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_2 id)
|
|
(select transfers_2.keys id)
|
|
(select transfers_2 id).pending_2 = true
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_2 t.id))
|
|
(select accounts_2.keys t.from)
|
|
(select accounts_2.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_2.keys replica)
|
|
(select replicaState_2 replica).role = "candidate"
|
|
(< (select replicaState_2 replica).currentTerm term)
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_2) 1)
|
|
term >= commitIndex_2
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 3 → 4
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_3.keys replica)
|
|
(select replicaState_3 replica).role = "candidate"
|
|
(< (select replicaState_3 replica).currentTerm term)
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_3) 1)
|
|
term >= commitIndex_3
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 4 → 5
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_4.keys replica)
|
|
(select replicaState_4 replica).role = "candidate"
|
|
(< (select replicaState_4 replica).currentTerm term)
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_4) 1)
|
|
term >= commitIndex_4
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 5 → 6
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_5.keys replica)
|
|
(select replicaState_5 replica).role = "candidate"
|
|
(< (select replicaState_5 replica).currentTerm term)
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_5) 1)
|
|
term >= commitIndex_5
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 6 → 7
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_6.keys replica)
|
|
(select replicaState_6 replica).role = "candidate"
|
|
(< (select replicaState_6 replica).currentTerm term)
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_6) 1)
|
|
term >= commitIndex_6
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 7 → 8
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_7.keys replica)
|
|
(select replicaState_7 replica).role = "candidate"
|
|
(< (select replicaState_7 replica).currentTerm term)
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_7) 1)
|
|
term >= commitIndex_7
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 8 → 9
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_8.keys replica)
|
|
(select replicaState_8 replica).role = "candidate"
|
|
(< (select replicaState_8 replica).currentTerm term)
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_8) 1)
|
|
term >= commitIndex_8
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 9 → 10
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_9.keys replica)
|
|
(select replicaState_9 replica).role = "candidate"
|
|
(< (select replicaState_9 replica).currentTerm term)
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_9) 1)
|
|
term >= commitIndex_9
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
)
|
|
)
|
|
|
|
; Property assertion: not(invariant at some step)
|
|
(assert
|
|
(or
|
|
(not (NoOverdraft_0))
|
|
(not (NoOverdraft_1))
|
|
(not (NoOverdraft_2))
|
|
(not (NoOverdraft_3))
|
|
(not (NoOverdraft_4))
|
|
(not (NoOverdraft_5))
|
|
(not (NoOverdraft_6))
|
|
(not (NoOverdraft_7))
|
|
(not (NoOverdraft_8))
|
|
(not (NoOverdraft_9))
|
|
(not (NoOverdraft_10))
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_0 () Bool
|
|
(and
|
|
forall (select accounts_0.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_1 () Bool
|
|
(and
|
|
forall (select accounts_1.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_2 () Bool
|
|
(and
|
|
forall (select accounts_2.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_3 () Bool
|
|
(and
|
|
forall (select accounts_3.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_4 () Bool
|
|
(and
|
|
forall (select accounts_4.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_5 () Bool
|
|
(and
|
|
forall (select accounts_5.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_6 () Bool
|
|
(and
|
|
forall (select accounts_6.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_7 () Bool
|
|
(and
|
|
forall (select accounts_7.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_8 () Bool
|
|
(and
|
|
forall (select accounts_8.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_9 () Bool
|
|
(and
|
|
forall (select accounts_9.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
(define-fun NoOverdraft_10 () Bool
|
|
(and
|
|
forall (select accounts_10.values: a)
|
|
(or a.balance >= 0 a.flags.allows_overdraft)
|
|
)
|
|
)
|
|
|
|
(echo "Checking: Always(NoOverdraft) for 10 steps")
|
|
(check-sat)
|
|
(get-model)
|
|
; Verification: Eventually(TransferStateConsistency)
|
|
; BMC depth: 10
|
|
|
|
; Declare state copies for 10 steps
|
|
(declare-const accounts_0 (Array Int Account))
|
|
(declare-const accounts_1 (Array Int Account))
|
|
(declare-const accounts_2 (Array Int Account))
|
|
(declare-const accounts_3 (Array Int Account))
|
|
(declare-const accounts_4 (Array Int Account))
|
|
(declare-const accounts_5 (Array Int Account))
|
|
(declare-const accounts_6 (Array Int Account))
|
|
(declare-const accounts_7 (Array Int Account))
|
|
(declare-const accounts_8 (Array Int Account))
|
|
(declare-const accounts_9 (Array Int Account))
|
|
(declare-const accounts_10 (Array Int Account))
|
|
(declare-const transfers_0 (Array Int Transfer))
|
|
(declare-const transfers_1 (Array Int Transfer))
|
|
(declare-const transfers_2 (Array Int Transfer))
|
|
(declare-const transfers_3 (Array Int Transfer))
|
|
(declare-const transfers_4 (Array Int Transfer))
|
|
(declare-const transfers_5 (Array Int Transfer))
|
|
(declare-const transfers_6 (Array Int Transfer))
|
|
(declare-const transfers_7 (Array Int Transfer))
|
|
(declare-const transfers_8 (Array Int Transfer))
|
|
(declare-const transfers_9 (Array Int Transfer))
|
|
(declare-const transfers_10 (Array Int Transfer))
|
|
(declare-const pending_0 (Array Int Bool))
|
|
(declare-const pending_1 (Array Int Bool))
|
|
(declare-const pending_2 (Array Int Bool))
|
|
(declare-const pending_3 (Array Int Bool))
|
|
(declare-const pending_4 (Array Int Bool))
|
|
(declare-const pending_5 (Array Int Bool))
|
|
(declare-const pending_6 (Array Int Bool))
|
|
(declare-const pending_7 (Array Int Bool))
|
|
(declare-const pending_8 (Array Int Bool))
|
|
(declare-const pending_9 (Array Int Bool))
|
|
(declare-const pending_10 (Array Int Bool))
|
|
(declare-const replicaState_0 (Array Int Replica))
|
|
(declare-const replicaState_1 (Array Int Replica))
|
|
(declare-const replicaState_2 (Array Int Replica))
|
|
(declare-const replicaState_3 (Array Int Replica))
|
|
(declare-const replicaState_4 (Array Int Replica))
|
|
(declare-const replicaState_5 (Array Int Replica))
|
|
(declare-const replicaState_6 (Array Int Replica))
|
|
(declare-const replicaState_7 (Array Int Replica))
|
|
(declare-const replicaState_8 (Array Int Replica))
|
|
(declare-const replicaState_9 (Array Int Replica))
|
|
(declare-const replicaState_10 (Array Int Replica))
|
|
(declare-const log_0 (Array Int LogEntry))
|
|
(declare-const log_1 (Array Int LogEntry))
|
|
(declare-const log_2 (Array Int LogEntry))
|
|
(declare-const log_3 (Array Int LogEntry))
|
|
(declare-const log_4 (Array Int LogEntry))
|
|
(declare-const log_5 (Array Int LogEntry))
|
|
(declare-const log_6 (Array Int LogEntry))
|
|
(declare-const log_7 (Array Int LogEntry))
|
|
(declare-const log_8 (Array Int LogEntry))
|
|
(declare-const log_9 (Array Int LogEntry))
|
|
(declare-const log_10 (Array Int LogEntry))
|
|
(declare-const commitIndex_0 Int)
|
|
(declare-const commitIndex_1 Int)
|
|
(declare-const commitIndex_2 Int)
|
|
(declare-const commitIndex_3 Int)
|
|
(declare-const commitIndex_4 Int)
|
|
(declare-const commitIndex_5 Int)
|
|
(declare-const commitIndex_6 Int)
|
|
(declare-const commitIndex_7 Int)
|
|
(declare-const commitIndex_8 Int)
|
|
(declare-const commitIndex_9 Int)
|
|
(declare-const commitIndex_10 Int)
|
|
(declare-const leader_0 Int)
|
|
(declare-const leader_1 Int)
|
|
(declare-const leader_2 Int)
|
|
(declare-const leader_3 Int)
|
|
(declare-const leader_4 Int)
|
|
(declare-const leader_5 Int)
|
|
(declare-const leader_6 Int)
|
|
(declare-const leader_7 Int)
|
|
(declare-const leader_8 Int)
|
|
(declare-const leader_9 Int)
|
|
(declare-const leader_10 Int)
|
|
|
|
; Initial state constraints
|
|
(assert
|
|
(and
|
|
(>= commitIndex_0 0)
|
|
(>= leader_0 0)
|
|
)
|
|
)
|
|
|
|
; Transition constraints
|
|
(assert ; Step 0 → 1
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_0 t.id))
|
|
(select accounts_0.keys t.from)
|
|
(select accounts_0.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_0 id)
|
|
(select transfers_0.keys id)
|
|
(select transfers_0 id).pending_0 = true
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_0 id)
|
|
(select transfers_0.keys id)
|
|
(select transfers_0 id).pending_0 = true
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_0 t.id))
|
|
(select accounts_0.keys t.from)
|
|
(select accounts_0.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_0 t.from).balance >= t.amount || (select accounts_0 t.from).flags.allows_overdraft
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_0.keys replica)
|
|
(select replicaState_0 replica).role = "candidate"
|
|
(< (select replicaState_0 replica).currentTerm term)
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_0) 1)
|
|
term >= commitIndex_0
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_1 accounts_0)
|
|
(= transfers_1 transfers_0)
|
|
(= pending_1 pending_0)
|
|
(= replicaState_1 replicaState_0)
|
|
(= log_1 log_0)
|
|
(= commitIndex_1 commitIndex_0)
|
|
(= leader_1 leader_0)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 1 → 2
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_1 t.id))
|
|
(select accounts_1.keys t.from)
|
|
(select accounts_1.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_1 id)
|
|
(select transfers_1.keys id)
|
|
(select transfers_1 id).pending_1 = true
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_1 id)
|
|
(select transfers_1.keys id)
|
|
(select transfers_1 id).pending_1 = true
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_1 t.id))
|
|
(select accounts_1.keys t.from)
|
|
(select accounts_1.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_1 t.from).balance >= t.amount || (select accounts_1 t.from).flags.allows_overdraft
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_1.keys replica)
|
|
(select replicaState_1 replica).role = "candidate"
|
|
(< (select replicaState_1 replica).currentTerm term)
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_1) 1)
|
|
term >= commitIndex_1
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_2 accounts_1)
|
|
(= transfers_2 transfers_1)
|
|
(= pending_2 pending_1)
|
|
(= replicaState_2 replicaState_1)
|
|
(= log_2 log_1)
|
|
(= commitIndex_2 commitIndex_1)
|
|
(= leader_2 leader_1)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 2 → 3
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_2 t.id))
|
|
(select accounts_2.keys t.from)
|
|
(select accounts_2.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_2 id)
|
|
(select transfers_2.keys id)
|
|
(select transfers_2 id).pending_2 = true
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_2 id)
|
|
(select transfers_2.keys id)
|
|
(select transfers_2 id).pending_2 = true
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_2 t.id))
|
|
(select accounts_2.keys t.from)
|
|
(select accounts_2.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_2 t.from).balance >= t.amount || (select accounts_2 t.from).flags.allows_overdraft
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_2.keys replica)
|
|
(select replicaState_2 replica).role = "candidate"
|
|
(< (select replicaState_2 replica).currentTerm term)
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_2) 1)
|
|
term >= commitIndex_2
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_3 accounts_2)
|
|
(= transfers_3 transfers_2)
|
|
(= pending_3 pending_2)
|
|
(= replicaState_3 replicaState_2)
|
|
(= log_3 log_2)
|
|
(= commitIndex_3 commitIndex_2)
|
|
(= leader_3 leader_2)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 3 → 4
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_3 id)
|
|
(select transfers_3.keys id)
|
|
(select transfers_3 id).pending_3 = true
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_3 t.id))
|
|
(select accounts_3.keys t.from)
|
|
(select accounts_3.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_3 t.from).balance >= t.amount || (select accounts_3 t.from).flags.allows_overdraft
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_3.keys replica)
|
|
(select replicaState_3 replica).role = "candidate"
|
|
(< (select replicaState_3 replica).currentTerm term)
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_3) 1)
|
|
term >= commitIndex_3
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_4 accounts_3)
|
|
(= transfers_4 transfers_3)
|
|
(= pending_4 pending_3)
|
|
(= replicaState_4 replicaState_3)
|
|
(= log_4 log_3)
|
|
(= commitIndex_4 commitIndex_3)
|
|
(= leader_4 leader_3)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 4 → 5
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_4 id)
|
|
(select transfers_4.keys id)
|
|
(select transfers_4 id).pending_4 = true
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_4 t.id))
|
|
(select accounts_4.keys t.from)
|
|
(select accounts_4.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_4 t.from).balance >= t.amount || (select accounts_4 t.from).flags.allows_overdraft
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_4.keys replica)
|
|
(select replicaState_4 replica).role = "candidate"
|
|
(< (select replicaState_4 replica).currentTerm term)
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_4) 1)
|
|
term >= commitIndex_4
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_5 accounts_4)
|
|
(= transfers_5 transfers_4)
|
|
(= pending_5 pending_4)
|
|
(= replicaState_5 replicaState_4)
|
|
(= log_5 log_4)
|
|
(= commitIndex_5 commitIndex_4)
|
|
(= leader_5 leader_4)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 5 → 6
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_5 id)
|
|
(select transfers_5.keys id)
|
|
(select transfers_5 id).pending_5 = true
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_5 t.id))
|
|
(select accounts_5.keys t.from)
|
|
(select accounts_5.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_5 t.from).balance >= t.amount || (select accounts_5 t.from).flags.allows_overdraft
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_5.keys replica)
|
|
(select replicaState_5 replica).role = "candidate"
|
|
(< (select replicaState_5 replica).currentTerm term)
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_5) 1)
|
|
term >= commitIndex_5
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_6 accounts_5)
|
|
(= transfers_6 transfers_5)
|
|
(= pending_6 pending_5)
|
|
(= replicaState_6 replicaState_5)
|
|
(= log_6 log_5)
|
|
(= commitIndex_6 commitIndex_5)
|
|
(= leader_6 leader_5)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 6 → 7
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_6 id)
|
|
(select transfers_6.keys id)
|
|
(select transfers_6 id).pending_6 = true
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_6 t.id))
|
|
(select accounts_6.keys t.from)
|
|
(select accounts_6.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_6 t.from).balance >= t.amount || (select accounts_6 t.from).flags.allows_overdraft
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_6.keys replica)
|
|
(select replicaState_6 replica).role = "candidate"
|
|
(< (select replicaState_6 replica).currentTerm term)
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_6) 1)
|
|
term >= commitIndex_6
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_7 accounts_6)
|
|
(= transfers_7 transfers_6)
|
|
(= pending_7 pending_6)
|
|
(= replicaState_7 replicaState_6)
|
|
(= log_7 log_6)
|
|
(= commitIndex_7 commitIndex_6)
|
|
(= leader_7 leader_6)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 7 → 8
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_7 id)
|
|
(select transfers_7.keys id)
|
|
(select transfers_7 id).pending_7 = true
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_7 t.id))
|
|
(select accounts_7.keys t.from)
|
|
(select accounts_7.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_7 t.from).balance >= t.amount || (select accounts_7 t.from).flags.allows_overdraft
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_7.keys replica)
|
|
(select replicaState_7 replica).role = "candidate"
|
|
(< (select replicaState_7 replica).currentTerm term)
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_7) 1)
|
|
term >= commitIndex_7
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_8 accounts_7)
|
|
(= transfers_8 transfers_7)
|
|
(= pending_8 pending_7)
|
|
(= replicaState_8 replicaState_7)
|
|
(= log_8 log_7)
|
|
(= commitIndex_8 commitIndex_7)
|
|
(= leader_8 leader_7)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 8 → 9
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_8 id)
|
|
(select transfers_8.keys id)
|
|
(select transfers_8 id).pending_8 = true
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_8 t.id))
|
|
(select accounts_8.keys t.from)
|
|
(select accounts_8.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_8 t.from).balance >= t.amount || (select accounts_8 t.from).flags.allows_overdraft
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_8.keys replica)
|
|
(select replicaState_8 replica).role = "candidate"
|
|
(< (select replicaState_8 replica).currentTerm term)
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_8) 1)
|
|
term >= commitIndex_8
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_9 accounts_8)
|
|
(= transfers_9 transfers_8)
|
|
(= pending_9 pending_8)
|
|
(= replicaState_9 replicaState_8)
|
|
(= log_9 log_8)
|
|
(= commitIndex_9 commitIndex_8)
|
|
(= leader_9 leader_8)
|
|
)
|
|
)
|
|
)
|
|
(assert ; Step 9 → 10
|
|
(or
|
|
(and ; Action: CreateTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: CommitTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: VoidTransfer
|
|
(select pending_9 id)
|
|
(select transfers_9.keys id)
|
|
(select transfers_9 id).pending_9 = true
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: PostTransfer
|
|
(not (select transfers_9 t.id))
|
|
(select accounts_9.keys t.from)
|
|
(select accounts_9.keys t.to)
|
|
t.from distinct t.to
|
|
(select accounts_9 t.from).balance >= t.amount || (select accounts_9 t.from).flags.allows_overdraft
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: BecomeLeader
|
|
(select replicaState_9.keys replica)
|
|
(select replicaState_9 replica).role = "candidate"
|
|
(< (select replicaState_9 replica).currentTerm term)
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
(and ; Action: AppendEntry
|
|
(+ entry.index = length(log_9) 1)
|
|
term >= commitIndex_9
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
; Stuttering
|
|
(and
|
|
(= accounts_10 accounts_9)
|
|
(= transfers_10 transfers_9)
|
|
(= pending_10 pending_9)
|
|
(= replicaState_10 replicaState_9)
|
|
(= log_10 log_9)
|
|
(= commitIndex_10 commitIndex_9)
|
|
(= leader_10 leader_9)
|
|
)
|
|
)
|
|
)
|
|
|
|
; Property assertion: not(invariant at some step)
|
|
(assert
|
|
(and
|
|
(not (TransferStateConsistency_0))
|
|
(not (TransferStateConsistency_1))
|
|
(not (TransferStateConsistency_2))
|
|
(not (TransferStateConsistency_3))
|
|
(not (TransferStateConsistency_4))
|
|
(not (TransferStateConsistency_5))
|
|
(not (TransferStateConsistency_6))
|
|
(not (TransferStateConsistency_7))
|
|
(not (TransferStateConsistency_8))
|
|
(not (TransferStateConsistency_9))
|
|
(not (TransferStateConsistency_10))
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_0 () Bool
|
|
(and
|
|
forall (select transfers_0.values: t)
|
|
t.pending_0 implies t.posted = false && t.voided = false
|
|
forall (select transfers_0.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_0.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_1 () Bool
|
|
(and
|
|
forall (select transfers_1.values: t)
|
|
t.pending_1 implies t.posted = false && t.voided = false
|
|
forall (select transfers_1.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_1.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_2 () Bool
|
|
(and
|
|
forall (select transfers_2.values: t)
|
|
t.pending_2 implies t.posted = false && t.voided = false
|
|
forall (select transfers_2.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_2.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_3 () Bool
|
|
(and
|
|
forall (select transfers_3.values: t)
|
|
t.pending_3 implies t.posted = false && t.voided = false
|
|
forall (select transfers_3.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_3.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_4 () Bool
|
|
(and
|
|
forall (select transfers_4.values: t)
|
|
t.pending_4 implies t.posted = false && t.voided = false
|
|
forall (select transfers_4.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_4.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_5 () Bool
|
|
(and
|
|
forall (select transfers_5.values: t)
|
|
t.pending_5 implies t.posted = false && t.voided = false
|
|
forall (select transfers_5.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_5.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_6 () Bool
|
|
(and
|
|
forall (select transfers_6.values: t)
|
|
t.pending_6 implies t.posted = false && t.voided = false
|
|
forall (select transfers_6.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_6.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_7 () Bool
|
|
(and
|
|
forall (select transfers_7.values: t)
|
|
t.pending_7 implies t.posted = false && t.voided = false
|
|
forall (select transfers_7.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_7.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_8 () Bool
|
|
(and
|
|
forall (select transfers_8.values: t)
|
|
t.pending_8 implies t.posted = false && t.voided = false
|
|
forall (select transfers_8.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_8.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_9 () Bool
|
|
(and
|
|
forall (select transfers_9.values: t)
|
|
t.pending_9 implies t.posted = false && t.voided = false
|
|
forall (select transfers_9.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_9.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(define-fun TransferStateConsistency_10 () Bool
|
|
(and
|
|
forall (select transfers_10.values: t)
|
|
t.pending_10 implies t.posted = false && t.voided = false
|
|
forall (select transfers_10.values: t)
|
|
t.posted implies t.voided = false
|
|
forall (select transfers_10.values: t)
|
|
t.voided implies t.posted = false
|
|
)
|
|
)
|
|
(echo "Checking: Eventually(TransferStateConsistency)")
|
|
(check-sat)
|
|
(get-model)
|