TSTP Solution File: SWV456+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV456+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:56:33 EDT 2023
% Result : Theorem 28.90s 4.63s
% Output : Proof 36.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV456+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 10:06:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.98/1.25 Prover 1: Preprocessing ...
% 3.98/1.26 Prover 4: Preprocessing ...
% 3.98/1.29 Prover 5: Preprocessing ...
% 3.98/1.29 Prover 3: Preprocessing ...
% 3.98/1.29 Prover 6: Preprocessing ...
% 3.98/1.29 Prover 2: Preprocessing ...
% 3.98/1.29 Prover 0: Preprocessing ...
% 10.92/2.24 Prover 6: Proving ...
% 10.92/2.25 Prover 3: Constructing countermodel ...
% 11.32/2.26 Prover 1: Constructing countermodel ...
% 11.32/2.32 Prover 5: Proving ...
% 11.32/2.35 Prover 2: Proving ...
% 12.27/2.44 Prover 0: Proving ...
% 12.62/2.46 Prover 4: Constructing countermodel ...
% 18.24/3.27 Prover 3: gave up
% 18.24/3.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.00/3.35 Prover 7: Preprocessing ...
% 22.08/3.71 Prover 7: Warning: ignoring some quantifiers
% 22.08/3.75 Prover 7: Constructing countermodel ...
% 28.90/4.63 Prover 2: proved (3996ms)
% 28.90/4.63
% 28.90/4.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.90/4.63
% 29.21/4.64 Prover 0: stopped
% 29.21/4.64 Prover 5: stopped
% 29.21/4.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 29.21/4.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 29.21/4.64 Prover 6: stopped
% 29.21/4.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.21/4.65 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 29.77/4.72 Prover 10: Preprocessing ...
% 29.77/4.75 Prover 13: Preprocessing ...
% 29.77/4.76 Prover 8: Preprocessing ...
% 30.28/4.79 Prover 11: Preprocessing ...
% 30.28/4.84 Prover 10: Warning: ignoring some quantifiers
% 30.28/4.85 Prover 10: Constructing countermodel ...
% 31.43/4.99 Prover 8: Warning: ignoring some quantifiers
% 31.43/5.00 Prover 8: Constructing countermodel ...
% 31.43/5.00 Prover 13: Warning: ignoring some quantifiers
% 31.99/5.02 Prover 13: Constructing countermodel ...
% 33.24/5.18 Prover 11: Constructing countermodel ...
% 35.61/5.55 Prover 10: Found proof (size 55)
% 35.61/5.55 Prover 10: proved (915ms)
% 35.61/5.55 Prover 11: stopped
% 35.61/5.55 Prover 13: stopped
% 35.61/5.55 Prover 8: stopped
% 35.61/5.55 Prover 1: stopped
% 35.61/5.55 Prover 4: stopped
% 36.28/5.57 Prover 7: stopped
% 36.28/5.57
% 36.28/5.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.28/5.57
% 36.28/5.58 % SZS output start Proof for theBenchmark
% 36.28/5.58 Assumptions after simplification:
% 36.28/5.58 ---------------------------------
% 36.28/5.58
% 36.28/5.58 (axiom_46)
% 36.37/5.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.37/5.61 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 36.37/5.61 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 36.37/5.61 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 36.37/5.61 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 36.37/5.61 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 36.37/5.61
% 36.37/5.61 (conj)
% 36.50/5.62 $i(elid) & $i(status) & $i(ldr) & $i(down) & $i(alive) & $i(norm) & $i(wait) &
% 36.50/5.62 $i(zero) & $i(pids) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 36.50/5.62 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 36.50/5.62 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 36.50/5.62 $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 36.50/5.62 $i] : ( ~ (v16 = v5) & ~ (v5 = v0) & index(status, v5) = v10 & index(down,
% 36.50/5.62 v16) = v17 & cons(v7, v1) = v6 & m_Down(v18) = v19 & m_Down(v4) = v7 &
% 36.50/5.62 s(zero) = v0 & host(v18) = v16 & host(v15) = v16 & host(v14) = v5 &
% 36.50/5.62 host(v13) = v5 & host(v4) = v8 & host(v3) = v5 & host(v2) = v5 & queue(v5) =
% 36.50/5.62 v6 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) &
% 36.50/5.62 $i(v10) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 36.50/5.62 $i(v1) & $i(v0) & setIn(v5, v17) & setIn(v3, alive) & elem(v19, v1) & ~
% 36.50/5.62 leq(v5, v8) & ~ setIn(v2, pids) & ! [v20: $i] : ! [v21: $i] : ! [v22:
% 36.50/5.62 $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27:
% 36.50/5.62 $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~ (m_Down(v21) = v27) | ~
% 36.50/5.62 (host(v22) = v24) | ~ (host(v20) = v25) | ~ $i(v23) | ~ $i(v22) | ~
% 36.50/5.62 $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20, alive) | ?
% 36.50/5.62 [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v29 = v24)
% 36.50/5.62 & host(v23) = v29 & $i(v29)) | ( ~ (v28 = v25) & host(v21) = v28 &
% 36.50/5.62 $i(v28)) | (queue(v25) = v30 & $i(v30) & ~ elem(v26, v30)) |
% 36.50/5.62 (queue(v24) = v31 & $i(v31) & ~ elem(v27, v31)))) & ! [v20: $i] : !
% 36.50/5.62 [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : !
% 36.50/5.62 [v26: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~ (host(v22) = v24) | ~
% 36.50/5.62 (host(v21) = v25) | ~ (host(v20) = v25) | ~ $i(v23) | ~ $i(v22) | ~
% 36.50/5.62 $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20, alive) | ?
% 36.50/5.62 [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v27 = v24) & host(v23) =
% 36.50/5.62 v27 & $i(v27)) | (index(down, v24) = v29 & $i(v29) & ~ setIn(v25,
% 36.54/5.62 v29)) | (queue(v25) = v28 & $i(v28) & ~ elem(v26, v28)))) & !
% 36.54/5.62 [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~
% 36.54/5.62 (m_Ack(v22, v20) = v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) |
% 36.54/5.62 ~ $i(v20) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ((host(v22) =
% 36.54/5.62 v27 & host(v20) = v26 & $i(v27) & $i(v26) & ~ leq(v26, v27)) |
% 36.54/5.62 (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v20: $i] : !
% 36.54/5.62 [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~
% 36.54/5.62 (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ?
% 36.54/5.62 [v24: $i] : (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24))) & ! [v20:
% 36.54/5.62 $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22)
% 36.54/5.62 | ~ (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25:
% 36.54/5.62 $i] : (( ~ (v25 = v23) & host(v21) = v25 & $i(v25)) | (queue(v23) = v24
% 36.54/5.62 & $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : !
% 36.54/5.62 [v22: $i] : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23) |
% 36.54/5.62 ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 &
% 36.54/5.62 $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~
% 36.54/5.62 elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (v21
% 36.54/5.62 = v20 | ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~ $i(v21) | ~
% 36.54/5.62 $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive)) & ! [v20: $i] : !
% 36.54/5.62 [v21: $i] : ! [v22: $i] : ( ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~
% 36.54/5.62 $i(v21) | ~ $i(v20) | ~ leq(v21, v20) | ~ setIn(v21, alive) |
% 36.54/5.62 setIn(v20, alive)) & ! [v20: $i] : ( ~ (host(v20) = v5) | ~ $i(v20) |
% 36.54/5.62 leq(v20, v2)) & (v15 = v2 | ( ~ (v15 = v3) & setIn(v15, alive))) & (v13 =
% 36.54/5.62 v2 | ( ~ (v13 = v3) & setIn(v13, alive))) & ((v12 = v8 & v10 = wait &
% 36.54/5.62 index(elid, v5) = v11 & host(v11) = v8 & $i(v11)) | (v10 = norm & v9 =
% 36.54/5.62 v8 & index(ldr, v5) = v8)))
% 36.54/5.62
% 36.54/5.62 (function-axioms)
% 36.54/5.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.54/5.63 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 36.54/5.63 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 36.54/5.63 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 36.54/5.63 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 36.54/5.63 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 36.54/5.63 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 36.54/5.63 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 36.54/5.63 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 36.54/5.63 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 36.54/5.63 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 36.54/5.63 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 36.54/5.63 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 36.54/5.63 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 36.54/5.63 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 36.54/5.63 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.54/5.63 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 36.54/5.63 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 36.54/5.63 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 36.54/5.63 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 36.54/5.63 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 36.54/5.63 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 36.54/5.63 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 36.54/5.63
% 36.54/5.63 Further assumptions not needed in the proof:
% 36.54/5.63 --------------------------------------------
% 36.54/5.63 axiom, axiom_01, axiom_02, axiom_03, axiom_04, axiom_05, axiom_06, axiom_07,
% 36.54/5.63 axiom_08, axiom_09, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15,
% 36.54/5.63 axiom_16, axiom_17, axiom_18, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23,
% 36.54/5.63 axiom_24, axiom_25, axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31,
% 36.54/5.63 axiom_32, axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39,
% 36.54/5.63 axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_47, axiom_48,
% 36.54/5.63 axiom_49, axiom_50, axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56,
% 36.54/5.63 axiom_57, axiom_58, axiom_59, axiom_60, axiom_61, axiom_62, axiom_63, axiom_64,
% 36.54/5.63 axiom_65
% 36.54/5.63
% 36.54/5.63 Those formulas are unsatisfiable:
% 36.54/5.63 ---------------------------------
% 36.54/5.63
% 36.54/5.63 Begin of proof
% 36.54/5.63 |
% 36.54/5.63 | ALPHA: (axiom_46) implies:
% 36.54/5.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 36.54/5.63 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 36.54/5.63 | elem(v0, v3))
% 36.54/5.63 |
% 36.54/5.63 | ALPHA: (conj) implies:
% 36.54/5.64 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 36.54/5.64 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 36.54/5.64 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 36.54/5.64 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 36.54/5.64 | $i] : ( ~ (v16 = v5) & ~ (v5 = v0) & index(status, v5) = v10 &
% 36.54/5.64 | index(down, v16) = v17 & cons(v7, v1) = v6 & m_Down(v18) = v19 &
% 36.54/5.64 | m_Down(v4) = v7 & s(zero) = v0 & host(v18) = v16 & host(v15) = v16 &
% 36.54/5.64 | host(v14) = v5 & host(v13) = v5 & host(v4) = v8 & host(v3) = v5 &
% 36.54/5.64 | host(v2) = v5 & queue(v5) = v6 & $i(v19) & $i(v18) & $i(v17) &
% 36.54/5.64 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v10) & $i(v8) & $i(v7) &
% 36.54/5.64 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 36.54/5.64 | setIn(v5, v17) & setIn(v3, alive) & elem(v19, v1) & ~ leq(v5, v8) &
% 36.54/5.64 | ~ setIn(v2, pids) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 36.54/5.64 | [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ! [v27: $i]
% 36.54/5.64 | : (v25 = v24 | ~ (m_Down(v23) = v26) | ~ (m_Down(v21) = v27) | ~
% 36.54/5.64 | (host(v22) = v24) | ~ (host(v20) = v25) | ~ $i(v23) | ~ $i(v22)
% 36.54/5.64 | | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20,
% 36.54/5.64 | alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31:
% 36.54/5.64 | $i] : (( ~ (v29 = v24) & host(v23) = v29 & $i(v29)) | ( ~ (v28 =
% 36.54/5.64 | v25) & host(v21) = v28 & $i(v28)) | (queue(v25) = v30 &
% 36.54/5.64 | $i(v30) & ~ elem(v26, v30)) | (queue(v24) = v31 & $i(v31) & ~
% 36.54/5.64 | elem(v27, v31)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 36.54/5.64 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : (v25 =
% 36.54/5.64 | v24 | ~ (m_Down(v23) = v26) | ~ (host(v22) = v24) | ~ (host(v21)
% 36.54/5.64 | = v25) | ~ (host(v20) = v25) | ~ $i(v23) | ~ $i(v22) | ~
% 36.54/5.64 | $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20, alive)
% 36.54/5.64 | | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v27 = v24) &
% 36.54/5.64 | host(v23) = v27 & $i(v27)) | (index(down, v24) = v29 & $i(v29)
% 36.54/5.64 | & ~ setIn(v25, v29)) | (queue(v25) = v28 & $i(v28) & ~
% 36.54/5.64 | elem(v26, v28)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 36.54/5.64 | : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = v23) | ~
% 36.54/5.64 | (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ? [v25:
% 36.54/5.64 | $i] : ? [v26: $i] : ? [v27: $i] : ((host(v22) = v27 & host(v20)
% 36.54/5.64 | = v26 & $i(v27) & $i(v26) & ~ leq(v26, v27)) | (queue(v24) =
% 36.54/5.64 | v25 & $i(v25) & ~ elem(v23, v25)))) & ! [v20: $i] : ! [v21:
% 36.54/5.64 | $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~
% 36.54/5.64 | (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive)
% 36.54/5.64 | | ? [v24: $i] : (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))
% 36.54/5.64 | & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 36.54/5.64 | (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~
% 36.54/5.64 | $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = v23) &
% 36.54/5.64 | host(v21) = v25 & $i(v25)) | (queue(v23) = v24 & $i(v24) & ~
% 36.54/5.64 | elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 36.54/5.64 | : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23) | ~
% 36.54/5.64 | $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) =
% 36.54/5.64 | v25 & $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24)
% 36.54/5.64 | & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22:
% 36.54/5.64 | $i] : (v21 = v20 | ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~
% 36.54/5.64 | $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive))
% 36.54/5.64 | & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (host(v21) = v22)
% 36.54/5.64 | | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ leq(v21, v20)
% 36.54/5.64 | | ~ setIn(v21, alive) | setIn(v20, alive)) & ! [v20: $i] : ( ~
% 36.54/5.64 | (host(v20) = v5) | ~ $i(v20) | leq(v20, v2)) & (v15 = v2 | ( ~
% 36.54/5.64 | (v15 = v3) & setIn(v15, alive))) & (v13 = v2 | ( ~ (v13 = v3) &
% 36.54/5.64 | setIn(v13, alive))) & ((v12 = v8 & v10 = wait & index(elid, v5) =
% 36.54/5.64 | v11 & host(v11) = v8 & $i(v11)) | (v10 = norm & v9 = v8 &
% 36.54/5.64 | index(ldr, v5) = v8)))
% 36.54/5.64 |
% 36.54/5.64 | ALPHA: (function-axioms) implies:
% 36.54/5.64 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 36.54/5.64 | v1) | ~ (queue(v2) = v0))
% 36.54/5.64 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 36.54/5.64 | | ~ (host(v2) = v0))
% 36.54/5.64 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 36.54/5.64 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 36.54/5.64 |
% 36.54/5.64 | DELTA: instantiating (2) with fresh symbols all_65_0, all_65_1, all_65_2,
% 36.54/5.64 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 36.54/5.64 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 36.54/5.64 | all_65_16, all_65_17, all_65_18, all_65_19 gives:
% 36.54/5.65 | (6) ~ (all_65_3 = all_65_14) & ~ (all_65_14 = all_65_19) & index(status,
% 36.54/5.65 | all_65_14) = all_65_9 & index(down, all_65_3) = all_65_2 &
% 36.54/5.65 | cons(all_65_12, all_65_18) = all_65_13 & m_Down(all_65_1) = all_65_0 &
% 36.54/5.65 | m_Down(all_65_15) = all_65_12 & s(zero) = all_65_19 & host(all_65_1) =
% 36.54/5.65 | all_65_3 & host(all_65_4) = all_65_3 & host(all_65_5) = all_65_14 &
% 36.54/5.65 | host(all_65_6) = all_65_14 & host(all_65_15) = all_65_11 &
% 36.54/5.65 | host(all_65_16) = all_65_14 & host(all_65_17) = all_65_14 &
% 36.54/5.65 | queue(all_65_14) = all_65_13 & $i(all_65_0) & $i(all_65_1) &
% 36.54/5.65 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) &
% 36.54/5.65 | $i(all_65_6) & $i(all_65_9) & $i(all_65_11) & $i(all_65_12) &
% 36.54/5.65 | $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & $i(all_65_16) &
% 36.54/5.65 | $i(all_65_17) & $i(all_65_18) & $i(all_65_19) & setIn(all_65_14,
% 36.54/5.65 | all_65_2) & setIn(all_65_16, alive) & elem(all_65_0, all_65_18) & ~
% 36.54/5.65 | leq(all_65_14, all_65_11) & ~ setIn(all_65_17, pids) & ! [v0: $i] :
% 36.54/5.65 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 36.54/5.65 | [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~
% 36.54/5.65 | (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~
% 36.54/5.65 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~
% 36.54/5.65 | setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 36.54/5.65 | [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9)) | ( ~ (v8 = v5)
% 36.54/5.65 | & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 & $i(v10) & ~
% 36.54/5.65 | elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~ elem(v7, v11))))
% 36.54/5.65 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 36.54/5.65 | ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~
% 36.54/5.65 | (host(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = v5) | ~ $i(v3)
% 36.54/5.65 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~
% 36.54/5.65 | setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v7
% 36.54/5.65 | = v4) & host(v3) = v7 & $i(v7)) | (index(down, v4) = v9 &
% 36.54/5.65 | $i(v9) & ~ setIn(v5, v9)) | (queue(v5) = v8 & $i(v8) & ~
% 36.54/5.65 | elem(v6, v8)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 36.54/5.65 | [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4)
% 36.54/5.65 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ?
% 36.54/5.65 | [v7: $i] : ((host(v2) = v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~
% 36.54/5.65 | leq(v6, v7)) | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) & !
% 36.54/5.65 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) =
% 36.54/5.65 | v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 36.54/5.65 | alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))
% 36.54/5.65 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 36.54/5.65 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 36.54/5.65 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) |
% 36.54/5.65 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : !
% 36.54/5.65 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) = v2) | ~
% 36.54/5.65 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] :
% 36.54/5.65 | ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 & $i(v4)
% 36.54/5.65 | & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 36.54/5.65 | (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~
% 36.54/5.65 | $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: $i] :
% 36.54/5.65 | ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) = v2) |
% 36.54/5.65 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~ setIn(v1, alive) |
% 36.54/5.65 | setIn(v0, alive)) & ! [v0: $i] : ( ~ (host(v0) = all_65_14) | ~
% 36.54/5.65 | $i(v0) | leq(v0, all_65_17)) & (all_65_4 = all_65_17 | ( ~ (all_65_4
% 36.54/5.65 | = all_65_16) & setIn(all_65_4, alive))) & (all_65_6 = all_65_17 |
% 36.54/5.65 | ( ~ (all_65_6 = all_65_16) & setIn(all_65_6, alive))) & ((all_65_7 =
% 36.54/5.65 | all_65_11 & all_65_9 = wait & index(elid, all_65_14) = all_65_8 &
% 36.54/5.65 | host(all_65_8) = all_65_11 & $i(all_65_8)) | (all_65_9 = norm &
% 36.54/5.65 | all_65_10 = all_65_11 & index(ldr, all_65_14) = all_65_11))
% 36.54/5.65 |
% 36.54/5.65 | ALPHA: (6) implies:
% 36.54/5.65 | (7) elem(all_65_0, all_65_18)
% 36.54/5.65 | (8) setIn(all_65_16, alive)
% 36.54/5.65 | (9) setIn(all_65_14, all_65_2)
% 36.54/5.65 | (10) $i(all_65_18)
% 36.54/5.65 | (11) $i(all_65_17)
% 36.54/5.65 | (12) $i(all_65_16)
% 36.54/5.65 | (13) $i(all_65_12)
% 36.54/5.65 | (14) $i(all_65_4)
% 36.54/5.65 | (15) $i(all_65_1)
% 36.54/5.65 | (16) $i(all_65_0)
% 36.54/5.65 | (17) queue(all_65_14) = all_65_13
% 36.54/5.65 | (18) host(all_65_17) = all_65_14
% 36.54/5.65 | (19) host(all_65_16) = all_65_14
% 36.54/5.65 | (20) host(all_65_4) = all_65_3
% 36.54/5.65 | (21) host(all_65_1) = all_65_3
% 36.54/5.65 | (22) m_Down(all_65_1) = all_65_0
% 36.54/5.65 | (23) cons(all_65_12, all_65_18) = all_65_13
% 36.54/5.65 | (24) index(down, all_65_3) = all_65_2
% 36.54/5.65 | (25) all_65_4 = all_65_17 | ( ~ (all_65_4 = all_65_16) & setIn(all_65_4,
% 36.54/5.65 | alive))
% 36.54/5.65 | (26) ! [v0: $i] : ( ~ (host(v0) = all_65_14) | ~ $i(v0) | leq(v0,
% 36.54/5.65 | all_65_17))
% 36.54/5.65 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~
% 36.54/5.65 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~
% 36.54/5.65 | setIn(v1, alive) | setIn(v0, alive))
% 36.54/5.66 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v1) =
% 36.54/5.66 | v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 36.54/5.66 | alive) | ~ setIn(v0, alive))
% 36.54/5.66 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 36.54/5.66 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 36.54/5.66 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) |
% 36.54/5.66 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))
% 36.54/5.66 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 36.54/5.66 | ! [v5: $i] : ! [v6: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~
% 36.54/5.66 | (host(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) = v5) | ~
% 36.54/5.66 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) |
% 36.54/5.66 | ~ setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~
% 36.54/5.66 | (v7 = v4) & host(v3) = v7 & $i(v7)) | (index(down, v4) = v9 &
% 36.54/5.66 | $i(v9) & ~ setIn(v5, v9)) | (queue(v5) = v8 & $i(v8) & ~
% 36.54/5.66 | elem(v6, v8))))
% 36.54/5.66 |
% 36.54/5.66 | GROUND_INST: instantiating (26) with all_65_16, simplifying with (12), (19)
% 36.54/5.66 | gives:
% 36.54/5.66 | (31) leq(all_65_16, all_65_17)
% 36.54/5.66 |
% 36.54/5.66 | GROUND_INST: instantiating (29) with all_65_17, all_65_1, all_65_0, all_65_14,
% 36.54/5.66 | simplifying with (11), (15), (18), (22) gives:
% 36.54/5.66 | (32) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_14) & host(all_65_1) =
% 36.54/5.66 | v1 & $i(v1)) | (queue(all_65_14) = v0 & $i(v0) & ~ elem(all_65_0,
% 36.54/5.66 | v0)))
% 36.54/5.66 |
% 36.54/5.66 | GROUND_INST: instantiating (1) with all_65_0, all_65_12, all_65_18, all_65_13,
% 36.54/5.66 | simplifying with (7), (10), (13), (16), (23) gives:
% 36.54/5.66 | (33) elem(all_65_0, all_65_13)
% 36.54/5.66 |
% 36.54/5.66 | DELTA: instantiating (32) with fresh symbols all_85_0, all_85_1 gives:
% 36.54/5.66 | (34) ( ~ (all_85_0 = all_65_14) & host(all_65_1) = all_85_0 & $i(all_85_0))
% 36.54/5.66 | | (queue(all_65_14) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0,
% 36.54/5.66 | all_85_1))
% 36.54/5.66 |
% 36.54/5.66 | BETA: splitting (34) gives:
% 36.54/5.66 |
% 36.54/5.66 | Case 1:
% 36.54/5.66 | |
% 36.54/5.66 | | (35) ~ (all_85_0 = all_65_14) & host(all_65_1) = all_85_0 & $i(all_85_0)
% 36.54/5.66 | |
% 36.54/5.66 | | ALPHA: (35) implies:
% 36.54/5.66 | | (36) ~ (all_85_0 = all_65_14)
% 36.54/5.66 | | (37) host(all_65_1) = all_85_0
% 36.54/5.66 | |
% 36.54/5.66 | | GROUND_INST: instantiating (4) with all_65_3, all_85_0, all_65_1,
% 36.54/5.66 | | simplifying with (21), (37) gives:
% 36.54/5.66 | | (38) all_85_0 = all_65_3
% 36.54/5.66 | |
% 36.54/5.66 | | REDUCE: (36), (38) imply:
% 36.54/5.66 | | (39) ~ (all_65_3 = all_65_14)
% 36.54/5.66 | |
% 36.54/5.66 | | GROUND_INST: instantiating (27) with all_65_17, all_65_16, all_65_14,
% 36.54/5.66 | | simplifying with (8), (11), (12), (18), (19), (31) gives:
% 36.54/5.66 | | (40) setIn(all_65_17, alive)
% 36.54/5.66 | |
% 36.54/5.66 | | GROUND_INST: instantiating (28) with all_65_17, all_65_16, all_65_14,
% 36.54/5.66 | | simplifying with (8), (11), (12), (18), (19), (40) gives:
% 36.54/5.66 | | (41) all_65_16 = all_65_17
% 36.54/5.66 | |
% 36.54/5.66 | | BETA: splitting (25) gives:
% 36.54/5.66 | |
% 36.54/5.66 | | Case 1:
% 36.54/5.66 | | |
% 36.54/5.66 | | | (42) all_65_4 = all_65_17
% 36.54/5.66 | | |
% 36.54/5.66 | | | REDUCE: (20), (42) imply:
% 36.54/5.66 | | | (43) host(all_65_17) = all_65_3
% 36.54/5.66 | | |
% 36.54/5.66 | | | GROUND_INST: instantiating (4) with all_65_14, all_65_3, all_65_17,
% 36.54/5.66 | | | simplifying with (18), (43) gives:
% 36.54/5.66 | | | (44) all_65_3 = all_65_14
% 36.54/5.66 | | |
% 36.54/5.67 | | | REDUCE: (39), (44) imply:
% 36.54/5.67 | | | (45) $false
% 36.54/5.67 | | |
% 36.54/5.67 | | | CLOSE: (45) is inconsistent.
% 36.54/5.67 | | |
% 36.54/5.67 | | Case 2:
% 36.54/5.67 | | |
% 36.54/5.67 | | | (46) ~ (all_65_4 = all_65_16) & setIn(all_65_4, alive)
% 36.54/5.67 | | |
% 36.54/5.67 | | | ALPHA: (46) implies:
% 36.54/5.67 | | | (47) setIn(all_65_4, alive)
% 36.54/5.67 | | |
% 36.54/5.67 | | | GROUND_INST: instantiating (30) with all_65_17, all_65_17, all_65_4,
% 36.54/5.67 | | | all_65_1, all_65_3, all_65_14, all_65_0, simplifying with
% 36.54/5.67 | | | (11), (14), (15), (18), (20), (22), (40), (47) gives:
% 36.54/5.67 | | | (48) all_65_3 = all_65_14 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] :
% 36.54/5.67 | | | (( ~ (v0 = all_65_3) & host(all_65_1) = v0 & $i(v0)) |
% 36.54/5.67 | | | (index(down, all_65_3) = v2 & $i(v2) & ~ setIn(all_65_14, v2))
% 36.54/5.67 | | | | (queue(all_65_14) = v1 & $i(v1) & ~ elem(all_65_0, v1)))
% 36.54/5.67 | | |
% 36.54/5.67 | | | BETA: splitting (48) gives:
% 36.54/5.67 | | |
% 36.54/5.67 | | | Case 1:
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | (49) all_65_3 = all_65_14
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | REDUCE: (39), (49) imply:
% 36.54/5.67 | | | | (50) $false
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | CLOSE: (50) is inconsistent.
% 36.54/5.67 | | | |
% 36.54/5.67 | | | Case 2:
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | (51) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (( ~ (v0 = all_65_3)
% 36.54/5.67 | | | | & host(all_65_1) = v0 & $i(v0)) | (index(down, all_65_3) =
% 36.54/5.67 | | | | v2 & $i(v2) & ~ setIn(all_65_14, v2)) | (queue(all_65_14) =
% 36.54/5.67 | | | | v1 & $i(v1) & ~ elem(all_65_0, v1)))
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | DELTA: instantiating (51) with fresh symbols all_234_0, all_234_1,
% 36.54/5.67 | | | | all_234_2 gives:
% 36.54/5.67 | | | | (52) ( ~ (all_234_2 = all_65_3) & host(all_65_1) = all_234_2 &
% 36.54/5.67 | | | | $i(all_234_2)) | (index(down, all_65_3) = all_234_0 &
% 36.54/5.67 | | | | $i(all_234_0) & ~ setIn(all_65_14, all_234_0)) |
% 36.54/5.67 | | | | (queue(all_65_14) = all_234_1 & $i(all_234_1) & ~
% 36.54/5.67 | | | | elem(all_65_0, all_234_1))
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | BETA: splitting (52) gives:
% 36.54/5.67 | | | |
% 36.54/5.67 | | | | Case 1:
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | (53) ~ (all_234_2 = all_65_3) & host(all_65_1) = all_234_2 &
% 36.54/5.67 | | | | | $i(all_234_2)
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | ALPHA: (53) implies:
% 36.54/5.67 | | | | | (54) ~ (all_234_2 = all_65_3)
% 36.54/5.67 | | | | | (55) host(all_65_1) = all_234_2
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | GROUND_INST: instantiating (4) with all_65_3, all_234_2, all_65_1,
% 36.54/5.67 | | | | | simplifying with (21), (55) gives:
% 36.54/5.67 | | | | | (56) all_234_2 = all_65_3
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | REDUCE: (54), (56) imply:
% 36.54/5.67 | | | | | (57) $false
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | CLOSE: (57) is inconsistent.
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | Case 2:
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | (58) (index(down, all_65_3) = all_234_0 & $i(all_234_0) & ~
% 36.54/5.67 | | | | | setIn(all_65_14, all_234_0)) | (queue(all_65_14) = all_234_1
% 36.54/5.67 | | | | | & $i(all_234_1) & ~ elem(all_65_0, all_234_1))
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | BETA: splitting (58) gives:
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | | Case 1:
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | (59) index(down, all_65_3) = all_234_0 & $i(all_234_0) & ~
% 36.54/5.67 | | | | | | setIn(all_65_14, all_234_0)
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | ALPHA: (59) implies:
% 36.54/5.67 | | | | | | (60) ~ setIn(all_65_14, all_234_0)
% 36.54/5.67 | | | | | | (61) index(down, all_65_3) = all_234_0
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | GROUND_INST: instantiating (5) with all_65_2, all_234_0, all_65_3,
% 36.54/5.67 | | | | | | down, simplifying with (24), (61) gives:
% 36.54/5.67 | | | | | | (62) all_234_0 = all_65_2
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | REDUCE: (60), (62) imply:
% 36.54/5.67 | | | | | | (63) ~ setIn(all_65_14, all_65_2)
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | PRED_UNIFY: (9), (63) imply:
% 36.54/5.67 | | | | | | (64) $false
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | CLOSE: (64) is inconsistent.
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | Case 2:
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | (65) queue(all_65_14) = all_234_1 & $i(all_234_1) & ~
% 36.54/5.67 | | | | | | elem(all_65_0, all_234_1)
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | ALPHA: (65) implies:
% 36.54/5.67 | | | | | | (66) ~ elem(all_65_0, all_234_1)
% 36.54/5.67 | | | | | | (67) queue(all_65_14) = all_234_1
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | GROUND_INST: instantiating (3) with all_65_13, all_234_1, all_65_14,
% 36.54/5.67 | | | | | | simplifying with (17), (67) gives:
% 36.54/5.67 | | | | | | (68) all_234_1 = all_65_13
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | REDUCE: (66), (68) imply:
% 36.54/5.67 | | | | | | (69) ~ elem(all_65_0, all_65_13)
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | PRED_UNIFY: (33), (69) imply:
% 36.54/5.67 | | | | | | (70) $false
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | | CLOSE: (70) is inconsistent.
% 36.54/5.67 | | | | | |
% 36.54/5.67 | | | | | End of split
% 36.54/5.67 | | | | |
% 36.54/5.67 | | | | End of split
% 36.54/5.67 | | | |
% 36.54/5.67 | | | End of split
% 36.54/5.67 | | |
% 36.54/5.67 | | End of split
% 36.54/5.67 | |
% 36.54/5.67 | Case 2:
% 36.54/5.67 | |
% 36.54/5.67 | | (71) queue(all_65_14) = all_85_1 & $i(all_85_1) & ~ elem(all_65_0,
% 36.54/5.67 | | all_85_1)
% 36.54/5.67 | |
% 36.54/5.67 | | ALPHA: (71) implies:
% 36.54/5.67 | | (72) ~ elem(all_65_0, all_85_1)
% 36.54/5.68 | | (73) queue(all_65_14) = all_85_1
% 36.54/5.68 | |
% 36.54/5.68 | | GROUND_INST: instantiating (3) with all_65_13, all_85_1, all_65_14,
% 36.54/5.68 | | simplifying with (17), (73) gives:
% 36.54/5.68 | | (74) all_85_1 = all_65_13
% 36.54/5.68 | |
% 36.54/5.68 | | REDUCE: (72), (74) imply:
% 36.54/5.68 | | (75) ~ elem(all_65_0, all_65_13)
% 36.54/5.68 | |
% 36.54/5.68 | | PRED_UNIFY: (33), (75) imply:
% 36.54/5.68 | | (76) $false
% 36.54/5.68 | |
% 36.54/5.68 | | CLOSE: (76) is inconsistent.
% 36.54/5.68 | |
% 36.54/5.68 | End of split
% 36.54/5.68 |
% 36.54/5.68 End of proof
% 36.54/5.68 % SZS output end Proof for theBenchmark
% 36.54/5.68
% 36.54/5.68 5065ms
%------------------------------------------------------------------------------