TSTP Solution File: SWV451+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV451+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 : n009.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 22:56:32 EDT 2023
% Result : Theorem 20.66s 3.37s
% Output : Proof 27.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV451+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 08:18:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.62/0.61 ________ _____
% 0.62/0.61 ___ __ \_________(_)________________________________
% 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.61
% 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.61 (2023-06-19)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2023
% 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.61 Amanda Stjerna.
% 0.62/0.61 Free software under BSD-3-Clause.
% 0.62/0.61
% 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.61
% 0.62/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.63 Running up to 7 provers in parallel.
% 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.19/1.15 Prover 1: Preprocessing ...
% 3.19/1.15 Prover 4: Preprocessing ...
% 3.94/1.20 Prover 6: Preprocessing ...
% 3.94/1.20 Prover 2: Preprocessing ...
% 3.94/1.20 Prover 0: Preprocessing ...
% 3.94/1.20 Prover 5: Preprocessing ...
% 3.94/1.20 Prover 3: Preprocessing ...
% 10.71/2.06 Prover 6: Proving ...
% 10.86/2.08 Prover 3: Constructing countermodel ...
% 10.86/2.11 Prover 5: Proving ...
% 10.86/2.11 Prover 1: Constructing countermodel ...
% 11.39/2.14 Prover 4: Constructing countermodel ...
% 11.39/2.18 Prover 0: Proving ...
% 11.39/2.19 Prover 2: Proving ...
% 17.21/2.89 Prover 3: gave up
% 17.21/2.89 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.21/2.95 Prover 7: Preprocessing ...
% 19.58/3.26 Prover 7: Warning: ignoring some quantifiers
% 20.34/3.29 Prover 7: Constructing countermodel ...
% 20.66/3.37 Prover 2: proved (2739ms)
% 20.66/3.37
% 20.66/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.66/3.37
% 20.66/3.37 Prover 0: stopped
% 20.66/3.37 Prover 6: stopped
% 20.66/3.39 Prover 5: stopped
% 20.66/3.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.66/3.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.66/3.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.66/3.39 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.40/3.45 Prover 8: Preprocessing ...
% 21.40/3.46 Prover 10: Preprocessing ...
% 21.40/3.46 Prover 11: Preprocessing ...
% 21.40/3.47 Prover 13: Preprocessing ...
% 22.62/3.64 Prover 10: Warning: ignoring some quantifiers
% 22.62/3.66 Prover 10: Constructing countermodel ...
% 23.55/3.69 Prover 8: Warning: ignoring some quantifiers
% 23.55/3.71 Prover 13: Warning: ignoring some quantifiers
% 23.55/3.71 Prover 8: Constructing countermodel ...
% 23.77/3.73 Prover 13: Constructing countermodel ...
% 23.77/3.78 Prover 11: Constructing countermodel ...
% 27.26/4.19 Prover 10: Found proof (size 95)
% 27.26/4.19 Prover 10: proved (805ms)
% 27.26/4.19 Prover 7: stopped
% 27.26/4.19 Prover 13: stopped
% 27.26/4.19 Prover 4: stopped
% 27.26/4.19 Prover 11: stopped
% 27.26/4.19 Prover 8: stopped
% 27.26/4.19 Prover 1: stopped
% 27.26/4.19
% 27.26/4.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.26/4.19
% 27.26/4.20 % SZS output start Proof for theBenchmark
% 27.26/4.21 Assumptions after simplification:
% 27.26/4.21 ---------------------------------
% 27.26/4.21
% 27.26/4.21 (axiom_03)
% 27.26/4.23 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0,
% 27.26/4.23 nbr_proc))
% 27.26/4.23
% 27.26/4.23 (axiom_17)
% 27.26/4.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~
% 27.26/4.23 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 27.26/4.23
% 27.26/4.23 (axiom_46)
% 27.26/4.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.26/4.24 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 27.26/4.24 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 27.26/4.24 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 27.26/4.24 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 27.26/4.24 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 27.26/4.24
% 27.26/4.24 (axiom_47)
% 27.26/4.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.26/4.24 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 27.26/4.24 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 27.26/4.24 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 27.26/4.24 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0)
% 27.26/4.24 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 27.26/4.24
% 27.26/4.24 (axiom_49)
% 27.26/4.24 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v0) = v1) | ~ $i(v0) | pidMsg(v1) =
% 27.26/4.24 v0)
% 27.26/4.24
% 27.26/4.24 (axiom_50)
% 27.26/4.24 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v0) = v1) | ~ $i(v0) | pidMsg(v1) =
% 27.26/4.24 v0)
% 27.26/4.24
% 27.26/4.24 (conj)
% 27.26/4.25 $i(elid) & $i(status) & $i(ldr) & $i(alive) & $i(norm) & $i(nbr_proc) &
% 27.26/4.25 $i(zero) & $i(pids) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.26/4.25 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 27.26/4.25 $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 27.26/4.25 $i] : ? [v15: $i] : ? [v16: $i] : ( ~ (v7 = v0) & index(elid, v0) = v3 &
% 27.26/4.25 index(status, v0) = norm & index(ldr, v0) = v0 & snoc(v10, v8) = v11 &
% 27.26/4.25 cons(v6, v1) = v5 & m_NotNorm(v3) = v6 & m_Down(v15) = v16 & m_Down(v12) =
% 27.26/4.25 v14 & m_Halt(v2) = v8 & s(v0) = v7 & s(zero) = v0 & host(v15) = v0 &
% 27.26/4.25 host(v13) = v0 & host(v12) = v7 & host(v9) = v7 & host(v4) = v0 & host(v2) =
% 27.26/4.25 v0 & queue(v7) = v10 & queue(v0) = v5 & $i(v16) & $i(v15) & $i(v14) &
% 27.26/4.25 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 27.26/4.25 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v4, alive) &
% 27.26/4.25 elem(v16, v11) & elem(v14, v1) & ~ leq(nbr_proc, v0) & ~ setIn(v2, pids) &
% 27.26/4.25 ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] :
% 27.26/4.25 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : (v22 = v21 | ~ (m_Down(v20) =
% 27.26/4.25 v23) | ~ (m_Down(v18) = v24) | ~ (host(v19) = v21) | ~ (host(v17) =
% 27.26/4.25 v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ setIn(v19,
% 27.26/4.25 alive) | ~ setIn(v17, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27:
% 27.26/4.25 $i] : ? [v28: $i] : (( ~ (v26 = v21) & host(v20) = v26 & $i(v26)) | ( ~
% 27.26/4.25 (v25 = v22) & host(v18) = v25 & $i(v25)) | (queue(v22) = v27 & $i(v27)
% 27.26/4.25 & ~ elem(v23, v27)) | (queue(v21) = v28 & $i(v28) & ~ elem(v24,
% 27.26/4.25 v28)))) & ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i]
% 27.26/4.25 : ! [v21: $i] : ( ~ (m_Ack(v19, v17) = v20) | ~ (host(v18) = v21) | ~
% 27.26/4.25 $i(v19) | ~ $i(v18) | ~ $i(v17) | ? [v22: $i] : ? [v23: $i] : ? [v24:
% 27.26/4.25 $i] : ((host(v19) = v24 & host(v17) = v23 & $i(v24) & $i(v23) & ~
% 27.26/4.25 leq(v23, v24)) | (queue(v21) = v22 & $i(v22) & ~ elem(v20, v22)))) &
% 27.26/4.25 ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ (m_Down(v18)
% 27.26/4.25 = v19) | ~ (host(v17) = v20) | ~ $i(v18) | ~ $i(v17) | ~ setIn(v18,
% 27.26/4.25 alive) | ? [v21: $i] : (queue(v20) = v21 & $i(v21) & ~ elem(v19,
% 27.26/4.25 v21))) & ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : (
% 27.26/4.25 ~ (m_Down(v18) = v19) | ~ (host(v17) = v20) | ~ $i(v18) | ~ $i(v17) |
% 27.26/4.25 ? [v21: $i] : ? [v22: $i] : (( ~ (v22 = v20) & host(v18) = v22 & $i(v22))
% 27.26/4.25 | (queue(v20) = v21 & $i(v21) & ~ elem(v19, v21)))) & ! [v17: $i] : !
% 27.26/4.25 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ (m_Halt(v18) = v19) | ~
% 27.26/4.25 (host(v17) = v20) | ~ $i(v18) | ~ $i(v17) | ? [v21: $i] : ? [v22: $i]
% 27.26/4.25 : ((host(v18) = v22 & $i(v22) & ~ leq(v20, v22)) | (queue(v20) = v21 &
% 27.26/4.25 $i(v21) & ~ elem(v19, v21)))) & ! [v17: $i] : ! [v18: $i] : !
% 27.26/4.25 [v19: $i] : (v18 = v17 | ~ (host(v18) = v19) | ~ (host(v17) = v19) | ~
% 27.26/4.25 $i(v18) | ~ $i(v17) | ~ setIn(v18, alive) | ~ setIn(v17, alive)) & !
% 27.26/4.25 [v17: $i] : ! [v18: $i] : ! [v19: $i] : ( ~ (host(v18) = v19) | ~
% 27.26/4.25 (host(v17) = v19) | ~ $i(v18) | ~ $i(v17) | ~ leq(v18, v17) | ~
% 27.26/4.25 setIn(v18, alive) | setIn(v17, alive)) & ! [v17: $i] : ( ~ (host(v17) =
% 27.26/4.25 v0) | ~ $i(v17) | leq(v17, v2)) & (v13 = v2 | ( ~ (v13 = v4) &
% 27.26/4.25 setIn(v13, alive))) & (v9 = v2 | ( ~ (v9 = v4) & setIn(v9, alive))))
% 27.26/4.25
% 27.26/4.25 (function-axioms)
% 27.26/4.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.26/4.26 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 27.26/4.26 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 27.26/4.26 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 27.26/4.26 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 27.26/4.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 27.26/4.26 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 27.26/4.26 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 27.26/4.26 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 27.26/4.26 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 27.26/4.26 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 27.26/4.26 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 27.26/4.26 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 27.26/4.26 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 27.26/4.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 27.26/4.26 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.26/4.26 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 27.26/4.26 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 27.26/4.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 27.26/4.26 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.26/4.26 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 27.26/4.26 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 27.26/4.26 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 27.26/4.26
% 27.26/4.26 Further assumptions not needed in the proof:
% 27.26/4.26 --------------------------------------------
% 27.26/4.26 axiom, axiom_01, axiom_02, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08,
% 27.26/4.26 axiom_09, axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16,
% 27.26/4.26 axiom_18, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25,
% 27.26/4.26 axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, axiom_32, axiom_33,
% 27.26/4.26 axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41,
% 27.26/4.26 axiom_42, axiom_43, axiom_44, axiom_45, axiom_48, axiom_51, axiom_52, axiom_53,
% 27.26/4.26 axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60, axiom_61,
% 27.26/4.26 axiom_62, axiom_63, axiom_64, axiom_65
% 27.26/4.26
% 27.26/4.26 Those formulas are unsatisfiable:
% 27.26/4.26 ---------------------------------
% 27.26/4.26
% 27.26/4.26 Begin of proof
% 27.26/4.26 |
% 27.26/4.26 | ALPHA: (axiom_03) implies:
% 27.26/4.26 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc))
% 27.26/4.26 |
% 27.26/4.26 | ALPHA: (axiom_46) implies:
% 27.26/4.26 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 27.26/4.26 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 27.26/4.26 | elem(v0, v3))
% 27.26/4.26 |
% 27.26/4.26 | ALPHA: (axiom_47) implies:
% 27.26/4.26 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.26/4.26 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0,
% 27.26/4.26 | v3) | elem(v0, v2))
% 27.26/4.26 |
% 27.26/4.26 | ALPHA: (conj) implies:
% 27.82/4.27 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 27.82/4.27 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 27.82/4.27 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 27.82/4.27 | ? [v15: $i] : ? [v16: $i] : ( ~ (v7 = v0) & index(elid, v0) = v3 &
% 27.82/4.27 | index(status, v0) = norm & index(ldr, v0) = v0 & snoc(v10, v8) = v11
% 27.82/4.27 | & cons(v6, v1) = v5 & m_NotNorm(v3) = v6 & m_Down(v15) = v16 &
% 27.82/4.27 | m_Down(v12) = v14 & m_Halt(v2) = v8 & s(v0) = v7 & s(zero) = v0 &
% 27.82/4.27 | host(v15) = v0 & host(v13) = v0 & host(v12) = v7 & host(v9) = v7 &
% 27.82/4.27 | host(v4) = v0 & host(v2) = v0 & queue(v7) = v10 & queue(v0) = v5 &
% 27.82/4.27 | $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) &
% 27.82/4.27 | $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 27.82/4.27 | & $i(v1) & $i(v0) & setIn(v4, alive) & elem(v16, v11) & elem(v14, v1)
% 27.82/4.27 | & ~ leq(nbr_proc, v0) & ~ setIn(v2, pids) & ! [v17: $i] : ! [v18:
% 27.82/4.27 | $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] :
% 27.82/4.27 | ! [v23: $i] : ! [v24: $i] : (v22 = v21 | ~ (m_Down(v20) = v23) | ~
% 27.82/4.27 | (m_Down(v18) = v24) | ~ (host(v19) = v21) | ~ (host(v17) = v22) |
% 27.82/4.27 | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ $i(v17) | ~ setIn(v19,
% 27.82/4.27 | alive) | ~ setIn(v17, alive) | ? [v25: $i] : ? [v26: $i] : ?
% 27.82/4.27 | [v27: $i] : ? [v28: $i] : (( ~ (v26 = v21) & host(v20) = v26 &
% 27.82/4.27 | $i(v26)) | ( ~ (v25 = v22) & host(v18) = v25 & $i(v25)) |
% 27.82/4.27 | (queue(v22) = v27 & $i(v27) & ~ elem(v23, v27)) | (queue(v21) =
% 27.82/4.27 | v28 & $i(v28) & ~ elem(v24, v28)))) & ! [v17: $i] : ! [v18:
% 27.82/4.27 | $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (m_Ack(v19,
% 27.82/4.27 | v17) = v20) | ~ (host(v18) = v21) | ~ $i(v19) | ~ $i(v18) |
% 27.82/4.27 | ~ $i(v17) | ? [v22: $i] : ? [v23: $i] : ? [v24: $i] :
% 27.82/4.27 | ((host(v19) = v24 & host(v17) = v23 & $i(v24) & $i(v23) & ~
% 27.82/4.27 | leq(v23, v24)) | (queue(v21) = v22 & $i(v22) & ~ elem(v20,
% 27.82/4.27 | v22)))) & ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : !
% 27.82/4.27 | [v20: $i] : ( ~ (m_Down(v18) = v19) | ~ (host(v17) = v20) | ~
% 27.82/4.27 | $i(v18) | ~ $i(v17) | ~ setIn(v18, alive) | ? [v21: $i] :
% 27.82/4.27 | (queue(v20) = v21 & $i(v21) & ~ elem(v19, v21))) & ! [v17: $i] :
% 27.82/4.27 | ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ (m_Down(v18) = v19) |
% 27.82/4.27 | ~ (host(v17) = v20) | ~ $i(v18) | ~ $i(v17) | ? [v21: $i] : ?
% 27.82/4.27 | [v22: $i] : (( ~ (v22 = v20) & host(v18) = v22 & $i(v22)) |
% 27.82/4.27 | (queue(v20) = v21 & $i(v21) & ~ elem(v19, v21)))) & ! [v17: $i]
% 27.82/4.27 | : ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ (m_Halt(v18) =
% 27.82/4.27 | v19) | ~ (host(v17) = v20) | ~ $i(v18) | ~ $i(v17) | ? [v21:
% 27.82/4.27 | $i] : ? [v22: $i] : ((host(v18) = v22 & $i(v22) & ~ leq(v20,
% 27.82/4.27 | v22)) | (queue(v20) = v21 & $i(v21) & ~ elem(v19, v21)))) &
% 27.82/4.27 | ! [v17: $i] : ! [v18: $i] : ! [v19: $i] : (v18 = v17 | ~
% 27.82/4.27 | (host(v18) = v19) | ~ (host(v17) = v19) | ~ $i(v18) | ~ $i(v17)
% 27.82/4.27 | | ~ setIn(v18, alive) | ~ setIn(v17, alive)) & ! [v17: $i] : !
% 27.82/4.27 | [v18: $i] : ! [v19: $i] : ( ~ (host(v18) = v19) | ~ (host(v17) =
% 27.82/4.27 | v19) | ~ $i(v18) | ~ $i(v17) | ~ leq(v18, v17) | ~ setIn(v18,
% 27.82/4.27 | alive) | setIn(v17, alive)) & ! [v17: $i] : ( ~ (host(v17) = v0)
% 27.82/4.27 | | ~ $i(v17) | leq(v17, v2)) & (v13 = v2 | ( ~ (v13 = v4) &
% 27.82/4.27 | setIn(v13, alive))) & (v9 = v2 | ( ~ (v9 = v4) & setIn(v9,
% 27.82/4.27 | alive))))
% 27.82/4.27 |
% 27.82/4.27 | ALPHA: (function-axioms) implies:
% 27.82/4.27 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 27.82/4.27 | v1) | ~ (queue(v2) = v0))
% 27.82/4.27 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 27.82/4.27 | | ~ (host(v2) = v0))
% 27.82/4.27 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) |
% 27.82/4.27 | ~ (s(v2) = v0))
% 27.82/4.27 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pidMsg(v2) =
% 27.82/4.27 | v1) | ~ (pidMsg(v2) = v0))
% 27.82/4.27 |
% 27.82/4.27 | DELTA: instantiating (1) with fresh symbol all_59_0 gives:
% 27.82/4.27 | (9) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc)
% 27.82/4.27 |
% 27.82/4.27 | ALPHA: (9) implies:
% 27.82/4.27 | (10) s(zero) = all_59_0
% 27.82/4.27 |
% 27.82/4.27 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1, all_65_2,
% 27.82/4.27 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 27.82/4.27 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 27.82/4.27 | all_65_16 gives:
% 27.82/4.28 | (11) ~ (all_65_9 = all_65_16) & index(elid, all_65_16) = all_65_13 &
% 27.82/4.28 | index(status, all_65_16) = norm & index(ldr, all_65_16) = all_65_16 &
% 27.82/4.28 | snoc(all_65_6, all_65_8) = all_65_5 & cons(all_65_10, all_65_15) =
% 27.82/4.28 | all_65_11 & m_NotNorm(all_65_13) = all_65_10 & m_Down(all_65_1) =
% 27.82/4.28 | all_65_0 & m_Down(all_65_4) = all_65_2 & m_Halt(all_65_14) = all_65_8
% 27.82/4.28 | & s(all_65_16) = all_65_9 & s(zero) = all_65_16 & host(all_65_1) =
% 27.82/4.28 | all_65_16 & host(all_65_3) = all_65_16 & host(all_65_4) = all_65_9 &
% 27.82/4.28 | host(all_65_7) = all_65_9 & host(all_65_12) = all_65_16 &
% 27.82/4.28 | host(all_65_14) = all_65_16 & queue(all_65_9) = all_65_6 &
% 27.82/4.28 | queue(all_65_16) = all_65_11 & $i(all_65_0) & $i(all_65_1) &
% 27.82/4.28 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) &
% 27.82/4.28 | $i(all_65_6) & $i(all_65_7) & $i(all_65_8) & $i(all_65_9) &
% 27.82/4.28 | $i(all_65_10) & $i(all_65_11) & $i(all_65_12) & $i(all_65_13) &
% 27.82/4.28 | $i(all_65_14) & $i(all_65_15) & $i(all_65_16) & setIn(all_65_12,
% 27.82/4.28 | alive) & elem(all_65_0, all_65_5) & elem(all_65_2, all_65_15) & ~
% 27.82/4.28 | leq(nbr_proc, all_65_16) & ~ setIn(all_65_14, pids) & ! [v0: $i] :
% 27.82/4.28 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 27.82/4.28 | ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~
% 27.82/4.28 | (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~
% 27.82/4.28 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) |
% 27.82/4.28 | ~ setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 27.82/4.28 | [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9)) | ( ~ (v8 = v5)
% 27.82/4.28 | & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 & $i(v10) & ~
% 27.82/4.28 | elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~ elem(v7,
% 27.82/4.28 | v11)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 27.82/4.28 | $i] : ! [v4: $i] : ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) |
% 27.82/4.28 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ?
% 27.82/4.28 | [v7: $i] : ((host(v2) = v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~
% 27.82/4.28 | leq(v6, v7)) | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) &
% 27.82/4.28 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1)
% 27.82/4.28 | = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 27.82/4.28 | alive) | ? [v4: $i] : (queue(v3) = v4 & $i(v4) & ~ elem(v2,
% 27.82/4.28 | v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 27.82/4.28 | ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 27.82/4.28 | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5))
% 27.82/4.28 | | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : !
% 27.82/4.28 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) = v2) | ~
% 27.82/4.28 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i]
% 27.82/4.28 | : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 &
% 27.82/4.28 | $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : !
% 27.82/4.28 | [v2: $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~
% 27.82/4.28 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & !
% 27.82/4.28 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~
% 27.82/4.28 | (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0) | ~
% 27.82/4.28 | setIn(v1, alive) | setIn(v0, alive)) & ! [v0: $i] : ( ~ (host(v0) =
% 27.82/4.28 | all_65_16) | ~ $i(v0) | leq(v0, all_65_14)) & (all_65_3 =
% 27.82/4.28 | all_65_14 | ( ~ (all_65_3 = all_65_12) & setIn(all_65_3, alive))) &
% 27.82/4.28 | (all_65_7 = all_65_14 | ( ~ (all_65_7 = all_65_12) & setIn(all_65_7,
% 27.82/4.28 | alive)))
% 27.82/4.28 |
% 27.82/4.28 | ALPHA: (11) implies:
% 27.82/4.28 | (12) ~ (all_65_9 = all_65_16)
% 27.82/4.29 | (13) elem(all_65_2, all_65_15)
% 27.82/4.29 | (14) elem(all_65_0, all_65_5)
% 27.82/4.29 | (15) setIn(all_65_12, alive)
% 27.82/4.29 | (16) $i(all_65_15)
% 27.82/4.29 | (17) $i(all_65_14)
% 27.82/4.29 | (18) $i(all_65_12)
% 27.82/4.29 | (19) $i(all_65_10)
% 27.82/4.29 | (20) $i(all_65_8)
% 27.82/4.29 | (21) $i(all_65_7)
% 27.82/4.29 | (22) $i(all_65_6)
% 27.82/4.29 | (23) $i(all_65_4)
% 27.82/4.29 | (24) $i(all_65_2)
% 27.82/4.29 | (25) $i(all_65_1)
% 27.82/4.29 | (26) $i(all_65_0)
% 27.82/4.29 | (27) queue(all_65_16) = all_65_11
% 27.82/4.29 | (28) queue(all_65_9) = all_65_6
% 27.82/4.29 | (29) host(all_65_14) = all_65_16
% 27.82/4.29 | (30) host(all_65_12) = all_65_16
% 27.82/4.29 | (31) host(all_65_7) = all_65_9
% 27.82/4.29 | (32) host(all_65_4) = all_65_9
% 27.82/4.29 | (33) host(all_65_1) = all_65_16
% 27.82/4.29 | (34) s(zero) = all_65_16
% 27.82/4.29 | (35) m_Halt(all_65_14) = all_65_8
% 27.82/4.29 | (36) m_Down(all_65_4) = all_65_2
% 27.82/4.29 | (37) m_Down(all_65_1) = all_65_0
% 27.82/4.29 | (38) cons(all_65_10, all_65_15) = all_65_11
% 27.82/4.29 | (39) snoc(all_65_6, all_65_8) = all_65_5
% 27.82/4.29 | (40) all_65_7 = all_65_14 | ( ~ (all_65_7 = all_65_12) & setIn(all_65_7,
% 27.82/4.29 | alive))
% 27.82/4.29 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.82/4.29 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) =
% 27.82/4.29 | v6) | ~ (m_Down(v1) = v7) | ~ (host(v2) = v4) | ~ (host(v0) =
% 27.82/4.29 | v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2,
% 27.82/4.29 | alive) | ~ setIn(v0, alive) | ? [v8: $i] : ? [v9: $i] : ?
% 27.82/4.29 | [v10: $i] : ? [v11: $i] : (( ~ (v9 = v4) & host(v3) = v9 & $i(v9))
% 27.82/4.29 | | ( ~ (v8 = v5) & host(v1) = v8 & $i(v8)) | (queue(v5) = v10 &
% 27.82/4.29 | $i(v10) & ~ elem(v6, v10)) | (queue(v4) = v11 & $i(v11) & ~
% 27.82/4.29 | elem(v7, v11))))
% 27.82/4.29 |
% 27.82/4.29 | GROUND_INST: instantiating (7) with all_59_0, all_65_16, zero, simplifying
% 27.82/4.29 | with (10), (34) gives:
% 27.82/4.29 | (42) all_65_16 = all_59_0
% 27.82/4.29 |
% 27.82/4.29 | REDUCE: (12), (42) imply:
% 27.82/4.29 | (43) ~ (all_65_9 = all_59_0)
% 27.82/4.29 |
% 27.82/4.29 | REDUCE: (33), (42) imply:
% 27.82/4.29 | (44) host(all_65_1) = all_59_0
% 27.82/4.29 |
% 27.82/4.29 | REDUCE: (30), (42) imply:
% 27.82/4.29 | (45) host(all_65_12) = all_59_0
% 27.82/4.29 |
% 27.82/4.29 | REDUCE: (29), (42) imply:
% 27.82/4.29 | (46) host(all_65_14) = all_59_0
% 27.82/4.29 |
% 27.82/4.29 | REDUCE: (27), (42) imply:
% 27.82/4.29 | (47) queue(all_59_0) = all_65_11
% 27.82/4.29 |
% 27.82/4.29 | GROUND_INST: instantiating (axiom_49) with all_65_14, all_65_8, simplifying
% 27.82/4.29 | with (17), (35) gives:
% 27.82/4.29 | (48) pidMsg(all_65_8) = all_65_14
% 27.82/4.29 |
% 27.82/4.29 | GROUND_INST: instantiating (axiom_50) with all_65_1, all_65_0, simplifying
% 27.82/4.29 | with (25), (37) gives:
% 27.82/4.29 | (49) pidMsg(all_65_0) = all_65_1
% 27.82/4.29 |
% 27.97/4.29 | GROUND_INST: instantiating (2) with all_65_2, all_65_10, all_65_15, all_65_11,
% 27.97/4.29 | simplifying with (13), (16), (19), (24), (38) gives:
% 27.97/4.29 | (50) elem(all_65_2, all_65_11)
% 27.97/4.29 |
% 27.97/4.29 | GROUND_INST: instantiating (3) with all_65_0, all_65_8, all_65_6, all_65_5,
% 27.97/4.29 | simplifying with (14), (20), (22), (26), (39) gives:
% 27.97/4.29 | (51) all_65_0 = all_65_8 | elem(all_65_0, all_65_6)
% 27.97/4.29 |
% 27.97/4.29 | BETA: splitting (40) gives:
% 27.97/4.29 |
% 27.97/4.29 | Case 1:
% 27.97/4.29 | |
% 27.97/4.29 | | (52) all_65_7 = all_65_14
% 27.97/4.29 | |
% 27.97/4.29 | | REDUCE: (31), (52) imply:
% 27.97/4.29 | | (53) host(all_65_14) = all_65_9
% 27.97/4.29 | |
% 27.97/4.29 | | GROUND_INST: instantiating (6) with all_59_0, all_65_9, all_65_14,
% 27.97/4.29 | | simplifying with (46), (53) gives:
% 27.97/4.29 | | (54) all_65_9 = all_59_0
% 27.97/4.29 | |
% 27.97/4.29 | | REDUCE: (43), (54) imply:
% 27.97/4.30 | | (55) $false
% 27.97/4.30 | |
% 27.97/4.30 | | CLOSE: (55) is inconsistent.
% 27.97/4.30 | |
% 27.97/4.30 | Case 2:
% 27.97/4.30 | |
% 27.97/4.30 | | (56) ~ (all_65_7 = all_65_12) & setIn(all_65_7, alive)
% 27.97/4.30 | |
% 27.97/4.30 | | ALPHA: (56) implies:
% 27.97/4.30 | | (57) setIn(all_65_7, alive)
% 27.97/4.30 | |
% 27.97/4.30 | | GROUND_INST: instantiating (41) with all_65_7, all_65_4, all_65_12,
% 27.97/4.30 | | all_65_1, all_59_0, all_65_9, all_65_0, all_65_2, simplifying
% 27.97/4.30 | | with (15), (18), (21), (23), (25), (31), (36), (37), (45), (57)
% 27.97/4.30 | | gives:
% 27.97/4.30 | | (58) all_65_9 = all_59_0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.97/4.30 | | [v3: $i] : (( ~ (v1 = all_59_0) & host(all_65_1) = v1 & $i(v1)) | (
% 27.97/4.30 | | ~ (v0 = all_65_9) & host(all_65_4) = v0 & $i(v0)) |
% 27.97/4.30 | | (queue(all_65_9) = v2 & $i(v2) & ~ elem(all_65_0, v2)) |
% 27.97/4.30 | | (queue(all_59_0) = v3 & $i(v3) & ~ elem(all_65_2, v3)))
% 27.97/4.30 | |
% 27.97/4.30 | | GROUND_INST: instantiating (41) with all_65_12, all_65_1, all_65_7,
% 27.97/4.30 | | all_65_4, all_65_9, all_59_0, all_65_2, all_65_0, simplifying
% 27.97/4.30 | | with (15), (18), (21), (23), (25), (31), (36), (37), (45), (57)
% 27.97/4.30 | | gives:
% 27.97/4.30 | | (59) all_65_9 = all_59_0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ?
% 27.97/4.30 | | [v3: $i] : (( ~ (v1 = all_65_9) & host(all_65_4) = v1 & $i(v1)) | (
% 27.97/4.30 | | ~ (v0 = all_59_0) & host(all_65_1) = v0 & $i(v0)) |
% 27.97/4.30 | | (queue(all_65_9) = v3 & $i(v3) & ~ elem(all_65_0, v3)) |
% 27.97/4.30 | | (queue(all_59_0) = v2 & $i(v2) & ~ elem(all_65_2, v2)))
% 27.97/4.30 | |
% 27.97/4.30 | | BETA: splitting (58) gives:
% 27.97/4.30 | |
% 27.97/4.30 | | Case 1:
% 27.97/4.30 | | |
% 27.97/4.30 | | | (60) all_65_9 = all_59_0
% 27.97/4.30 | | |
% 27.97/4.30 | | | REDUCE: (43), (60) imply:
% 27.97/4.30 | | | (61) $false
% 27.97/4.30 | | |
% 27.97/4.30 | | | CLOSE: (61) is inconsistent.
% 27.97/4.30 | | |
% 27.97/4.30 | | Case 2:
% 27.97/4.30 | | |
% 27.97/4.30 | | | (62) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~ (v1
% 27.97/4.30 | | | = all_59_0) & host(all_65_1) = v1 & $i(v1)) | ( ~ (v0 =
% 27.97/4.30 | | | all_65_9) & host(all_65_4) = v0 & $i(v0)) | (queue(all_65_9)
% 27.97/4.30 | | | = v2 & $i(v2) & ~ elem(all_65_0, v2)) | (queue(all_59_0) = v3
% 27.97/4.30 | | | & $i(v3) & ~ elem(all_65_2, v3)))
% 27.97/4.30 | | |
% 27.97/4.30 | | | DELTA: instantiating (62) with fresh symbols all_167_0, all_167_1,
% 27.97/4.30 | | | all_167_2, all_167_3 gives:
% 27.97/4.30 | | | (63) ( ~ (all_167_2 = all_59_0) & host(all_65_1) = all_167_2 &
% 27.97/4.30 | | | $i(all_167_2)) | ( ~ (all_167_3 = all_65_9) & host(all_65_4) =
% 27.97/4.30 | | | all_167_3 & $i(all_167_3)) | (queue(all_65_9) = all_167_1 &
% 27.97/4.30 | | | $i(all_167_1) & ~ elem(all_65_0, all_167_1)) | (queue(all_59_0)
% 27.97/4.30 | | | = all_167_0 & $i(all_167_0) & ~ elem(all_65_2, all_167_0))
% 27.97/4.30 | | |
% 27.97/4.30 | | | BETA: splitting (59) gives:
% 27.97/4.30 | | |
% 27.97/4.30 | | | Case 1:
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | (64) all_65_9 = all_59_0
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | REDUCE: (43), (64) imply:
% 27.97/4.30 | | | | (65) $false
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | CLOSE: (65) is inconsistent.
% 27.97/4.30 | | | |
% 27.97/4.30 | | | Case 2:
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | (66) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~
% 27.97/4.30 | | | | (v1 = all_65_9) & host(all_65_4) = v1 & $i(v1)) | ( ~ (v0 =
% 27.97/4.30 | | | | all_59_0) & host(all_65_1) = v0 & $i(v0)) |
% 27.97/4.30 | | | | (queue(all_65_9) = v3 & $i(v3) & ~ elem(all_65_0, v3)) |
% 27.97/4.30 | | | | (queue(all_59_0) = v2 & $i(v2) & ~ elem(all_65_2, v2)))
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | DELTA: instantiating (66) with fresh symbols all_180_0, all_180_1,
% 27.97/4.30 | | | | all_180_2, all_180_3 gives:
% 27.97/4.30 | | | | (67) ( ~ (all_180_2 = all_65_9) & host(all_65_4) = all_180_2 &
% 27.97/4.30 | | | | $i(all_180_2)) | ( ~ (all_180_3 = all_59_0) & host(all_65_1) =
% 27.97/4.30 | | | | all_180_3 & $i(all_180_3)) | (queue(all_65_9) = all_180_0 &
% 27.97/4.30 | | | | $i(all_180_0) & ~ elem(all_65_0, all_180_0)) |
% 27.97/4.30 | | | | (queue(all_59_0) = all_180_1 & $i(all_180_1) & ~ elem(all_65_2,
% 27.97/4.30 | | | | all_180_1))
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | BETA: splitting (63) gives:
% 27.97/4.30 | | | |
% 27.97/4.30 | | | | Case 1:
% 27.97/4.30 | | | | |
% 27.97/4.30 | | | | | (68) ( ~ (all_167_2 = all_59_0) & host(all_65_1) = all_167_2 &
% 27.97/4.30 | | | | | $i(all_167_2)) | ( ~ (all_167_3 = all_65_9) & host(all_65_4)
% 27.97/4.30 | | | | | = all_167_3 & $i(all_167_3))
% 27.97/4.30 | | | | |
% 27.97/4.30 | | | | | BETA: splitting (68) gives:
% 27.97/4.30 | | | | |
% 27.97/4.30 | | | | | Case 1:
% 27.97/4.30 | | | | | |
% 27.97/4.30 | | | | | | (69) ~ (all_167_2 = all_59_0) & host(all_65_1) = all_167_2 &
% 27.97/4.30 | | | | | | $i(all_167_2)
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | ALPHA: (69) implies:
% 27.97/4.31 | | | | | | (70) ~ (all_167_2 = all_59_0)
% 27.97/4.31 | | | | | | (71) host(all_65_1) = all_167_2
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | GROUND_INST: instantiating (6) with all_59_0, all_167_2, all_65_1,
% 27.97/4.31 | | | | | | simplifying with (44), (71) gives:
% 27.97/4.31 | | | | | | (72) all_167_2 = all_59_0
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | REDUCE: (70), (72) imply:
% 27.97/4.31 | | | | | | (73) $false
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | CLOSE: (73) is inconsistent.
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | Case 2:
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | (74) ~ (all_167_3 = all_65_9) & host(all_65_4) = all_167_3 &
% 27.97/4.31 | | | | | | $i(all_167_3)
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | ALPHA: (74) implies:
% 27.97/4.31 | | | | | | (75) ~ (all_167_3 = all_65_9)
% 27.97/4.31 | | | | | | (76) host(all_65_4) = all_167_3
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | GROUND_INST: instantiating (6) with all_65_9, all_167_3, all_65_4,
% 27.97/4.31 | | | | | | simplifying with (32), (76) gives:
% 27.97/4.31 | | | | | | (77) all_167_3 = all_65_9
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | REDUCE: (75), (77) imply:
% 27.97/4.31 | | | | | | (78) $false
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | CLOSE: (78) is inconsistent.
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | End of split
% 27.97/4.31 | | | | |
% 27.97/4.31 | | | | Case 2:
% 27.97/4.31 | | | | |
% 27.97/4.31 | | | | | (79) (queue(all_65_9) = all_167_1 & $i(all_167_1) & ~
% 27.97/4.31 | | | | | elem(all_65_0, all_167_1)) | (queue(all_59_0) = all_167_0 &
% 27.97/4.31 | | | | | $i(all_167_0) & ~ elem(all_65_2, all_167_0))
% 27.97/4.31 | | | | |
% 27.97/4.31 | | | | | BETA: splitting (79) gives:
% 27.97/4.31 | | | | |
% 27.97/4.31 | | | | | Case 1:
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | (80) queue(all_65_9) = all_167_1 & $i(all_167_1) & ~
% 27.97/4.31 | | | | | | elem(all_65_0, all_167_1)
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | ALPHA: (80) implies:
% 27.97/4.31 | | | | | | (81) ~ elem(all_65_0, all_167_1)
% 27.97/4.31 | | | | | | (82) queue(all_65_9) = all_167_1
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | BETA: splitting (67) gives:
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | | Case 1:
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | (83) ( ~ (all_180_2 = all_65_9) & host(all_65_4) = all_180_2 &
% 27.97/4.31 | | | | | | | $i(all_180_2)) | ( ~ (all_180_3 = all_59_0) &
% 27.97/4.31 | | | | | | | host(all_65_1) = all_180_3 & $i(all_180_3))
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | BETA: splitting (83) gives:
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | Case 1:
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | (84) ~ (all_180_2 = all_65_9) & host(all_65_4) = all_180_2 &
% 27.97/4.31 | | | | | | | | $i(all_180_2)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | ALPHA: (84) implies:
% 27.97/4.31 | | | | | | | | (85) ~ (all_180_2 = all_65_9)
% 27.97/4.31 | | | | | | | | (86) host(all_65_4) = all_180_2
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | GROUND_INST: instantiating (6) with all_65_9, all_180_2,
% 27.97/4.31 | | | | | | | | all_65_4, simplifying with (32), (86) gives:
% 27.97/4.31 | | | | | | | | (87) all_180_2 = all_65_9
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | REDUCE: (85), (87) imply:
% 27.97/4.31 | | | | | | | | (88) $false
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | CLOSE: (88) is inconsistent.
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | Case 2:
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | (89) ~ (all_180_3 = all_59_0) & host(all_65_1) = all_180_3 &
% 27.97/4.31 | | | | | | | | $i(all_180_3)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | ALPHA: (89) implies:
% 27.97/4.31 | | | | | | | | (90) ~ (all_180_3 = all_59_0)
% 27.97/4.31 | | | | | | | | (91) host(all_65_1) = all_180_3
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | GROUND_INST: instantiating (6) with all_59_0, all_180_3,
% 27.97/4.31 | | | | | | | | all_65_1, simplifying with (44), (91) gives:
% 27.97/4.31 | | | | | | | | (92) all_180_3 = all_59_0
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | REDUCE: (90), (92) imply:
% 27.97/4.31 | | | | | | | | (93) $false
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | CLOSE: (93) is inconsistent.
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | End of split
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | Case 2:
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | (94) (queue(all_65_9) = all_180_0 & $i(all_180_0) & ~
% 27.97/4.31 | | | | | | | elem(all_65_0, all_180_0)) | (queue(all_59_0) =
% 27.97/4.31 | | | | | | | all_180_1 & $i(all_180_1) & ~ elem(all_65_2,
% 27.97/4.31 | | | | | | | all_180_1))
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | BETA: splitting (94) gives:
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | | Case 1:
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | (95) queue(all_65_9) = all_180_0 & $i(all_180_0) & ~
% 27.97/4.31 | | | | | | | | elem(all_65_0, all_180_0)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | ALPHA: (95) implies:
% 27.97/4.31 | | | | | | | | (96) queue(all_65_9) = all_180_0
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | GROUND_INST: instantiating (5) with all_65_6, all_180_0,
% 27.97/4.31 | | | | | | | | all_65_9, simplifying with (28), (96) gives:
% 27.97/4.31 | | | | | | | | (97) all_180_0 = all_65_6
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | GROUND_INST: instantiating (5) with all_167_1, all_180_0,
% 27.97/4.31 | | | | | | | | all_65_9, simplifying with (82), (96) gives:
% 27.97/4.31 | | | | | | | | (98) all_180_0 = all_167_1
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | COMBINE_EQS: (97), (98) imply:
% 27.97/4.31 | | | | | | | | (99) all_167_1 = all_65_6
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | REDUCE: (81), (99) imply:
% 27.97/4.31 | | | | | | | | (100) ~ elem(all_65_0, all_65_6)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | BETA: splitting (51) gives:
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | Case 1:
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | (101) elem(all_65_0, all_65_6)
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | PRED_UNIFY: (100), (101) imply:
% 27.97/4.31 | | | | | | | | | (102) $false
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | CLOSE: (102) is inconsistent.
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | Case 2:
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | (103) all_65_0 = all_65_8
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | REDUCE: (49), (103) imply:
% 27.97/4.31 | | | | | | | | | (104) pidMsg(all_65_8) = all_65_1
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | REDUCE: (37), (103) imply:
% 27.97/4.31 | | | | | | | | | (105) m_Down(all_65_1) = all_65_8
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | GROUND_INST: instantiating (8) with all_65_14, all_65_1,
% 27.97/4.31 | | | | | | | | | all_65_8, simplifying with (48), (104) gives:
% 27.97/4.31 | | | | | | | | | (106) all_65_1 = all_65_14
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | REDUCE: (105), (106) imply:
% 27.97/4.31 | | | | | | | | | (107) m_Down(all_65_14) = all_65_8
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | GROUND_INST: instantiating (axiom_17) with all_65_14,
% 27.97/4.31 | | | | | | | | | all_65_14, all_65_8, simplifying with (17), (35),
% 27.97/4.31 | | | | | | | | | (107) gives:
% 27.97/4.31 | | | | | | | | | (108) $false
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | | CLOSE: (108) is inconsistent.
% 27.97/4.31 | | | | | | | | |
% 27.97/4.31 | | | | | | | | End of split
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | Case 2:
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | (109) queue(all_59_0) = all_180_1 & $i(all_180_1) & ~
% 27.97/4.31 | | | | | | | | elem(all_65_2, all_180_1)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | ALPHA: (109) implies:
% 27.97/4.31 | | | | | | | | (110) ~ elem(all_65_2, all_180_1)
% 27.97/4.31 | | | | | | | | (111) queue(all_59_0) = all_180_1
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | GROUND_INST: instantiating (5) with all_65_11, all_180_1,
% 27.97/4.31 | | | | | | | | all_59_0, simplifying with (47), (111) gives:
% 27.97/4.31 | | | | | | | | (112) all_180_1 = all_65_11
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | REDUCE: (110), (112) imply:
% 27.97/4.31 | | | | | | | | (113) ~ elem(all_65_2, all_65_11)
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | PRED_UNIFY: (50), (113) imply:
% 27.97/4.31 | | | | | | | | (114) $false
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | | CLOSE: (114) is inconsistent.
% 27.97/4.31 | | | | | | | |
% 27.97/4.31 | | | | | | | End of split
% 27.97/4.31 | | | | | | |
% 27.97/4.31 | | | | | | End of split
% 27.97/4.31 | | | | | |
% 27.97/4.31 | | | | | Case 2:
% 27.97/4.31 | | | | | |
% 27.97/4.32 | | | | | | (115) queue(all_59_0) = all_167_0 & $i(all_167_0) & ~
% 27.97/4.32 | | | | | | elem(all_65_2, all_167_0)
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | | ALPHA: (115) implies:
% 27.97/4.32 | | | | | | (116) ~ elem(all_65_2, all_167_0)
% 27.97/4.32 | | | | | | (117) queue(all_59_0) = all_167_0
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | | GROUND_INST: instantiating (5) with all_65_11, all_167_0, all_59_0,
% 27.97/4.32 | | | | | | simplifying with (47), (117) gives:
% 27.97/4.32 | | | | | | (118) all_167_0 = all_65_11
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | | REDUCE: (116), (118) imply:
% 27.97/4.32 | | | | | | (119) ~ elem(all_65_2, all_65_11)
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | | PRED_UNIFY: (50), (119) imply:
% 27.97/4.32 | | | | | | (120) $false
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | | CLOSE: (120) is inconsistent.
% 27.97/4.32 | | | | | |
% 27.97/4.32 | | | | | End of split
% 27.97/4.32 | | | | |
% 27.97/4.32 | | | | End of split
% 27.97/4.32 | | | |
% 27.97/4.32 | | | End of split
% 27.97/4.32 | | |
% 27.97/4.32 | | End of split
% 27.97/4.32 | |
% 27.97/4.32 | End of split
% 27.97/4.32 |
% 27.97/4.32 End of proof
% 27.97/4.32 % SZS output end Proof for theBenchmark
% 27.97/4.32
% 27.97/4.32 3703ms
%------------------------------------------------------------------------------