TSTP Solution File: SWV462+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV462+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 : n005.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 22:56:35 EDT 2023
% Result : Theorem 141.24s 19.16s
% Output : Proof 142.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWV462+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 03:43:53 EDT 2023
% 0.13/0.35 % 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.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.91/1.29 Prover 1: Preprocessing ...
% 4.42/1.29 Prover 4: Preprocessing ...
% 4.42/1.32 Prover 5: Preprocessing ...
% 4.42/1.32 Prover 3: Preprocessing ...
% 4.42/1.32 Prover 0: Preprocessing ...
% 4.42/1.32 Prover 2: Preprocessing ...
% 4.42/1.32 Prover 6: Preprocessing ...
% 10.78/2.23 Prover 1: Constructing countermodel ...
% 11.33/2.26 Prover 6: Proving ...
% 11.59/2.28 Prover 3: Constructing countermodel ...
% 13.06/2.48 Prover 2: Proving ...
% 13.06/2.52 Prover 5: Proving ...
% 15.03/2.75 Prover 0: Proving ...
% 15.26/2.76 Prover 4: Constructing countermodel ...
% 18.36/3.25 Prover 3: gave up
% 18.36/3.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.60/3.37 Prover 7: Preprocessing ...
% 24.20/4.00 Prover 7: Warning: ignoring some quantifiers
% 24.87/4.04 Prover 7: Constructing countermodel ...
% 25.50/4.12 Prover 1: gave up
% 25.50/4.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.06/4.26 Prover 8: Preprocessing ...
% 27.82/4.45 Prover 8: Warning: ignoring some quantifiers
% 27.82/4.48 Prover 8: Constructing countermodel ...
% 39.63/5.94 Prover 8: gave up
% 39.63/5.94 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 39.63/5.98 Prover 9: Preprocessing ...
% 42.64/6.35 Prover 9: Constructing countermodel ...
% 60.64/8.66 Prover 2: stopped
% 60.64/8.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 61.01/8.74 Prover 10: Preprocessing ...
% 62.20/8.91 Prover 10: Warning: ignoring some quantifiers
% 62.20/8.91 Prover 10: Constructing countermodel ...
% 101.18/13.97 Prover 5: stopped
% 101.18/13.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 101.85/14.04 Prover 11: Preprocessing ...
% 105.79/14.54 Prover 11: Constructing countermodel ...
% 130.84/17.88 Prover 6: stopped
% 130.84/17.90 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 130.84/17.94 Prover 12: Preprocessing ...
% 132.98/18.11 Prover 12: Proving ...
% 140.73/19.14 Prover 10: Found proof (size 809)
% 140.73/19.14 Prover 10: proved (10480ms)
% 140.73/19.15 Prover 9: stopped
% 140.73/19.15 Prover 7: stopped
% 140.73/19.15 Prover 0: stopped
% 140.73/19.15 Prover 11: stopped
% 140.73/19.15 Prover 12: stopped
% 141.24/19.16 Prover 4: stopped
% 141.24/19.16
% 141.24/19.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 141.24/19.16
% 141.24/19.18 % SZS output start Proof for theBenchmark
% 141.24/19.19 Assumptions after simplification:
% 141.24/19.19 ---------------------------------
% 141.24/19.19
% 141.24/19.19 (axiom_01)
% 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) =
% 141.24/19.22 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v2) & s(v2) = v3 &
% 141.24/19.22 $i(v3)))
% 141.24/19.22
% 141.24/19.22 (axiom_04)
% 141.24/19.22 $i(nbr_proc) & ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) |
% 141.24/19.22 leq(v1, nbr_proc))
% 141.24/19.22
% 141.24/19.22 (axiom_09)
% 141.24/19.22 ~ (norm = elec_2) & $i(norm) & $i(elec_2)
% 141.24/19.22
% 141.24/19.22 (axiom_12)
% 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v2) = v3)
% 141.24/19.22 | ~ (m_Ack(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 141.24/19.22
% 141.24/19.22 (axiom_17)
% 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~
% 141.24/19.22 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 141.24/19.22
% 141.24/19.22 (axiom_26)
% 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2) | ~
% 141.24/19.22 (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 141.24/19.22
% 141.24/19.22 (axiom_31)
% 141.24/19.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 141.24/19.22 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2)
% 141.24/19.22 | ~ $i(v1) | ~ $i(v0))
% 141.24/19.22
% 141.24/19.22 (axiom_32)
% 141.24/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2
% 141.24/19.23 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) | ~ $i(v2)
% 141.24/19.23 | ~ $i(v1) | ~ $i(v0))
% 141.24/19.23
% 141.24/19.23 (axiom_46)
% 141.24/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.24/19.23 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 141.24/19.23 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 141.24/19.23 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 141.24/19.23 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 141.24/19.23 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 141.24/19.23
% 141.24/19.23 (axiom_47)
% 141.47/19.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.47/19.23 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 141.47/19.23 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 141.47/19.23 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 141.47/19.23 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0)
% 141.47/19.23 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 141.47/19.23
% 141.47/19.23 (axiom_48)
% 141.47/19.23 ! [v0: $i] : ! [v1: $i] : ( ~ (m_Down(v1) = v0) | ~ $i(v1) | ~ $i(v0) |
% 141.47/19.23 pidElem(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1)
% 141.47/19.23 | ~ $i(v0) | pidElem(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ?
% 141.47/19.23 [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) =
% 141.47/19.23 v0) | (v2 = v0 & m_Halt(v1) = v0))))
% 141.47/19.23
% 141.47/19.23 (axiom_61)
% 141.47/19.23 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1, v0)
% 141.47/19.23 | ~ leq(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | leq(v0, v0))
% 141.47/19.23
% 141.47/19.23 (axiom_62)
% 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 141.47/19.24 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 141.47/19.24
% 141.47/19.24 (axiom_63)
% 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~
% 141.47/19.24 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) | leq(v0, v1)) & !
% 141.47/19.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) = v3) | ~
% 141.47/19.24 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1) | leq(v2, v3))
% 141.47/19.24
% 141.47/19.24 (axiom_64)
% 141.47/19.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) | ~
% 141.47/19.24 $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1)) & ! [v0: $i] : ! [v1:
% 141.47/19.24 $i] : ! [v2: $i] : ( ~ (s(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v0,
% 141.47/19.24 v1) | leq(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~
% 141.47/19.24 $i(v1) | ~ $i(v0) | leq(v0, v0))
% 141.47/19.24
% 141.47/19.24 (conj)
% 141.47/19.26 $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(pendack) & $i(alive) &
% 141.47/19.26 $i(norm) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ? [v0: $i] :
% 141.47/19.26 ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 141.47/19.26 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 141.47/19.26 : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] :
% 141.47/19.26 ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ( ~ (v10 = v4) & ~ (v7 = v4) &
% 141.47/19.26 index(ldr, v10) = v10 & index(status, v10) = norm & index(status, v7) =
% 141.47/19.26 elec_2 & index(pendack, v7) = v14 & snoc(v17, v8) = v18 & cons(v6, v1) = v5
% 141.47/19.26 & m_Down(v12) = v16 & m_Halt(v3) = v6 & s(v14) = v15 & s(zero) = v0 &
% 141.47/19.26 m_Ack(v13, v11) = v19 & m_Ack(v3, v2) = v8 & host(v13) = v7 & host(v12) =
% 141.47/19.26 v15 & host(v11) = v14 & host(v9) = v10 & host(v3) = v7 & host(v2) = v4 &
% 141.47/19.26 queue(v7) = v17 & queue(v4) = v5 & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 141.47/19.26 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 141.47/19.26 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 141.47/19.26 leq(nbr_proc, v15) & setIn(v13, alive) & setIn(v9, alive) & setIn(v2, alive)
% 141.47/19.26 & elem(v19, v18) & elem(v16, v18) & ! [v20: $i] : ! [v21: $i] : ! [v22:
% 141.47/19.26 $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~
% 141.47/19.26 (m_Down(v22) = v25) | ~ (m_Ack(v23, v21) = v24) | ~ (host(v20) = v26) |
% 141.47/19.26 ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v23, alive) |
% 141.47/19.26 ~ setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ?
% 141.47/19.26 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ? [v34: $i] : ?
% 141.47/19.26 [v35: $i] : (( ~ (v35 = norm) & index(status, v26) = v35 & $i(v35)) | ( ~
% 141.47/19.26 (v34 = v26) & index(ldr, v26) = v34 & $i(v34)) | (host(v23) = v27 &
% 141.47/19.26 $i(v27) & (( ~ (v33 = v30) & index(pendack, v27) = v29 & s(v29) = v30
% 141.47/19.26 & host(v22) = v33 & $i(v33) & $i(v30) & $i(v29)) | ( ~ (v32 = v29)
% 141.47/19.26 & index(pendack, v27) = v29 & host(v21) = v32 & $i(v32) & $i(v29))
% 141.47/19.26 | ( ~ (v31 = elec_2) & index(status, v27) = v31 & $i(v31)) |
% 141.47/19.26 (index(pendack, v27) = v29 & s(v29) = v30 & $i(v30) & $i(v29) & ~
% 141.47/19.26 leq(nbr_proc, v30)) | (queue(v27) = v28 & $i(v28) & ( ~ elem(v25,
% 141.47/19.26 v28) | ~ elem(v24, v28))))))) & ! [v20: $i] : ! [v21: $i] :
% 141.47/19.26 ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : (
% 141.47/19.26 ~ (m_Down(v22) = v24) | ~ (m_Down(v21) = v25) | ~ (host(v23) = nbr_proc)
% 141.47/19.26 | ~ (host(v20) = v26) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20)
% 141.47/19.26 | ~ setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ?
% 141.47/19.26 [v30: $i] : ? [v31: $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) & (( ~
% 141.47/19.26 (v33 = v28) & index(down, nbr_proc) = v27 & host(v22) = v28 &
% 141.47/19.26 $i(v28) & $i(v27) & leq(v0, v33) & ~ leq(nbr_proc, v33) & ~
% 141.47/19.26 setIn(v33, v27)) | ( ~ (v31 = elec_1) & index(status, nbr_proc) =
% 141.47/19.26 v31 & $i(v31)) | ( ~ (v30 = nbr_proc) & host(v21) = v30 & $i(v30)) |
% 141.47/19.26 (queue(v26) = v32 & $i(v32) & ~ elem(v25, v32)) | (queue(nbr_proc) =
% 141.47/19.26 v29 & $i(v29) & ~ elem(v24, v29))))) & ! [v20: $i] : ! [v21: $i]
% 141.47/19.26 : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~
% 141.47/19.26 (m_Down(v21) = v23) | ~ (host(v22) = v24) | ~ (host(v20) = v25) | ~
% 141.47/19.26 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~ setIn(v20,
% 141.47/19.26 alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ((
% 141.47/19.26 ~ (v29 = norm) & index(status, v25) = v29 & $i(v29)) | ( ~ (v28 = v25)
% 141.47/19.26 & index(ldr, v25) = v28 & $i(v28)) | ( ~ (v27 = v25) & host(v21) = v27
% 141.47/19.26 & $i(v27)) | (queue(v24) = v26 & $i(v26) & ~ elem(v23, v26)))) & !
% 141.47/19.26 [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : !
% 141.47/19.26 [v25: $i] : ( ~ (m_Halt(v22) = v24) | ~ (host(v21) = v25) | ~ (host(v20) =
% 141.47/19.26 v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 141.47/19.26 setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29:
% 141.47/19.26 $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31 = norm) & index(status,
% 141.47/19.26 v23) = v31 & $i(v31)) | ( ~ (v30 = v23) & index(ldr, v23) = v30 &
% 141.47/19.26 $i(v30)) | ( ~ (v29 = elec_2) & index(status, v26) = v29 & host(v22) =
% 141.47/19.26 v26 & $i(v29) & $i(v26)) | (index(pendack, v26) = v27 & host(v22) =
% 141.47/19.26 v26 & $i(v27) & $i(v26) & leq(v27, v23)) | (queue(v25) = v28 & $i(v28)
% 141.47/19.26 & ~ elem(v24, v28)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] :
% 141.47/19.26 ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) = v23) | ~ (host(v21) =
% 141.47/19.26 v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ? [v25: $i] : ? [v26:
% 141.47/19.26 $i] : ? [v27: $i] : ((host(v22) = v27 & host(v20) = v26 & $i(v27) &
% 141.47/19.26 $i(v26) & ~ leq(v26, v27)) | (queue(v24) = v25 & $i(v25) & ~
% 141.47/19.26 elem(v23, v25)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 141.47/19.26 [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v20, v21) = v24) | ~ (host(v22) =
% 141.47/19.26 v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 141.47/19.26 setIn(v20, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ? [v28:
% 141.47/19.26 $i] : ? [v29: $i] : (( ~ (v28 = elec_2) & index(status, v23) = v28 &
% 141.47/19.26 $i(v28)) | ( ~ (v27 = elec_2) & index(status, v26) = v27 & host(v20) =
% 141.47/19.26 v26 & $i(v27) & $i(v26)) | ( ~ (v25 = v23) & host(v21) = v25 &
% 141.47/19.26 $i(v25)) | (host(v20) = v26 & queue(v26) = v29 & $i(v29) & $i(v26) &
% 141.47/19.26 ~ elem(v24, v29)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 141.47/19.26 [v23: $i] : ( ~ (m_Ldr(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~
% 141.47/19.26 $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 & $i(v25) & ~
% 141.47/19.26 leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) &
% 141.47/19.26 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v21)
% 141.47/19.26 = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] :
% 141.47/19.26 ? [v25: $i] : (( ~ (v25 = v23) & host(v21) = v25 & $i(v25)) | (queue(v23)
% 141.47/19.26 = v24 & $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] :
% 141.47/19.26 ! [v22: $i] : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~ (host(v20) = v23)
% 141.47/19.26 | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) =
% 141.47/19.26 v25 & $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~
% 141.47/19.26 elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 141.47/19.26 [v23: $i] : ( ~ (host(v21) = v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~
% 141.47/19.26 $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive) | leq(v22, v23) | ?
% 141.47/19.26 [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25 =
% 141.47/19.26 elec_2) & index(status, v23) = v25 & $i(v25)) | ( ~ (v24 = elec_2) &
% 141.47/19.26 index(status, v22) = v24 & $i(v24)) | (index(pendack, v23) = v27 &
% 141.47/19.26 index(pendack, v22) = v26 & $i(v27) & $i(v26) & ~ leq(v26, v27)))) &
% 141.47/19.26 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21) =
% 141.47/19.26 v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21,
% 141.47/19.26 alive) | ~ setIn(v20, alive) | leq(v22, v23) | ? [v24: $i] : ? [v25:
% 141.47/19.26 $i] : ? [v26: $i] : (( ~ (v25 = elec_2) & index(status, v23) = v25 &
% 141.47/19.26 $i(v25)) | ( ~ (v24 = elec_2) & index(status, v22) = v24 & $i(v24)) |
% 141.47/19.27 (index(pendack, v23) = v26 & $i(v26) & leq(v26, v22)))) & ! [v20: $i] :
% 141.47/19.27 ! [v21: $i] : ! [v22: $i] : (v21 = v20 | ~ (host(v21) = v22) | ~
% 141.47/19.27 (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ~
% 141.47/19.27 setIn(v20, alive)) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~
% 141.47/19.27 (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) |
% 141.47/19.27 ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : (host(v21) =
% 141.47/19.27 v23 & $i(v23) & ((index(pendack, v23) = v26 & host(v20) = v25 & $i(v26)
% 141.47/19.27 & $i(v25) & leq(v25, v26)) | (queue(v23) = v24 & $i(v24) & ~
% 141.47/19.27 elem(v22, v24))))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (
% 141.47/19.27 ~ (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive)
% 141.47/19.27 | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : (host(v21) = v23 & $i(v23)
% 141.47/19.27 & (( ~ (v24 = elec_1) & index(status, v23) = v24 & $i(v24)) |
% 141.47/19.27 (queue(v23) = v25 & $i(v25) & ~ elem(v22, v25))))) & ! [v20: $i] :
% 141.47/19.27 ! [v21: $i] : ( ~ (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) | ?
% 141.47/19.27 [v22: $i] : ? [v23: $i] : ((v23 = v20 & index(elid, v21) = v20) | ( ~
% 141.47/19.27 (v22 = elec_1) & ~ (v22 = elec_2) & index(status, v21) = v22 &
% 141.47/19.27 $i(v22)))))
% 141.47/19.27
% 141.47/19.27 (function-axioms)
% 141.47/19.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.47/19.27 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 141.47/19.27 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 141.47/19.27 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 141.47/19.27 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 141.47/19.27 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 141.47/19.27 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 141.47/19.27 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 141.47/19.27 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 141.47/19.27 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 141.47/19.27 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 141.47/19.27 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 141.47/19.27 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 141.47/19.27 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 141.47/19.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 141.47/19.27 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.47/19.27 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 141.47/19.27 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 141.47/19.27 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 141.47/19.27 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 141.47/19.27 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 141.47/19.27 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 141.47/19.27 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 141.47/19.27
% 141.47/19.27 Further assumptions not needed in the proof:
% 141.47/19.27 --------------------------------------------
% 141.79/19.27 axiom, axiom_02, axiom_03, axiom_05, axiom_06, axiom_07, axiom_08, axiom_10,
% 141.79/19.27 axiom_11, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18, axiom_19, axiom_20,
% 141.79/19.27 axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_27, axiom_28, axiom_29,
% 141.79/19.27 axiom_30, axiom_33, axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39,
% 141.79/19.27 axiom_40, axiom_41, axiom_42, axiom_43, axiom_44, axiom_45, axiom_49, axiom_50,
% 141.79/19.27 axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_58,
% 141.79/19.27 axiom_59, axiom_60, axiom_65
% 141.79/19.27
% 141.79/19.27 Those formulas are unsatisfiable:
% 141.79/19.27 ---------------------------------
% 141.79/19.27
% 141.79/19.27 Begin of proof
% 141.79/19.27 |
% 141.79/19.27 | ALPHA: (axiom_04) implies:
% 141.79/19.27 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | leq(v1,
% 141.79/19.27 | nbr_proc))
% 141.79/19.27 |
% 141.79/19.27 | ALPHA: (axiom_09) implies:
% 141.79/19.27 | (2) ~ (norm = elec_2)
% 141.79/19.27 |
% 141.79/19.27 | ALPHA: (axiom_46) implies:
% 141.79/19.27 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~
% 141.79/19.27 | $i(v1) | ~ $i(v0) | elem(v0, v2))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (axiom_47) implies:
% 141.79/19.28 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.79/19.28 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0,
% 141.79/19.28 | v3) | elem(v0, v2))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (axiom_48) implies:
% 141.79/19.28 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ pidElem(v0) | ? [v1: $i] : ? [v2: $i] :
% 141.79/19.28 | ? [v3: $i] : ($i(v1) & ((v3 = v0 & m_Down(v1) = v0) | (v2 = v0 &
% 141.79/19.28 | m_Halt(v1) = v0))))
% 141.79/19.28 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (m_Halt(v1) = v0) | ~ $i(v1) | ~
% 141.79/19.28 | $i(v0) | pidElem(v0))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (axiom_61) implies:
% 141.79/19.28 | (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 141.79/19.28 | leq(v1, v0) | ~ leq(v0, v1))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (axiom_63) implies:
% 141.79/19.28 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (s(v1) =
% 141.79/19.28 | v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ leq(v2, v3) |
% 141.79/19.28 | leq(v0, v1))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (axiom_64) implies:
% 141.79/19.28 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v1) = v0) | ~ $i(v1) | ~ $i(v0) |
% 141.79/19.28 | leq(v0, v0))
% 141.79/19.28 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (s(v1) = v2) |
% 141.79/19.28 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v2) | leq(v0, v1))
% 141.79/19.28 |
% 141.79/19.28 | ALPHA: (conj) implies:
% 141.79/19.28 | (11) $i(nbr_proc)
% 141.79/19.30 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 141.79/19.30 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 141.79/19.30 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 141.79/19.30 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ?
% 141.79/19.30 | [v19: $i] : ( ~ (v10 = v4) & ~ (v7 = v4) & index(ldr, v10) = v10 &
% 141.79/19.30 | index(status, v10) = norm & index(status, v7) = elec_2 &
% 141.79/19.30 | index(pendack, v7) = v14 & snoc(v17, v8) = v18 & cons(v6, v1) = v5 &
% 141.79/19.30 | m_Down(v12) = v16 & m_Halt(v3) = v6 & s(v14) = v15 & s(zero) = v0 &
% 141.79/19.30 | m_Ack(v13, v11) = v19 & m_Ack(v3, v2) = v8 & host(v13) = v7 &
% 141.79/19.30 | host(v12) = v15 & host(v11) = v14 & host(v9) = v10 & host(v3) = v7 &
% 141.79/19.30 | host(v2) = v4 & queue(v7) = v17 & queue(v4) = v5 & $i(v19) & $i(v18)
% 141.79/19.30 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 141.79/19.30 | $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 141.79/19.30 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & leq(nbr_proc, v15) &
% 141.79/19.30 | setIn(v13, alive) & setIn(v9, alive) & setIn(v2, alive) & elem(v19,
% 141.79/19.30 | v18) & elem(v16, v18) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 141.79/19.30 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~
% 141.79/19.30 | (m_Down(v22) = v25) | ~ (m_Ack(v23, v21) = v24) | ~ (host(v20) =
% 141.79/19.30 | v26) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~
% 141.79/19.30 | setIn(v23, alive) | ~ setIn(v20, alive) | ? [v27: $i] : ? [v28:
% 141.79/19.30 | $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : ? [v32: $i]
% 141.79/19.30 | : ? [v33: $i] : ? [v34: $i] : ? [v35: $i] : (( ~ (v35 = norm) &
% 141.79/19.30 | index(status, v26) = v35 & $i(v35)) | ( ~ (v34 = v26) &
% 141.79/19.30 | index(ldr, v26) = v34 & $i(v34)) | (host(v23) = v27 & $i(v27)
% 141.79/19.30 | & (( ~ (v33 = v30) & index(pendack, v27) = v29 & s(v29) = v30
% 141.79/19.30 | & host(v22) = v33 & $i(v33) & $i(v30) & $i(v29)) | ( ~
% 141.79/19.30 | (v32 = v29) & index(pendack, v27) = v29 & host(v21) = v32
% 141.79/19.30 | & $i(v32) & $i(v29)) | ( ~ (v31 = elec_2) & index(status,
% 141.79/19.30 | v27) = v31 & $i(v31)) | (index(pendack, v27) = v29 &
% 141.79/19.30 | s(v29) = v30 & $i(v30) & $i(v29) & ~ leq(nbr_proc, v30))
% 141.79/19.30 | | (queue(v27) = v28 & $i(v28) & ( ~ elem(v25, v28) | ~
% 141.79/19.30 | elem(v24, v28))))))) & ! [v20: $i] : ! [v21: $i] : !
% 141.79/19.30 | [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26:
% 141.79/19.30 | $i] : ( ~ (m_Down(v22) = v24) | ~ (m_Down(v21) = v25) | ~
% 141.79/19.30 | (host(v23) = nbr_proc) | ~ (host(v20) = v26) | ~ $i(v23) | ~
% 141.79/19.30 | $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v20, alive) | ?
% 141.79/19.30 | [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31:
% 141.79/19.30 | $i] : ? [v32: $i] : ? [v33: $i] : ($i(v33) & (( ~ (v33 = v28)
% 141.79/19.30 | & index(down, nbr_proc) = v27 & host(v22) = v28 & $i(v28) &
% 141.79/19.30 | $i(v27) & leq(v0, v33) & ~ leq(nbr_proc, v33) & ~
% 141.79/19.30 | setIn(v33, v27)) | ( ~ (v31 = elec_1) & index(status,
% 141.79/19.30 | nbr_proc) = v31 & $i(v31)) | ( ~ (v30 = nbr_proc) &
% 141.79/19.30 | host(v21) = v30 & $i(v30)) | (queue(v26) = v32 & $i(v32) &
% 141.79/19.30 | ~ elem(v25, v32)) | (queue(nbr_proc) = v29 & $i(v29) & ~
% 141.79/19.30 | elem(v24, v29))))) & ! [v20: $i] : ! [v21: $i] : ! [v22:
% 141.79/19.30 | $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ( ~
% 141.79/19.30 | (m_Down(v21) = v23) | ~ (host(v22) = v24) | ~ (host(v20) = v25)
% 141.79/19.30 | | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 141.79/19.30 | setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] :
% 141.79/19.30 | ? [v29: $i] : (( ~ (v29 = norm) & index(status, v25) = v29 &
% 141.79/19.30 | $i(v29)) | ( ~ (v28 = v25) & index(ldr, v25) = v28 & $i(v28))
% 141.79/19.30 | | ( ~ (v27 = v25) & host(v21) = v27 & $i(v27)) | (queue(v24) =
% 141.79/19.30 | v26 & $i(v26) & ~ elem(v23, v26)))) & ! [v20: $i] : ! [v21:
% 141.79/19.30 | $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] :
% 141.79/19.30 | ( ~ (m_Halt(v22) = v24) | ~ (host(v21) = v25) | ~ (host(v20) =
% 141.79/19.30 | v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22,
% 141.79/19.30 | alive) | ~ setIn(v20, alive) | ? [v26: $i] : ? [v27: $i] : ?
% 141.79/19.30 | [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] : (( ~ (v31
% 141.79/19.30 | = norm) & index(status, v23) = v31 & $i(v31)) | ( ~ (v30 =
% 141.79/19.30 | v23) & index(ldr, v23) = v30 & $i(v30)) | ( ~ (v29 = elec_2)
% 141.79/19.30 | & index(status, v26) = v29 & host(v22) = v26 & $i(v29) &
% 141.79/19.30 | $i(v26)) | (index(pendack, v26) = v27 & host(v22) = v26 &
% 141.79/19.30 | $i(v27) & $i(v26) & leq(v27, v23)) | (queue(v25) = v28 &
% 141.79/19.30 | $i(v28) & ~ elem(v24, v28)))) & ! [v20: $i] : ! [v21: $i] :
% 141.79/19.30 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ( ~ (m_Ack(v22, v20) =
% 141.79/19.30 | v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~
% 141.79/19.30 | $i(v20) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : ((host(v22)
% 141.79/19.30 | = v27 & host(v20) = v26 & $i(v27) & $i(v26) & ~ leq(v26,
% 141.79/19.30 | v27)) | (queue(v24) = v25 & $i(v25) & ~ elem(v23, v25)))) &
% 141.79/19.30 | ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24:
% 141.79/19.30 | $i] : ( ~ (m_Ack(v20, v21) = v24) | ~ (host(v22) = v23) | ~
% 141.79/19.30 | $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 141.79/19.30 | setIn(v20, alive) | ? [v25: $i] : ? [v26: $i] : ? [v27: $i] :
% 141.79/19.30 | ? [v28: $i] : ? [v29: $i] : (( ~ (v28 = elec_2) & index(status,
% 141.79/19.30 | v23) = v28 & $i(v28)) | ( ~ (v27 = elec_2) & index(status,
% 141.79/19.30 | v26) = v27 & host(v20) = v26 & $i(v27) & $i(v26)) | ( ~ (v25
% 141.79/19.30 | = v23) & host(v21) = v25 & $i(v25)) | (host(v20) = v26 &
% 141.79/19.30 | queue(v26) = v29 & $i(v29) & $i(v26) & ~ elem(v24, v29)))) &
% 141.79/19.30 | ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~
% 141.79/19.30 | (m_Ldr(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~
% 141.79/19.30 | $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 &
% 141.79/19.30 | $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~
% 141.79/19.30 | elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 141.79/19.30 | : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~
% 141.79/19.30 | $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 =
% 141.79/19.30 | v23) & host(v21) = v25 & $i(v25)) | (queue(v23) = v24 &
% 141.79/19.30 | $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] :
% 141.79/19.30 | ! [v22: $i] : ! [v23: $i] : ( ~ (m_Halt(v21) = v22) | ~
% 141.79/19.30 | (host(v20) = v23) | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ?
% 141.79/19.30 | [v25: $i] : ((host(v21) = v25 & $i(v25) & ~ leq(v23, v25)) |
% 141.79/19.30 | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) & ! [v20:
% 141.79/19.30 | $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21)
% 141.79/19.30 | = v23) | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~
% 141.79/19.30 | setIn(v21, alive) | ~ setIn(v20, alive) | leq(v22, v23) | ?
% 141.79/19.30 | [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v25
% 141.79/19.30 | = elec_2) & index(status, v23) = v25 & $i(v25)) | ( ~ (v24 =
% 141.79/19.30 | elec_2) & index(status, v22) = v24 & $i(v24)) |
% 141.79/19.30 | (index(pendack, v23) = v27 & index(pendack, v22) = v26 & $i(v27)
% 141.79/19.30 | & $i(v26) & ~ leq(v26, v27)))) & ! [v20: $i] : ! [v21: $i]
% 141.79/19.30 | : ! [v22: $i] : ! [v23: $i] : ( ~ (host(v21) = v23) | ~
% 141.79/19.30 | (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive)
% 141.79/19.30 | | ~ setIn(v20, alive) | leq(v22, v23) | ? [v24: $i] : ? [v25:
% 141.79/19.30 | $i] : ? [v26: $i] : (( ~ (v25 = elec_2) & index(status, v23) =
% 141.79/19.30 | v25 & $i(v25)) | ( ~ (v24 = elec_2) & index(status, v22) = v24
% 141.79/19.30 | & $i(v24)) | (index(pendack, v23) = v26 & $i(v26) & leq(v26,
% 141.79/19.30 | v22)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (v21
% 141.79/19.30 | = v20 | ~ (host(v21) = v22) | ~ (host(v20) = v22) | ~ $i(v21) |
% 141.79/19.30 | ~ $i(v20) | ~ setIn(v21, alive) | ~ setIn(v20, alive)) & !
% 141.79/19.30 | [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v21, v20) =
% 141.79/19.30 | v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ? [v23:
% 141.79/19.30 | $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : (host(v21) =
% 141.79/19.30 | v23 & $i(v23) & ((index(pendack, v23) = v26 & host(v20) = v25 &
% 141.79/19.30 | $i(v26) & $i(v25) & leq(v25, v26)) | (queue(v23) = v24 &
% 141.79/19.30 | $i(v24) & ~ elem(v22, v24))))) & ! [v20: $i] : ! [v21:
% 141.79/19.30 | $i] : ! [v22: $i] : ( ~ (m_Ack(v21, v20) = v22) | ~ $i(v21) | ~
% 141.79/19.30 | $i(v20) | ~ setIn(v21, alive) | ? [v23: $i] : ? [v24: $i] : ?
% 141.79/19.30 | [v25: $i] : (host(v21) = v23 & $i(v23) & (( ~ (v24 = elec_1) &
% 141.79/19.30 | index(status, v23) = v24 & $i(v24)) | (queue(v23) = v25 &
% 141.79/19.30 | $i(v25) & ~ elem(v22, v25))))) & ! [v20: $i] : ! [v21:
% 141.79/19.30 | $i] : ( ~ (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) |
% 141.79/19.30 | ? [v22: $i] : ? [v23: $i] : ((v23 = v20 & index(elid, v21) = v20)
% 141.79/19.30 | | ( ~ (v22 = elec_1) & ~ (v22 = elec_2) & index(status, v21) =
% 141.79/19.30 | v22 & $i(v22)))))
% 141.79/19.30 |
% 141.79/19.30 | ALPHA: (function-axioms) implies:
% 141.79/19.30 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 141.79/19.30 | v1) | ~ (queue(v2) = v0))
% 141.79/19.30 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) =
% 141.79/19.30 | v1) | ~ (host(v2) = v0))
% 141.79/19.30 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) |
% 141.79/19.30 | ~ (s(v2) = v0))
% 141.79/19.30 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.79/19.30 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 141.79/19.30 |
% 141.79/19.30 | DELTA: instantiating (12) with fresh symbols all_65_0, all_65_1, all_65_2,
% 141.79/19.30 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 141.79/19.30 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 141.79/19.30 | all_65_16, all_65_17, all_65_18, all_65_19 gives:
% 141.94/19.32 | (17) ~ (all_65_9 = all_65_15) & ~ (all_65_12 = all_65_15) & index(ldr,
% 141.94/19.32 | all_65_9) = all_65_9 & index(status, all_65_9) = norm &
% 141.94/19.32 | index(status, all_65_12) = elec_2 & index(pendack, all_65_12) =
% 141.94/19.32 | all_65_5 & snoc(all_65_2, all_65_11) = all_65_1 & cons(all_65_13,
% 141.94/19.32 | all_65_18) = all_65_14 & m_Down(all_65_7) = all_65_3 &
% 141.94/19.32 | m_Halt(all_65_16) = all_65_13 & s(all_65_5) = all_65_4 & s(zero) =
% 141.94/19.32 | all_65_19 & m_Ack(all_65_6, all_65_8) = all_65_0 & m_Ack(all_65_16,
% 141.94/19.32 | all_65_17) = all_65_11 & host(all_65_6) = all_65_12 & host(all_65_7)
% 141.94/19.32 | = all_65_4 & host(all_65_8) = all_65_5 & host(all_65_10) = all_65_9 &
% 141.94/19.32 | host(all_65_16) = all_65_12 & host(all_65_17) = all_65_15 &
% 141.94/19.32 | queue(all_65_12) = all_65_2 & queue(all_65_15) = all_65_14 &
% 141.94/19.32 | $i(all_65_0) & $i(all_65_1) & $i(all_65_2) & $i(all_65_3) &
% 141.94/19.32 | $i(all_65_4) & $i(all_65_5) & $i(all_65_6) & $i(all_65_7) &
% 141.94/19.32 | $i(all_65_8) & $i(all_65_9) & $i(all_65_10) & $i(all_65_11) &
% 141.94/19.32 | $i(all_65_12) & $i(all_65_13) & $i(all_65_14) & $i(all_65_15) &
% 141.94/19.32 | $i(all_65_16) & $i(all_65_17) & $i(all_65_18) & $i(all_65_19) &
% 141.94/19.32 | leq(nbr_proc, all_65_4) & setIn(all_65_6, alive) & setIn(all_65_10,
% 141.94/19.32 | alive) & setIn(all_65_17, alive) & elem(all_65_0, all_65_1) &
% 141.94/19.32 | elem(all_65_3, all_65_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 141.94/19.32 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2)
% 141.94/19.32 | = v5) | ~ (m_Ack(v3, v1) = v4) | ~ (host(v0) = v6) | ~ $i(v3) |
% 141.94/19.32 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v3, alive) | ~
% 141.94/19.32 | setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 141.94/19.32 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 141.94/19.32 | $i] : ? [v15: $i] : (( ~ (v15 = norm) & index(status, v6) = v15 &
% 141.94/19.32 | $i(v15)) | ( ~ (v14 = v6) & index(ldr, v6) = v14 & $i(v14)) |
% 141.94/19.32 | (host(v3) = v7 & $i(v7) & (( ~ (v13 = v10) & index(pendack, v7) =
% 141.94/19.32 | v9 & s(v9) = v10 & host(v2) = v13 & $i(v13) & $i(v10) &
% 141.94/19.32 | $i(v9)) | ( ~ (v12 = v9) & index(pendack, v7) = v9 &
% 141.94/19.32 | host(v1) = v12 & $i(v12) & $i(v9)) | ( ~ (v11 = elec_2) &
% 141.94/19.32 | index(status, v7) = v11 & $i(v11)) | (index(pendack, v7) =
% 141.94/19.32 | v9 & s(v9) = v10 & $i(v10) & $i(v9) & ~ leq(nbr_proc, v10))
% 141.94/19.32 | | (queue(v7) = v8 & $i(v8) & ( ~ elem(v5, v8) | ~ elem(v4,
% 141.94/19.32 | v8))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 141.94/19.32 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) =
% 141.94/19.32 | v4) | ~ (m_Down(v1) = v5) | ~ (host(v3) = nbr_proc) | ~
% 141.94/19.32 | (host(v0) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 141.94/19.32 | setIn(v0, alive) | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 141.94/19.32 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ($i(v13) &
% 141.94/19.32 | (( ~ (v13 = v8) & index(down, nbr_proc) = v7 & host(v2) = v8 &
% 141.94/19.32 | $i(v8) & $i(v7) & leq(all_65_19, v13) & ~ leq(nbr_proc, v13)
% 141.94/19.32 | & ~ setIn(v13, v7)) | ( ~ (v11 = elec_1) & index(status,
% 141.94/19.32 | nbr_proc) = v11 & $i(v11)) | ( ~ (v10 = nbr_proc) & host(v1)
% 141.94/19.32 | = v10 & $i(v10)) | (queue(v6) = v12 & $i(v12) & ~ elem(v5,
% 141.94/19.32 | v12)) | (queue(nbr_proc) = v9 & $i(v9) & ~ elem(v4, v9)))))
% 141.94/19.32 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 141.94/19.32 | : ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~
% 141.94/19.32 | (host(v0) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2,
% 141.94/19.32 | alive) | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8:
% 141.94/19.32 | $i] : ? [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 &
% 141.94/19.32 | $i(v9)) | ( ~ (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~
% 141.94/19.32 | (v7 = v5) & host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) &
% 141.94/19.32 | ~ elem(v3, v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 141.94/19.32 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~
% 141.94/19.32 | (host(v1) = v5) | ~ (host(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 141.94/19.32 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v6: $i] :
% 141.94/19.32 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i]
% 141.94/19.32 | : (( ~ (v11 = norm) & index(status, v3) = v11 & $i(v11)) | ( ~ (v10
% 141.94/19.32 | = v3) & index(ldr, v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) &
% 141.94/19.32 | index(status, v6) = v9 & host(v2) = v6 & $i(v9) & $i(v6)) |
% 141.94/19.32 | (index(pendack, v6) = v7 & host(v2) = v6 & $i(v7) & $i(v6) &
% 141.94/19.32 | leq(v7, v3)) | (queue(v5) = v8 & $i(v8) & ~ elem(v4, v8)))) &
% 141.94/19.32 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 141.94/19.32 | ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1)
% 141.94/19.32 | | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) =
% 141.94/19.32 | v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) |
% 141.94/19.32 | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) & ! [v0: $i] : !
% 141.94/19.32 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (m_Ack(v0,
% 141.94/19.32 | v1) = v4) | ~ (host(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 141.94/19.32 | $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v5: $i] :
% 141.94/19.32 | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v8 =
% 141.94/19.32 | elec_2) & index(status, v3) = v8 & $i(v8)) | ( ~ (v7 = elec_2)
% 141.94/19.32 | & index(status, v6) = v7 & host(v0) = v6 & $i(v7) & $i(v6)) | (
% 141.94/19.32 | ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | (host(v0) = v6 &
% 141.94/19.32 | queue(v6) = v9 & $i(v9) & $i(v6) & ~ elem(v4, v9)))) & ! [v0:
% 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2)
% 141.94/19.32 | | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 141.94/19.32 | $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4
% 141.94/19.32 | & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : !
% 141.94/19.32 | [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) |
% 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) &
% 141.94/19.32 | host(v1) = v5 & $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2,
% 141.94/19.32 | v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 141.94/19.32 | : ( ~ (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) |
% 141.94/19.32 | ? [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3,
% 141.94/19.32 | v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0:
% 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = v3)
% 141.94/19.32 | | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) |
% 141.94/19.32 | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5: $i] : ?
% 141.94/19.32 | [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5
% 141.94/19.32 | & $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4))
% 141.94/19.32 | | (index(pendack, v3) = v7 & index(pendack, v2) = v6 & $i(v7) &
% 141.94/19.32 | $i(v6) & ~ leq(v6, v7)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.94/19.32 | $i] : ! [v3: $i] : ( ~ (host(v1) = v3) | ~ (host(v0) = v2) | ~
% 141.94/19.32 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive) |
% 141.94/19.32 | leq(v2, v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (( ~ (v5 =
% 141.94/19.32 | elec_2) & index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2)
% 141.94/19.32 | & index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v6 &
% 141.94/19.32 | $i(v6) & leq(v6, v2)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 141.94/19.32 | $i] : (v1 = v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1)
% 141.94/19.32 | | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0:
% 141.94/19.32 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) | ~
% 141.94/19.32 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: $i]
% 141.94/19.32 | : ? [v5: $i] : ? [v6: $i] : (host(v1) = v3 & $i(v3) &
% 141.94/19.32 | ((index(pendack, v3) = v6 & host(v0) = v5 & $i(v6) & $i(v5) &
% 141.94/19.32 | leq(v5, v6)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))))
% 141.94/19.32 | & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) |
% 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4:
% 141.94/19.32 | $i] : ? [v5: $i] : (host(v1) = v3 & $i(v3) & (( ~ (v4 = elec_1) &
% 141.94/19.32 | index(status, v3) = v4 & $i(v4)) | (queue(v3) = v5 & $i(v5) &
% 141.94/19.32 | ~ elem(v2, v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0)
% 141.94/19.32 | = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ? [v3:
% 141.94/19.32 | $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) & ~
% 141.94/19.32 | (v2 = elec_2) & index(status, v1) = v2 & $i(v2))))
% 141.94/19.32 |
% 141.94/19.32 | ALPHA: (17) implies:
% 141.94/19.32 | (18) ~ (all_65_9 = all_65_15)
% 141.94/19.32 | (19) elem(all_65_3, all_65_1)
% 141.94/19.32 | (20) elem(all_65_0, all_65_1)
% 141.94/19.32 | (21) setIn(all_65_17, alive)
% 141.94/19.32 | (22) setIn(all_65_10, alive)
% 141.94/19.32 | (23) setIn(all_65_6, alive)
% 141.94/19.32 | (24) leq(nbr_proc, all_65_4)
% 141.94/19.32 | (25) $i(all_65_18)
% 141.94/19.32 | (26) $i(all_65_17)
% 141.94/19.32 | (27) $i(all_65_16)
% 141.94/19.32 | (28) $i(all_65_15)
% 141.94/19.32 | (29) $i(all_65_13)
% 141.94/19.32 | (30) $i(all_65_11)
% 141.94/19.32 | (31) $i(all_65_10)
% 141.94/19.32 | (32) $i(all_65_9)
% 141.94/19.32 | (33) $i(all_65_8)
% 141.94/19.32 | (34) $i(all_65_7)
% 141.94/19.32 | (35) $i(all_65_6)
% 141.94/19.32 | (36) $i(all_65_5)
% 141.94/19.32 | (37) $i(all_65_4)
% 141.94/19.32 | (38) $i(all_65_3)
% 141.94/19.32 | (39) $i(all_65_2)
% 141.94/19.32 | (40) $i(all_65_0)
% 141.94/19.32 | (41) queue(all_65_15) = all_65_14
% 141.94/19.32 | (42) queue(all_65_12) = all_65_2
% 141.94/19.32 | (43) host(all_65_17) = all_65_15
% 141.94/19.32 | (44) host(all_65_16) = all_65_12
% 141.94/19.32 | (45) host(all_65_10) = all_65_9
% 141.94/19.32 | (46) host(all_65_8) = all_65_5
% 141.94/19.32 | (47) host(all_65_7) = all_65_4
% 141.94/19.32 | (48) host(all_65_6) = all_65_12
% 141.94/19.32 | (49) m_Ack(all_65_16, all_65_17) = all_65_11
% 141.94/19.32 | (50) m_Ack(all_65_6, all_65_8) = all_65_0
% 141.94/19.32 | (51) s(all_65_5) = all_65_4
% 141.94/19.32 | (52) m_Halt(all_65_16) = all_65_13
% 141.94/19.32 | (53) m_Down(all_65_7) = all_65_3
% 141.94/19.32 | (54) cons(all_65_13, all_65_18) = all_65_14
% 141.94/19.32 | (55) snoc(all_65_2, all_65_11) = all_65_1
% 141.94/19.32 | (56) index(pendack, all_65_12) = all_65_5
% 141.94/19.32 | (57) index(status, all_65_12) = elec_2
% 141.94/19.32 | (58) index(status, all_65_9) = norm
% 141.94/19.32 | (59) index(ldr, all_65_9) = all_65_9
% 141.94/19.32 | (60) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) |
% 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4:
% 141.94/19.32 | $i] : ? [v5: $i] : (host(v1) = v3 & $i(v3) & (( ~ (v4 = elec_1) &
% 141.94/19.32 | index(status, v3) = v4 & $i(v4)) | (queue(v3) = v5 & $i(v5) &
% 141.94/19.32 | ~ elem(v2, v5)))))
% 141.94/19.32 | (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Ack(v1, v0) = v2) |
% 141.94/19.32 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4:
% 141.94/19.32 | $i] : ? [v5: $i] : ? [v6: $i] : (host(v1) = v3 & $i(v3) &
% 141.94/19.32 | ((index(pendack, v3) = v6 & host(v0) = v5 & $i(v6) & $i(v5) &
% 141.94/19.32 | leq(v5, v6)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4)))))
% 141.94/19.33 | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1)
% 141.94/19.33 | = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 141.94/19.33 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5:
% 141.94/19.33 | $i] : ? [v6: $i] : (( ~ (v5 = elec_2) & index(status, v3) = v5 &
% 141.94/19.33 | $i(v5)) | ( ~ (v4 = elec_2) & index(status, v2) = v4 & $i(v4)) |
% 141.94/19.33 | (index(pendack, v3) = v6 & $i(v6) & leq(v6, v2))))
% 141.94/19.33 | (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1)
% 141.94/19.33 | = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 141.94/19.33 | alive) | ~ setIn(v0, alive) | leq(v2, v3) | ? [v4: $i] : ? [v5:
% 141.94/19.33 | $i] : ? [v6: $i] : ? [v7: $i] : (( ~ (v5 = elec_2) &
% 141.94/19.33 | index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) &
% 141.94/19.33 | index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v7 &
% 141.94/19.33 | index(pendack, v2) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7))))
% 141.94/19.33 | (64) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 141.94/19.33 | (m_Halt(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 141.94/19.33 | [v4: $i] : ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5))
% 141.94/19.33 | | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))
% 142.05/19.33 | (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 142.05/19.33 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 142.05/19.33 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) |
% 142.05/19.33 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))
% 142.05/19.33 | (66) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 142.05/19.33 | ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~ $i(v2) | ~ $i(v1)
% 142.05/19.33 | | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((host(v2) =
% 142.05/19.33 | v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~ leq(v6, v7)) |
% 142.05/19.33 | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5))))
% 142.05/19.33 | (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 142.05/19.33 | ! [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0)
% 142.05/19.33 | = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) |
% 142.05/19.33 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 142.05/19.33 | [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) &
% 142.05/19.33 | index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr,
% 142.05/19.33 | v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) =
% 142.05/19.33 | v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7
% 142.05/19.33 | & host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) =
% 142.05/19.33 | v8 & $i(v8) & ~ elem(v4, v8))))
% 142.05/19.33 | (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 142.05/19.33 | ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v4) | ~ (host(v0)
% 142.05/19.33 | = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) |
% 142.05/19.33 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 142.05/19.33 | [v9: $i] : (( ~ (v9 = norm) & index(status, v5) = v9 & $i(v9)) | ( ~
% 142.05/19.33 | (v8 = v5) & index(ldr, v5) = v8 & $i(v8)) | ( ~ (v7 = v5) &
% 142.05/19.33 | host(v1) = v7 & $i(v7)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3,
% 142.05/19.33 | v6))))
% 142.05/19.33 | (69) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 142.05/19.33 | ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v5) | ~ (m_Ack(v3, v1) =
% 142.05/19.33 | v4) | ~ (host(v0) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 142.05/19.33 | $i(v0) | ~ setIn(v3, alive) | ~ setIn(v0, alive) | ? [v7: $i] :
% 142.05/19.33 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12:
% 142.05/19.33 | $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : (( ~ (v15 =
% 142.05/19.33 | norm) & index(status, v6) = v15 & $i(v15)) | ( ~ (v14 = v6) &
% 142.05/19.33 | index(ldr, v6) = v14 & $i(v14)) | (host(v3) = v7 & $i(v7) & (( ~
% 142.05/19.33 | (v13 = v10) & index(pendack, v7) = v9 & s(v9) = v10 &
% 142.05/19.33 | host(v2) = v13 & $i(v13) & $i(v10) & $i(v9)) | ( ~ (v12 =
% 142.05/19.33 | v9) & index(pendack, v7) = v9 & host(v1) = v12 & $i(v12) &
% 142.05/19.33 | $i(v9)) | ( ~ (v11 = elec_2) & index(status, v7) = v11 &
% 142.05/19.33 | $i(v11)) | (index(pendack, v7) = v9 & s(v9) = v10 & $i(v10)
% 142.05/19.33 | & $i(v9) & ~ leq(nbr_proc, v10)) | (queue(v7) = v8 & $i(v8)
% 142.05/19.33 | & ( ~ elem(v5, v8) | ~ elem(v4, v8)))))))
% 142.05/19.33 |
% 142.05/19.33 | GROUND_INST: instantiating (63) with all_65_17, all_65_10, all_65_15,
% 142.05/19.33 | all_65_9, simplifying with (21), (22), (26), (31), (43), (45)
% 142.05/19.33 | gives:
% 142.05/19.34 | (70) leq(all_65_15, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 &
% 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_15) = v0 &
% 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v3 & index(pendack,
% 142.05/19.34 | all_65_15) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_10, all_65_17, all_65_9,
% 142.05/19.34 | all_65_15, simplifying with (21), (22), (26), (31), (43), (45)
% 142.05/19.34 | gives:
% 142.05/19.34 | (71) leq(all_65_9, all_65_15) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_15) = v1 &
% 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_9) = v0 &
% 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v2 & index(pendack,
% 142.05/19.34 | all_65_15) = v3 & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_10, all_65_17, all_65_9,
% 142.05/19.34 | all_65_15, simplifying with (21), (22), (26), (31), (43), (45)
% 142.05/19.34 | gives:
% 142.05/19.34 | (72) leq(all_65_9, all_65_15) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_15) = v1 & $i(v1)) | ( ~ (v0
% 142.05/19.34 | = elec_2) & index(status, all_65_9) = v0 & $i(v0)) |
% 142.05/19.34 | (index(pendack, all_65_15) = v2 & $i(v2) & leq(v2, all_65_9)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (1) with all_65_10, all_65_9, simplifying with
% 142.05/19.34 | (31), (45) gives:
% 142.05/19.34 | (73) leq(all_65_9, nbr_proc)
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (axiom_01) with all_65_8, all_65_8, all_65_5,
% 142.05/19.34 | simplifying with (33), (46) gives:
% 142.05/19.34 | (74) ? [v0: any] : ( ~ (v0 = all_65_5) & s(all_65_5) = v0 & $i(v0))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (1) with all_65_7, all_65_4, simplifying with (34),
% 142.05/19.34 | (47) gives:
% 142.05/19.34 | (75) leq(all_65_4, nbr_proc)
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_6, all_65_6, all_65_12, all_65_12,
% 142.05/19.34 | simplifying with (23), (35), (48) gives:
% 142.05/19.34 | (76) leq(all_65_12, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 &
% 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_12) = v0 &
% 142.05/19.34 | $i(v0)) | (index(pendack, all_65_12) = v3 & index(pendack,
% 142.05/19.34 | all_65_12) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_6, all_65_6, all_65_12, all_65_12,
% 142.05/19.34 | simplifying with (23), (35), (48) gives:
% 142.05/19.34 | (77) leq(all_65_12, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 & $i(v1)) | ( ~ (v0
% 142.05/19.34 | = elec_2) & index(status, all_65_12) = v0 & $i(v0)) |
% 142.05/19.34 | (index(pendack, all_65_12) = v2 & $i(v2) & leq(v2, all_65_12)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_10, all_65_6, all_65_9, all_65_12,
% 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives:
% 142.05/19.34 | (78) leq(all_65_9, all_65_12) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 &
% 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_9) = v0 &
% 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v2 & index(pendack,
% 142.05/19.34 | all_65_12) = v3 & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (63) with all_65_6, all_65_10, all_65_12, all_65_9,
% 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives:
% 142.05/19.34 | (79) leq(all_65_12, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | ? [v3: $i] : (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 &
% 142.05/19.34 | $i(v1)) | ( ~ (v0 = elec_2) & index(status, all_65_12) = v0 &
% 142.05/19.34 | $i(v0)) | (index(pendack, all_65_9) = v3 & index(pendack,
% 142.05/19.34 | all_65_12) = v2 & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (62) with all_65_6, all_65_10, all_65_12, all_65_9,
% 142.05/19.34 | simplifying with (22), (23), (31), (35), (45), (48) gives:
% 142.05/19.34 | (80) leq(all_65_12, all_65_9) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 142.05/19.34 | (( ~ (v1 = elec_2) & index(status, all_65_9) = v1 & $i(v1)) | ( ~ (v0
% 142.05/19.34 | = elec_2) & index(status, all_65_12) = v0 & $i(v0)) |
% 142.05/19.34 | (index(pendack, all_65_9) = v2 & $i(v2) & leq(v2, all_65_12)))
% 142.05/19.34 |
% 142.05/19.34 | GROUND_INST: instantiating (66) with all_65_8, all_65_7, all_65_6, all_65_0,
% 142.05/19.34 | all_65_4, simplifying with (33), (34), (35), (47), (50) gives:
% 142.05/19.35 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((host(all_65_6) = v2 &
% 142.05/19.35 | host(all_65_8) = v1 & $i(v2) & $i(v1) & ~ leq(v1, v2)) |
% 142.05/19.35 | (queue(all_65_4) = v0 & $i(v0) & ~ elem(all_65_0, v0)))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (61) with all_65_8, all_65_6, all_65_0, simplifying
% 142.05/19.35 | with (23), (33), (35), (50) gives:
% 142.05/19.35 | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 142.05/19.35 | (host(all_65_6) = v0 & $i(v0) & ((index(pendack, v0) = v3 &
% 142.05/19.35 | host(all_65_8) = v2 & $i(v3) & $i(v2) & leq(v2, v3)) |
% 142.05/19.35 | (queue(v0) = v1 & $i(v1) & ~ elem(all_65_0, v1))))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (60) with all_65_8, all_65_6, all_65_0, simplifying
% 142.05/19.35 | with (23), (33), (35), (50) gives:
% 142.05/19.35 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (host(all_65_6) = v0 &
% 142.05/19.35 | $i(v0) & (( ~ (v1 = elec_1) & index(status, v0) = v1 & $i(v1)) |
% 142.05/19.35 | (queue(v0) = v2 & $i(v2) & ~ elem(all_65_0, v2))))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (9) with all_65_4, all_65_5, simplifying with (36),
% 142.05/19.35 | (37), (51) gives:
% 142.05/19.35 | (84) leq(all_65_4, all_65_4)
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (64) with all_65_17, all_65_16, all_65_13,
% 142.05/19.35 | all_65_15, simplifying with (26), (27), (43), (52) gives:
% 142.05/19.35 | (85) ? [v0: $i] : ? [v1: $i] : ((host(all_65_16) = v1 & $i(v1) & ~
% 142.05/19.35 | leq(all_65_15, v1)) | (queue(all_65_15) = v0 & $i(v0) & ~
% 142.05/19.35 | elem(all_65_13, v0)))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (6) with all_65_13, all_65_16, simplifying with
% 142.05/19.35 | (27), (29), (52) gives:
% 142.05/19.35 | (86) pidElem(all_65_13)
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (69) with all_65_10, all_65_8, all_65_7, all_65_6,
% 142.05/19.35 | all_65_0, all_65_3, all_65_9, simplifying with (22), (23), (31),
% 142.05/19.35 | (33), (34), (35), (45), (50), (53) gives:
% 142.05/19.35 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 142.05/19.35 | ? [v5: $i] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : (( ~ (v8 =
% 142.05/19.35 | norm) & index(status, all_65_9) = v8 & $i(v8)) | ( ~ (v7 =
% 142.05/19.35 | all_65_9) & index(ldr, all_65_9) = v7 & $i(v7)) |
% 142.05/19.35 | (host(all_65_6) = v0 & $i(v0) & (( ~ (v6 = v3) & index(pendack, v0)
% 142.05/19.35 | = v2 & s(v2) = v3 & host(all_65_7) = v6 & $i(v6) & $i(v3) &
% 142.05/19.35 | $i(v2)) | ( ~ (v5 = v2) & index(pendack, v0) = v2 &
% 142.05/19.35 | host(all_65_8) = v5 & $i(v5) & $i(v2)) | ( ~ (v4 = elec_2) &
% 142.05/19.35 | index(status, v0) = v4 & $i(v4)) | (index(pendack, v0) = v2 &
% 142.05/19.35 | s(v2) = v3 & $i(v3) & $i(v2) & ~ leq(nbr_proc, v3)) |
% 142.05/19.35 | (queue(v0) = v1 & $i(v1) & ( ~ elem(all_65_0, v1) | ~
% 142.05/19.35 | elem(all_65_3, v1))))))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (68) with all_65_10, all_65_7, all_65_6, all_65_3,
% 142.05/19.35 | all_65_12, all_65_9, simplifying with (22), (23), (31), (34),
% 142.05/19.35 | (35), (45), (48), (53) gives:
% 142.05/19.35 | (88) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: $i] : (( ~ (v3 =
% 142.05/19.35 | norm) & index(status, all_65_9) = v3 & $i(v3)) | ( ~ (v2 =
% 142.05/19.35 | all_65_9) & index(ldr, all_65_9) = v2 & $i(v2)) | ( ~ (v1 =
% 142.05/19.35 | all_65_9) & host(all_65_7) = v1 & $i(v1)) | (queue(all_65_12) =
% 142.05/19.35 | v0 & $i(v0) & ~ elem(all_65_3, v0)))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (65) with all_65_16, all_65_7, all_65_3, all_65_12,
% 142.05/19.35 | simplifying with (27), (34), (44), (53) gives:
% 142.05/19.35 | (89) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_12) & host(all_65_7) =
% 142.05/19.35 | v1 & $i(v1)) | (queue(all_65_12) = v0 & $i(v0) & ~ elem(all_65_3,
% 142.05/19.35 | v0)))
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (3) with all_65_13, all_65_18, all_65_14,
% 142.05/19.35 | simplifying with (25), (29), (54) gives:
% 142.05/19.35 | (90) elem(all_65_13, all_65_14)
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (4) with all_65_0, all_65_11, all_65_2, all_65_1,
% 142.05/19.35 | simplifying with (20), (30), (39), (40), (55) gives:
% 142.05/19.35 | (91) all_65_0 = all_65_11 | elem(all_65_0, all_65_2)
% 142.05/19.35 |
% 142.05/19.35 | GROUND_INST: instantiating (4) with all_65_3, all_65_11, all_65_2, all_65_1,
% 142.05/19.35 | simplifying with (19), (30), (38), (39), (55) gives:
% 142.05/19.35 | (92) all_65_3 = all_65_11 | elem(all_65_3, all_65_2)
% 142.05/19.35 |
% 142.05/19.35 | DELTA: instantiating (74) with fresh symbol all_84_0 gives:
% 142.05/19.35 | (93) ~ (all_84_0 = all_65_5) & s(all_65_5) = all_84_0 & $i(all_84_0)
% 142.05/19.35 |
% 142.05/19.35 | ALPHA: (93) implies:
% 142.05/19.35 | (94) $i(all_84_0)
% 142.05/19.35 | (95) s(all_65_5) = all_84_0
% 142.05/19.35 |
% 142.05/19.35 | DELTA: instantiating (89) with fresh symbols all_96_0, all_96_1 gives:
% 142.05/19.35 | (96) ( ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 & $i(all_96_0))
% 142.05/19.35 | | (queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3,
% 142.05/19.35 | all_96_1))
% 142.05/19.35 |
% 142.05/19.35 | DELTA: instantiating (85) with fresh symbols all_97_0, all_97_1 gives:
% 142.05/19.35 | (97) (host(all_65_16) = all_97_0 & $i(all_97_0) & ~ leq(all_65_15,
% 142.05/19.35 | all_97_0)) | (queue(all_65_15) = all_97_1 & $i(all_97_1) & ~
% 142.05/19.35 | elem(all_65_13, all_97_1))
% 142.05/19.35 |
% 142.05/19.35 | DELTA: instantiating (83) with fresh symbols all_105_0, all_105_1, all_105_2
% 142.05/19.35 | gives:
% 142.05/19.35 | (98) host(all_65_6) = all_105_2 & $i(all_105_2) & (( ~ (all_105_1 = elec_1)
% 142.05/19.35 | & index(status, all_105_2) = all_105_1 & $i(all_105_1)) |
% 142.05/19.35 | (queue(all_105_2) = all_105_0 & $i(all_105_0) & ~ elem(all_65_0,
% 142.05/19.35 | all_105_0)))
% 142.05/19.35 |
% 142.05/19.35 | ALPHA: (98) implies:
% 142.05/19.35 | (99) host(all_65_6) = all_105_2
% 142.05/19.36 | (100) ( ~ (all_105_1 = elec_1) & index(status, all_105_2) = all_105_1 &
% 142.05/19.36 | $i(all_105_1)) | (queue(all_105_2) = all_105_0 & $i(all_105_0) & ~
% 142.05/19.36 | elem(all_65_0, all_105_0))
% 142.05/19.36 |
% 142.05/19.36 | DELTA: instantiating (81) with fresh symbols all_107_0, all_107_1, all_107_2
% 142.05/19.36 | gives:
% 142.05/19.36 | (101) (host(all_65_6) = all_107_0 & host(all_65_8) = all_107_1 &
% 142.05/19.36 | $i(all_107_0) & $i(all_107_1) & ~ leq(all_107_1, all_107_0)) |
% 142.05/19.36 | (queue(all_65_4) = all_107_2 & $i(all_107_2) & ~ elem(all_65_0,
% 142.05/19.36 | all_107_2))
% 142.05/19.36 |
% 142.05/19.36 | DELTA: instantiating (82) with fresh symbols all_113_0, all_113_1, all_113_2,
% 142.05/19.36 | all_113_3 gives:
% 142.05/19.36 | (102) host(all_65_6) = all_113_3 & $i(all_113_3) & ((index(pendack,
% 142.05/19.36 | all_113_3) = all_113_0 & host(all_65_8) = all_113_1 &
% 142.05/19.36 | $i(all_113_0) & $i(all_113_1) & leq(all_113_1, all_113_0)) |
% 142.05/19.36 | (queue(all_113_3) = all_113_2 & $i(all_113_2) & ~ elem(all_65_0,
% 142.05/19.36 | all_113_2)))
% 142.05/19.36 |
% 142.05/19.36 | ALPHA: (102) implies:
% 142.05/19.36 | (103) host(all_65_6) = all_113_3
% 142.05/19.36 |
% 142.05/19.36 | DELTA: instantiating (88) with fresh symbols all_123_0, all_123_1, all_123_2,
% 142.05/19.36 | all_123_3 gives:
% 142.05/19.36 | (104) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0 &
% 142.05/19.36 | $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr, all_65_9)
% 142.05/19.36 | = all_123_1 & $i(all_123_1)) | ( ~ (all_123_2 = all_65_9) &
% 142.05/19.36 | host(all_65_7) = all_123_2 & $i(all_123_2)) | (queue(all_65_12) =
% 142.05/19.36 | all_123_3 & $i(all_123_3) & ~ elem(all_65_3, all_123_3))
% 142.05/19.36 |
% 142.05/19.36 | DELTA: instantiating (87) with fresh symbols all_128_0, all_128_1, all_128_2,
% 142.05/19.36 | all_128_3, all_128_4, all_128_5, all_128_6, all_128_7, all_128_8 gives:
% 142.05/19.36 | (105) ( ~ (all_128_0 = norm) & index(status, all_65_9) = all_128_0 &
% 142.05/19.36 | $i(all_128_0)) | ( ~ (all_128_1 = all_65_9) & index(ldr, all_65_9)
% 142.05/19.36 | = all_128_1 & $i(all_128_1)) | (host(all_65_6) = all_128_8 &
% 142.05/19.36 | $i(all_128_8) & (( ~ (all_128_2 = all_128_5) & index(pendack,
% 142.05/19.36 | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 &
% 142.05/19.36 | host(all_65_7) = all_128_2 & $i(all_128_2) & $i(all_128_5) &
% 142.05/19.36 | $i(all_128_6)) | ( ~ (all_128_3 = all_128_6) & index(pendack,
% 142.05/19.36 | all_128_8) = all_128_6 & host(all_65_8) = all_128_3 &
% 142.05/19.36 | $i(all_128_3) & $i(all_128_6)) | ( ~ (all_128_4 = elec_2) &
% 142.05/19.36 | index(status, all_128_8) = all_128_4 & $i(all_128_4)) |
% 142.05/19.36 | (index(pendack, all_128_8) = all_128_6 & s(all_128_6) = all_128_5
% 142.05/19.36 | & $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, all_128_5))
% 142.05/19.36 | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~
% 142.05/19.36 | elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7)))))
% 142.05/19.36 |
% 142.05/19.36 | BETA: splitting (97) gives:
% 142.05/19.36 |
% 142.05/19.36 | Case 1:
% 142.05/19.36 | |
% 142.05/19.36 | | (106) host(all_65_16) = all_97_0 & $i(all_97_0) & ~ leq(all_65_15,
% 142.05/19.36 | | all_97_0)
% 142.05/19.36 | |
% 142.05/19.36 | | ALPHA: (106) implies:
% 142.05/19.36 | | (107) $i(all_97_0)
% 142.05/19.36 | | (108) host(all_65_16) = all_97_0
% 142.05/19.36 | |
% 142.05/19.36 | | BETA: splitting (105) gives:
% 142.05/19.36 | |
% 142.05/19.36 | | Case 1:
% 142.05/19.36 | | |
% 142.05/19.36 | | | (109) ~ (all_128_0 = norm) & index(status, all_65_9) = all_128_0 &
% 142.05/19.36 | | | $i(all_128_0)
% 142.05/19.36 | | |
% 142.05/19.36 | | | ALPHA: (109) implies:
% 142.05/19.36 | | | (110) ~ (all_128_0 = norm)
% 142.05/19.36 | | | (111) index(status, all_65_9) = all_128_0
% 142.05/19.36 | | |
% 142.05/19.36 | | | GROUND_INST: instantiating (16) with norm, all_128_0, all_65_9, status,
% 142.05/19.36 | | | simplifying with (58), (111) gives:
% 142.05/19.36 | | | (112) all_128_0 = norm
% 142.05/19.36 | | |
% 142.05/19.36 | | | REDUCE: (110), (112) imply:
% 142.05/19.36 | | | (113) $false
% 142.05/19.36 | | |
% 142.05/19.36 | | | CLOSE: (113) is inconsistent.
% 142.05/19.36 | | |
% 142.05/19.36 | | Case 2:
% 142.05/19.36 | | |
% 142.05/19.36 | | | (114) ( ~ (all_128_1 = all_65_9) & index(ldr, all_65_9) = all_128_1 &
% 142.05/19.36 | | | $i(all_128_1)) | (host(all_65_6) = all_128_8 & $i(all_128_8) &
% 142.05/19.36 | | | (( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) =
% 142.05/19.36 | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) =
% 142.05/19.36 | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6))
% 142.05/19.36 | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) =
% 142.05/19.36 | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) &
% 142.05/19.36 | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status,
% 142.05/19.36 | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack,
% 142.05/19.36 | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 &
% 142.05/19.36 | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc,
% 142.05/19.36 | | | all_128_5)) | (queue(all_128_8) = all_128_7 &
% 142.05/19.36 | | | $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~
% 142.05/19.36 | | | elem(all_65_3, all_128_7)))))
% 142.05/19.36 | | |
% 142.05/19.36 | | | BETA: splitting (114) gives:
% 142.05/19.36 | | |
% 142.05/19.36 | | | Case 1:
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | (115) ~ (all_128_1 = all_65_9) & index(ldr, all_65_9) = all_128_1 &
% 142.05/19.36 | | | | $i(all_128_1)
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | ALPHA: (115) implies:
% 142.05/19.36 | | | | (116) ~ (all_128_1 = all_65_9)
% 142.05/19.36 | | | | (117) index(ldr, all_65_9) = all_128_1
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | GROUND_INST: instantiating (16) with all_65_9, all_128_1, all_65_9, ldr,
% 142.05/19.36 | | | | simplifying with (59), (117) gives:
% 142.05/19.36 | | | | (118) all_128_1 = all_65_9
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | REDUCE: (116), (118) imply:
% 142.05/19.36 | | | | (119) $false
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | CLOSE: (119) is inconsistent.
% 142.05/19.36 | | | |
% 142.05/19.36 | | | Case 2:
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | (120) host(all_65_6) = all_128_8 & $i(all_128_8) & (( ~ (all_128_2 =
% 142.05/19.36 | | | | all_128_5) & index(pendack, all_128_8) = all_128_6 &
% 142.05/19.36 | | | | s(all_128_6) = all_128_5 & host(all_65_7) = all_128_2 &
% 142.05/19.36 | | | | $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) | ( ~
% 142.05/19.36 | | | | (all_128_3 = all_128_6) & index(pendack, all_128_8) =
% 142.05/19.36 | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) &
% 142.05/19.36 | | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status,
% 142.05/19.36 | | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack,
% 142.05/19.36 | | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 &
% 142.05/19.36 | | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc,
% 142.05/19.36 | | | | all_128_5)) | (queue(all_128_8) = all_128_7 &
% 142.05/19.36 | | | | $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~
% 142.05/19.36 | | | | elem(all_65_3, all_128_7))))
% 142.05/19.36 | | | |
% 142.05/19.36 | | | | ALPHA: (120) implies:
% 142.05/19.36 | | | | (121) host(all_65_6) = all_128_8
% 142.05/19.37 | | | | (122) ( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) =
% 142.05/19.37 | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6)) |
% 142.05/19.37 | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) &
% 142.05/19.37 | | | | $i(all_128_6)) | ( ~ (all_128_4 = elec_2) & index(status,
% 142.05/19.37 | | | | all_128_8) = all_128_4 & $i(all_128_4)) | (index(pendack,
% 142.05/19.37 | | | | all_128_8) = all_128_6 & s(all_128_6) = all_128_5 &
% 142.05/19.37 | | | | $i(all_128_5) & $i(all_128_6) & ~ leq(nbr_proc, all_128_5))
% 142.05/19.37 | | | | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~
% 142.05/19.37 | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7)))
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_65_12, all_97_0, all_65_16,
% 142.05/19.37 | | | | simplifying with (44), (108) gives:
% 142.05/19.37 | | | | (123) all_97_0 = all_65_12
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_65_12, all_128_8, all_65_6,
% 142.05/19.37 | | | | simplifying with (48), (121) gives:
% 142.05/19.37 | | | | (124) all_128_8 = all_65_12
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_113_3, all_128_8, all_65_6,
% 142.05/19.37 | | | | simplifying with (103), (121) gives:
% 142.05/19.37 | | | | (125) all_128_8 = all_113_3
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | GROUND_INST: instantiating (14) with all_105_2, all_128_8, all_65_6,
% 142.05/19.37 | | | | simplifying with (99), (121) gives:
% 142.05/19.37 | | | | (126) all_128_8 = all_105_2
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | GROUND_INST: instantiating (15) with all_65_4, all_84_0, all_65_5,
% 142.05/19.37 | | | | simplifying with (51), (95) gives:
% 142.05/19.37 | | | | (127) all_84_0 = all_65_4
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | COMBINE_EQS: (124), (125) imply:
% 142.05/19.37 | | | | (128) all_113_3 = all_65_12
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | COMBINE_EQS: (125), (126) imply:
% 142.05/19.37 | | | | (129) all_113_3 = all_105_2
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | COMBINE_EQS: (128), (129) imply:
% 142.05/19.37 | | | | (130) all_105_2 = all_65_12
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | REDUCE: (107), (123) imply:
% 142.05/19.37 | | | | (131) $i(all_65_12)
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | BETA: splitting (122) gives:
% 142.05/19.37 | | | |
% 142.05/19.37 | | | | Case 1:
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | (132) ( ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) =
% 142.05/19.37 | | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6))
% 142.05/19.37 | | | | | | ( ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) &
% 142.05/19.37 | | | | | $i(all_128_6))
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | BETA: splitting (132) gives:
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | Case 1:
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | (133) ~ (all_128_2 = all_128_5) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | | | all_128_6 & s(all_128_6) = all_128_5 & host(all_65_7) =
% 142.05/19.37 | | | | | | all_128_2 & $i(all_128_2) & $i(all_128_5) & $i(all_128_6)
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | ALPHA: (133) implies:
% 142.05/19.37 | | | | | | (134) ~ (all_128_2 = all_128_5)
% 142.05/19.37 | | | | | | (135) host(all_65_7) = all_128_2
% 142.05/19.37 | | | | | | (136) s(all_128_6) = all_128_5
% 142.05/19.37 | | | | | | (137) index(pendack, all_128_8) = all_128_6
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (124), (137) imply:
% 142.05/19.37 | | | | | | (138) index(pendack, all_65_12) = all_128_6
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (14) with all_65_4, all_128_2, all_65_7,
% 142.05/19.37 | | | | | | simplifying with (47), (135) gives:
% 142.05/19.37 | | | | | | (139) all_128_2 = all_65_4
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6, all_65_12,
% 142.05/19.37 | | | | | | pendack, simplifying with (56), (138) gives:
% 142.05/19.37 | | | | | | (140) all_128_6 = all_65_5
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (134), (139) imply:
% 142.05/19.37 | | | | | | (141) ~ (all_128_5 = all_65_4)
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | SIMP: (141) implies:
% 142.05/19.37 | | | | | | (142) ~ (all_128_5 = all_65_4)
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (136), (140) imply:
% 142.05/19.37 | | | | | | (143) s(all_65_5) = all_128_5
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (15) with all_65_4, all_128_5, all_65_5,
% 142.05/19.37 | | | | | | simplifying with (51), (143) gives:
% 142.05/19.37 | | | | | | (144) all_128_5 = all_65_4
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (142), (144) imply:
% 142.05/19.37 | | | | | | (145) $false
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | CLOSE: (145) is inconsistent.
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | Case 2:
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | (146) ~ (all_128_3 = all_128_6) & index(pendack, all_128_8) =
% 142.05/19.37 | | | | | | all_128_6 & host(all_65_8) = all_128_3 & $i(all_128_3) &
% 142.05/19.37 | | | | | | $i(all_128_6)
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | ALPHA: (146) implies:
% 142.05/19.37 | | | | | | (147) ~ (all_128_3 = all_128_6)
% 142.05/19.37 | | | | | | (148) host(all_65_8) = all_128_3
% 142.05/19.37 | | | | | | (149) index(pendack, all_128_8) = all_128_6
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (124), (149) imply:
% 142.05/19.37 | | | | | | (150) index(pendack, all_65_12) = all_128_6
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (14) with all_65_5, all_128_3, all_65_8,
% 142.05/19.37 | | | | | | simplifying with (46), (148) gives:
% 142.05/19.37 | | | | | | (151) all_128_3 = all_65_5
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6, all_65_12,
% 142.05/19.37 | | | | | | pendack, simplifying with (56), (150) gives:
% 142.05/19.37 | | | | | | (152) all_128_6 = all_65_5
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (147), (151), (152) imply:
% 142.05/19.37 | | | | | | (153) $false
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | CLOSE: (153) is inconsistent.
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | End of split
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | Case 2:
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | (154) ( ~ (all_128_4 = elec_2) & index(status, all_128_8) =
% 142.05/19.37 | | | | | all_128_4 & $i(all_128_4)) | (index(pendack, all_128_8) =
% 142.05/19.37 | | | | | all_128_6 & s(all_128_6) = all_128_5 & $i(all_128_5) &
% 142.05/19.37 | | | | | $i(all_128_6) & ~ leq(nbr_proc, all_128_5)) |
% 142.05/19.37 | | | | | (queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~
% 142.05/19.37 | | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3,
% 142.05/19.37 | | | | | all_128_7)))
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | BETA: splitting (154) gives:
% 142.05/19.37 | | | | |
% 142.05/19.37 | | | | | Case 1:
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | (155) ~ (all_128_4 = elec_2) & index(status, all_128_8) =
% 142.05/19.37 | | | | | | all_128_4 & $i(all_128_4)
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | ALPHA: (155) implies:
% 142.05/19.37 | | | | | | (156) ~ (all_128_4 = elec_2)
% 142.05/19.37 | | | | | | (157) index(status, all_128_8) = all_128_4
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (124), (157) imply:
% 142.05/19.37 | | | | | | (158) index(status, all_65_12) = all_128_4
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | GROUND_INST: instantiating (16) with elec_2, all_128_4, all_65_12,
% 142.05/19.37 | | | | | | status, simplifying with (57), (158) gives:
% 142.05/19.37 | | | | | | (159) all_128_4 = elec_2
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | REDUCE: (156), (159) imply:
% 142.05/19.37 | | | | | | (160) $false
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | CLOSE: (160) is inconsistent.
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | Case 2:
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | (161) (index(pendack, all_128_8) = all_128_6 & s(all_128_6) =
% 142.05/19.37 | | | | | | all_128_5 & $i(all_128_5) & $i(all_128_6) & ~
% 142.05/19.37 | | | | | | leq(nbr_proc, all_128_5)) | (queue(all_128_8) = all_128_7
% 142.05/19.37 | | | | | | & $i(all_128_7) & ( ~ elem(all_65_0, all_128_7) | ~
% 142.05/19.37 | | | | | | elem(all_65_3, all_128_7)))
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | BETA: splitting (161) gives:
% 142.05/19.37 | | | | | |
% 142.05/19.37 | | | | | | Case 1:
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | (162) index(pendack, all_128_8) = all_128_6 & s(all_128_6) =
% 142.05/19.37 | | | | | | | all_128_5 & $i(all_128_5) & $i(all_128_6) & ~
% 142.05/19.37 | | | | | | | leq(nbr_proc, all_128_5)
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | ALPHA: (162) implies:
% 142.05/19.37 | | | | | | | (163) ~ leq(nbr_proc, all_128_5)
% 142.05/19.37 | | | | | | | (164) s(all_128_6) = all_128_5
% 142.05/19.37 | | | | | | | (165) index(pendack, all_128_8) = all_128_6
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | REDUCE: (124), (165) imply:
% 142.05/19.37 | | | | | | | (166) index(pendack, all_65_12) = all_128_6
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_128_6,
% 142.05/19.37 | | | | | | | all_65_12, pendack, simplifying with (56), (166)
% 142.05/19.37 | | | | | | | gives:
% 142.05/19.37 | | | | | | | (167) all_128_6 = all_65_5
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | REDUCE: (164), (167) imply:
% 142.05/19.37 | | | | | | | (168) s(all_65_5) = all_128_5
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | GROUND_INST: instantiating (15) with all_65_4, all_128_5,
% 142.05/19.37 | | | | | | | all_65_5, simplifying with (51), (168) gives:
% 142.05/19.37 | | | | | | | (169) all_128_5 = all_65_4
% 142.05/19.37 | | | | | | |
% 142.05/19.37 | | | | | | | REDUCE: (163), (169) imply:
% 142.05/19.38 | | | | | | | (170) ~ leq(nbr_proc, all_65_4)
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | PRED_UNIFY: (24), (170) imply:
% 142.05/19.38 | | | | | | | (171) $false
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | CLOSE: (171) is inconsistent.
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | Case 2:
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | (172) queue(all_128_8) = all_128_7 & $i(all_128_7) & ( ~
% 142.05/19.38 | | | | | | | elem(all_65_0, all_128_7) | ~ elem(all_65_3,
% 142.05/19.38 | | | | | | | all_128_7))
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | ALPHA: (172) implies:
% 142.05/19.38 | | | | | | | (173) queue(all_128_8) = all_128_7
% 142.05/19.38 | | | | | | | (174) ~ elem(all_65_0, all_128_7) | ~ elem(all_65_3,
% 142.05/19.38 | | | | | | | all_128_7)
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | REDUCE: (124), (173) imply:
% 142.05/19.38 | | | | | | | (175) queue(all_65_12) = all_128_7
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | GROUND_INST: instantiating (13) with all_65_2, all_128_7,
% 142.05/19.38 | | | | | | | all_65_12, simplifying with (42), (175) gives:
% 142.05/19.38 | | | | | | | (176) all_128_7 = all_65_2
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | GROUND_INST: instantiating (axiom_62) with all_65_9, nbr_proc,
% 142.05/19.38 | | | | | | | all_65_4, simplifying with (11), (24), (32), (37),
% 142.05/19.38 | | | | | | | (73) gives:
% 142.05/19.38 | | | | | | | (177) leq(all_65_9, all_65_4)
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | GROUND_INST: instantiating (7) with nbr_proc, all_65_4,
% 142.05/19.38 | | | | | | | simplifying with (11), (24), (37), (75) gives:
% 142.05/19.38 | | | | | | | (178) all_65_4 = nbr_proc
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | GROUND_INST: instantiating (8) with all_65_5, all_65_5, all_65_4,
% 142.05/19.38 | | | | | | | all_65_4, simplifying with (36), (51), (84) gives:
% 142.05/19.38 | | | | | | | (179) leq(all_65_5, all_65_5)
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | GROUND_INST: instantiating (5) with all_65_13, simplifying with
% 142.05/19.38 | | | | | | | (29), (86) gives:
% 142.05/19.38 | | | | | | | (180) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ($i(v0) &
% 142.05/19.38 | | | | | | | ((v2 = all_65_13 & m_Down(v0) = all_65_13) | (v1 =
% 142.05/19.38 | | | | | | | all_65_13 & m_Halt(v0) = all_65_13)))
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | DELTA: instantiating (180) with fresh symbols all_174_0,
% 142.05/19.38 | | | | | | | all_174_1, all_174_2 gives:
% 142.05/19.38 | | | | | | | (181) $i(all_174_2) & ((all_174_0 = all_65_13 &
% 142.05/19.38 | | | | | | | m_Down(all_174_2) = all_65_13) | (all_174_1 =
% 142.05/19.38 | | | | | | | all_65_13 & m_Halt(all_174_2) = all_65_13))
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | ALPHA: (181) implies:
% 142.05/19.38 | | | | | | | (182) $i(all_174_2)
% 142.05/19.38 | | | | | | | (183) (all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13) |
% 142.05/19.38 | | | | | | | (all_174_1 = all_65_13 & m_Halt(all_174_2) = all_65_13)
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | REDUCE: (51), (178) imply:
% 142.05/19.38 | | | | | | | (184) s(all_65_5) = nbr_proc
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | REDUCE: (47), (178) imply:
% 142.05/19.38 | | | | | | | (185) host(all_65_7) = nbr_proc
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | BETA: splitting (76) gives:
% 142.05/19.38 | | | | | | |
% 142.05/19.38 | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | |
% 142.05/19.38 | | | | | | | | (186) leq(all_65_12, all_65_12)
% 142.05/19.38 | | | | | | | |
% 142.05/19.38 | | | | | | | | GROUND_INST: instantiating (10) with all_65_9, all_65_5,
% 142.05/19.38 | | | | | | | | nbr_proc, simplifying with (32), (36), (73), (184)
% 142.05/19.38 | | | | | | | | gives:
% 142.05/19.38 | | | | | | | | (187) all_65_9 = nbr_proc | leq(all_65_9, all_65_5)
% 142.05/19.38 | | | | | | | |
% 142.05/19.38 | | | | | | | | BETA: splitting (80) gives:
% 142.05/19.38 | | | | | | | |
% 142.05/19.38 | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | |
% 142.05/19.38 | | | | | | | | | (188) leq(all_65_12, all_65_9)
% 142.05/19.38 | | | | | | | | |
% 142.05/19.38 | | | | | | | | | BETA: splitting (71) gives:
% 142.05/19.38 | | | | | | | | |
% 142.05/19.38 | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | (189) leq(all_65_9, all_65_15)
% 142.05/19.38 | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | BETA: splitting (70) gives:
% 142.05/19.38 | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | (190) leq(all_65_15, all_65_9)
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | REF_CLOSE: (7), (18), (28), (32), (189), (190) are
% 142.05/19.38 | | | | | | | | | | | inconsistent by sub-proof #4.
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | Case 2:
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | (191) ~ leq(all_65_15, all_65_9)
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | BETA: splitting (78) gives:
% 142.05/19.38 | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | (192) leq(all_65_9, all_65_12)
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_65_12, all_65_9,
% 142.05/19.38 | | | | | | | | | | | | simplifying with (32), (131), (188), (192) gives:
% 142.05/19.38 | | | | | | | | | | | | (193) all_65_9 = all_65_12
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | REDUCE: (58), (193) imply:
% 142.05/19.38 | | | | | | | | | | | | (194) index(status, all_65_12) = norm
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, norm, all_65_12,
% 142.05/19.38 | | | | | | | | | | | | status, simplifying with (57), (194) gives:
% 142.05/19.38 | | | | | | | | | | | | (195) norm = elec_2
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | REDUCE: (2), (195) imply:
% 142.05/19.38 | | | | | | | | | | | | (196) $false
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | Case 2:
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | (197) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 142.05/19.38 | | | | | | | | | | | | $i] : (( ~ (v1 = elec_2) & index(status,
% 142.05/19.38 | | | | | | | | | | | | all_65_12) = v1 & $i(v1)) | ( ~ (v0 =
% 142.05/19.38 | | | | | | | | | | | | elec_2) & index(status, all_65_9) = v0 &
% 142.05/19.38 | | | | | | | | | | | | $i(v0)) | (index(pendack, all_65_9) = v2 &
% 142.05/19.38 | | | | | | | | | | | | index(pendack, all_65_12) = v3 & $i(v3) &
% 142.05/19.38 | | | | | | | | | | | | $i(v2) & ~ leq(v2, v3)))
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_254_0,
% 142.05/19.38 | | | | | | | | | | | | all_254_1, all_254_2, all_254_3 gives:
% 142.05/19.38 | | | | | | | | | | | | (198) ( ~ (all_254_2 = elec_2) & index(status,
% 142.05/19.38 | | | | | | | | | | | | all_65_12) = all_254_2 & $i(all_254_2)) | ( ~
% 142.05/19.38 | | | | | | | | | | | | (all_254_3 = elec_2) & index(status, all_65_9) =
% 142.05/19.38 | | | | | | | | | | | | all_254_3 & $i(all_254_3)) | (index(pendack,
% 142.05/19.38 | | | | | | | | | | | | all_65_9) = all_254_1 & index(pendack,
% 142.05/19.38 | | | | | | | | | | | | all_65_12) = all_254_0 & $i(all_254_0) &
% 142.05/19.38 | | | | | | | | | | | | $i(all_254_1) & ~ leq(all_254_1, all_254_0))
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | BETA: splitting (92) gives:
% 142.05/19.38 | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | (199) elem(all_65_3, all_65_2)
% 142.05/19.38 | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | BETA: splitting (174) gives:
% 142.05/19.38 | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | (200) ~ elem(all_65_0, all_128_7)
% 142.05/19.38 | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | REDUCE: (176), (200) imply:
% 142.05/19.38 | | | | | | | | | | | | | | (201) ~ elem(all_65_0, all_65_2)
% 142.05/19.38 | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 142.05/19.38 | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | (202) elem(all_65_0, all_65_2)
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | PRED_UNIFY: (201), (202) imply:
% 142.05/19.38 | | | | | | | | | | | | | | | (203) $false
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | Case 2:
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | (204) all_65_0 = all_65_11
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | REDUCE: (50), (204) imply:
% 142.05/19.38 | | | | | | | | | | | | | | | (205) m_Ack(all_65_6, all_65_8) = all_65_11
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 142.05/19.38 | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | Case 1:
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | | (206) host(all_65_6) = all_107_0 & host(all_65_8) =
% 142.05/19.38 | | | | | | | | | | | | | | | | all_107_1 & $i(all_107_0) & $i(all_107_1) & ~
% 142.05/19.38 | | | | | | | | | | | | | | | | leq(all_107_1, all_107_0)
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 142.05/19.38 | | | | | | | | | | | | | | | | (207) host(all_65_8) = all_107_1
% 142.05/19.38 | | | | | | | | | | | | | | | | (208) host(all_65_6) = all_107_0
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_65_5, all_107_1,
% 142.05/19.38 | | | | | | | | | | | | | | | | all_65_8, simplifying with (46), (207) gives:
% 142.05/19.38 | | | | | | | | | | | | | | | | (209) all_107_1 = all_65_5
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_65_12, all_107_0,
% 142.05/19.38 | | | | | | | | | | | | | | | | all_65_6, simplifying with (48), (208) gives:
% 142.05/19.38 | | | | | | | | | | | | | | | | (210) all_107_0 = all_65_12
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.38 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6,
% 142.05/19.38 | | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with
% 142.05/19.38 | | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (205) gives:
% 142.05/19.38 | | | | | | | | | | | | | | | | (211) all_65_8 = all_65_17
% 142.05/19.38 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31),
% 142.05/19.39 | | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49),
% 142.05/19.39 | | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (67), (90), (191),
% 142.05/19.39 | | | | | | | | | | | | | | | | (198), (205), (211), (axiom_31) are inconsistent
% 142.05/19.39 | | | | | | | | | | | | | | | | by sub-proof #3.
% 142.05/19.39 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6,
% 142.05/19.39 | | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with
% 142.05/19.39 | | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (205) gives:
% 142.05/19.39 | | | | | | | | | | | | | | | | (212) all_65_8 = all_65_17
% 142.05/19.39 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31),
% 142.05/19.39 | | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49),
% 142.05/19.39 | | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (67), (90), (191),
% 142.05/19.39 | | | | | | | | | | | | | | | | (198), (205), (212), (axiom_31) are inconsistent
% 142.05/19.39 | | | | | | | | | | | | | | | | by sub-proof #3.
% 142.05/19.39 | | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | (213) ~ elem(all_65_3, all_128_7)
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | REDUCE: (176), (213) imply:
% 142.05/19.39 | | | | | | | | | | | | | | (214) ~ elem(all_65_3, all_65_2)
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | PRED_UNIFY: (199), (214) imply:
% 142.05/19.39 | | | | | | | | | | | | | | (215) $false
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | (216) all_65_3 = all_65_11
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | REDUCE: (53), (216) imply:
% 142.05/19.39 | | | | | | | | | | | | | (217) m_Down(all_65_7) = all_65_11
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_12) with all_65_16,
% 142.05/19.39 | | | | | | | | | | | | | all_65_17, all_65_7, all_65_11, simplifying with
% 142.05/19.39 | | | | | | | | | | | | | (26), (27), (34), (49), (217) gives:
% 142.05/19.39 | | | | | | | | | | | | | (218) $false
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | (219) ~ leq(all_65_9, all_65_15)
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (27), (33), (34), (35),
% 142.05/19.39 | | | | | | | | | | (42), (43), (46), (49), (50), (53), (58), (59),
% 142.05/19.39 | | | | | | | | | | (91), (92), (96), (104), (174), (176), (185),
% 142.05/19.39 | | | | | | | | | | (187), (219), (axiom_12), (axiom_32) are
% 142.05/19.39 | | | | | | | | | | inconsistent by sub-proof #2.
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | |
% 142.05/19.39 | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | |
% 142.05/19.39 | | | | | | | | | (220) ~ leq(all_65_12, all_65_9)
% 142.05/19.39 | | | | | | | | |
% 142.05/19.39 | | | | | | | | | BETA: splitting (79) gives:
% 142.05/19.39 | | | | | | | | |
% 142.05/19.39 | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | (221) leq(all_65_12, all_65_9)
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | PRED_UNIFY: (220), (221) imply:
% 142.05/19.39 | | | | | | | | | | (222) $false
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | CLOSE: (222) is inconsistent.
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | (223) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 142.05/19.39 | | | | | | | | | | $i] : (( ~ (v1 = elec_2) & index(status,
% 142.05/19.39 | | | | | | | | | | all_65_9) = v1 & $i(v1)) | ( ~ (v0 = elec_2)
% 142.05/19.39 | | | | | | | | | | & index(status, all_65_12) = v0 & $i(v0)) |
% 142.05/19.39 | | | | | | | | | | (index(pendack, all_65_9) = v3 & index(pendack,
% 142.05/19.39 | | | | | | | | | | all_65_12) = v2 & $i(v3) & $i(v2) & ~
% 142.05/19.39 | | | | | | | | | | leq(v2, v3)))
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | DELTA: instantiating (223) with fresh symbols all_229_0,
% 142.05/19.39 | | | | | | | | | | all_229_1, all_229_2, all_229_3 gives:
% 142.05/19.39 | | | | | | | | | | (224) ( ~ (all_229_2 = elec_2) & index(status, all_65_9)
% 142.05/19.39 | | | | | | | | | | = all_229_2 & $i(all_229_2)) | ( ~ (all_229_3 =
% 142.05/19.39 | | | | | | | | | | elec_2) & index(status, all_65_12) = all_229_3
% 142.05/19.39 | | | | | | | | | | & $i(all_229_3)) | (index(pendack, all_65_9) =
% 142.05/19.39 | | | | | | | | | | all_229_0 & index(pendack, all_65_12) = all_229_1
% 142.05/19.39 | | | | | | | | | | & $i(all_229_0) & $i(all_229_1) & ~
% 142.05/19.39 | | | | | | | | | | leq(all_229_1, all_229_0))
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | BETA: splitting (70) gives:
% 142.05/19.39 | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | (225) leq(all_65_15, all_65_9)
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | BETA: splitting (72) gives:
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | (226) leq(all_65_9, all_65_15)
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | REF_CLOSE: (7), (18), (28), (32), (225), (226) are
% 142.05/19.39 | | | | | | | | | | | | inconsistent by sub-proof #4.
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | (227) ~ leq(all_65_9, all_65_15)
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (27), (33), (34), (35),
% 142.05/19.39 | | | | | | | | | | | | (42), (43), (46), (49), (50), (53), (58), (59),
% 142.05/19.39 | | | | | | | | | | | | (91), (92), (96), (104), (174), (176), (185),
% 142.05/19.39 | | | | | | | | | | | | (187), (227), (axiom_12), (axiom_32) are
% 142.05/19.39 | | | | | | | | | | | | inconsistent by sub-proof #2.
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | (228) ~ leq(all_65_15, all_65_9)
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | BETA: splitting (92) gives:
% 142.05/19.39 | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | (229) elem(all_65_3, all_65_2)
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | BETA: splitting (174) gives:
% 142.05/19.39 | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | (230) ~ elem(all_65_0, all_128_7)
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | REDUCE: (176), (230) imply:
% 142.05/19.39 | | | | | | | | | | | | | (231) ~ elem(all_65_0, all_65_2)
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | BETA: splitting (91) gives:
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | (232) elem(all_65_0, all_65_2)
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | PRED_UNIFY: (231), (232) imply:
% 142.05/19.39 | | | | | | | | | | | | | | (233) $false
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | (234) all_65_0 = all_65_11
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | REDUCE: (50), (234) imply:
% 142.05/19.39 | | | | | | | | | | | | | | (235) m_Ack(all_65_6, all_65_8) = all_65_11
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | Case 1:
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | (236) ~ (all_105_1 = elec_1) & index(status, all_105_2)
% 142.05/19.39 | | | | | | | | | | | | | | | = all_105_1 & $i(all_105_1)
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 142.05/19.39 | | | | | | | | | | | | | | | (237) index(status, all_105_2) = all_105_1
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | REDUCE: (130), (237) imply:
% 142.05/19.39 | | | | | | | | | | | | | | | (238) index(status, all_65_12) = all_105_1
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_105_1,
% 142.05/19.39 | | | | | | | | | | | | | | | all_65_12, status, simplifying with (57), (238)
% 142.05/19.39 | | | | | | | | | | | | | | | gives:
% 142.05/19.39 | | | | | | | | | | | | | | | (239) all_105_1 = elec_2
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6,
% 142.05/19.39 | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with
% 142.05/19.39 | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (235) gives:
% 142.05/19.39 | | | | | | | | | | | | | | | (240) all_65_8 = all_65_17
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31),
% 142.05/19.39 | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49),
% 142.05/19.39 | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (64), (67), (90),
% 142.05/19.39 | | | | | | | | | | | | | | | (182), (183), (186), (224), (228), (235), (240),
% 142.05/19.39 | | | | | | | | | | | | | | | (axiom_17), (axiom_26), (axiom_31) are
% 142.05/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | GROUND_INST: instantiating (axiom_32) with all_65_16, all_65_6,
% 142.05/19.39 | | | | | | | | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with
% 142.05/19.39 | | | | | | | | | | | | | | | (26), (27), (33), (35), (49), (235) gives:
% 142.05/19.39 | | | | | | | | | | | | | | | (241) all_65_8 = all_65_17
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (22), (23), (26), (27), (31),
% 142.05/19.39 | | | | | | | | | | | | | | | (33), (35), (41), (43), (45), (46), (48), (49),
% 142.05/19.39 | | | | | | | | | | | | | | | (52), (56), (57), (58), (59), (64), (67), (90),
% 142.05/19.39 | | | | | | | | | | | | | | | (182), (183), (186), (224), (228), (235), (241),
% 142.05/19.39 | | | | | | | | | | | | | | | (axiom_17), (axiom_26), (axiom_31) are
% 142.05/19.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 142.05/19.39 | | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | | End of split
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.39 | | | | | | | | | | | | Case 2:
% 142.05/19.39 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | (242) ~ elem(all_65_3, all_128_7)
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | REDUCE: (176), (242) imply:
% 142.05/19.40 | | | | | | | | | | | | | (243) ~ elem(all_65_3, all_65_2)
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | PRED_UNIFY: (229), (243) imply:
% 142.05/19.40 | | | | | | | | | | | | | (244) $false
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | (245) all_65_3 = all_65_11
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | REDUCE: (53), (245) imply:
% 142.05/19.40 | | | | | | | | | | | | (246) m_Down(all_65_7) = all_65_11
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | GROUND_INST: instantiating (axiom_12) with all_65_16,
% 142.05/19.40 | | | | | | | | | | | | all_65_17, all_65_7, all_65_11, simplifying with
% 142.05/19.40 | | | | | | | | | | | | (26), (27), (34), (49), (246) gives:
% 142.05/19.40 | | | | | | | | | | | | (247) $false
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | End of split
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | | (248) ~ leq(all_65_12, all_65_12)
% 142.05/19.40 | | | | | | | | (249) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 142.05/19.40 | | | | | | | | (( ~ (v1 = elec_2) & index(status, all_65_12) = v1 &
% 142.05/19.40 | | | | | | | | $i(v1)) | ( ~ (v0 = elec_2) & index(status,
% 142.05/19.40 | | | | | | | | all_65_12) = v0 & $i(v0)) | (index(pendack,
% 142.05/19.40 | | | | | | | | all_65_12) = v3 & index(pendack, all_65_12) = v2
% 142.05/19.40 | | | | | | | | & $i(v3) & $i(v2) & ~ leq(v2, v3)))
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | | DELTA: instantiating (249) with fresh symbols all_180_0,
% 142.05/19.40 | | | | | | | | all_180_1, all_180_2, all_180_3 gives:
% 142.05/19.40 | | | | | | | | (250) ( ~ (all_180_2 = elec_2) & index(status, all_65_12) =
% 142.05/19.40 | | | | | | | | all_180_2 & $i(all_180_2)) | ( ~ (all_180_3 = elec_2)
% 142.05/19.40 | | | | | | | | & index(status, all_65_12) = all_180_3 &
% 142.05/19.40 | | | | | | | | $i(all_180_3)) | (index(pendack, all_65_12) =
% 142.05/19.40 | | | | | | | | all_180_0 & index(pendack, all_65_12) = all_180_1 &
% 142.05/19.40 | | | | | | | | $i(all_180_0) & $i(all_180_1) & ~ leq(all_180_1,
% 142.05/19.40 | | | | | | | | all_180_0))
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | | BETA: splitting (250) gives:
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | | Case 1:
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | (251) ~ (all_180_2 = elec_2) & index(status, all_65_12) =
% 142.05/19.40 | | | | | | | | | all_180_2 & $i(all_180_2)
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | ALPHA: (251) implies:
% 142.05/19.40 | | | | | | | | | (252) ~ (all_180_2 = elec_2)
% 142.05/19.40 | | | | | | | | | (253) index(status, all_65_12) = all_180_2
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_180_2,
% 142.05/19.40 | | | | | | | | | all_65_12, status, simplifying with (57), (253)
% 142.05/19.40 | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | (254) all_180_2 = elec_2
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | REDUCE: (252), (254) imply:
% 142.05/19.40 | | | | | | | | | (255) $false
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | CLOSE: (255) is inconsistent.
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | (256) ( ~ (all_180_3 = elec_2) & index(status, all_65_12) =
% 142.05/19.40 | | | | | | | | | all_180_3 & $i(all_180_3)) | (index(pendack,
% 142.05/19.40 | | | | | | | | | all_65_12) = all_180_0 & index(pendack,
% 142.05/19.40 | | | | | | | | | all_65_12) = all_180_1 & $i(all_180_0) &
% 142.05/19.40 | | | | | | | | | $i(all_180_1) & ~ leq(all_180_1, all_180_0))
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | BETA: splitting (256) gives:
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | | Case 1:
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | (257) ~ (all_180_3 = elec_2) & index(status, all_65_12)
% 142.05/19.40 | | | | | | | | | | = all_180_3 & $i(all_180_3)
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | ALPHA: (257) implies:
% 142.05/19.40 | | | | | | | | | | (258) ~ (all_180_3 = elec_2)
% 142.05/19.40 | | | | | | | | | | (259) index(status, all_65_12) = all_180_3
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_180_3,
% 142.05/19.40 | | | | | | | | | | all_65_12, status, simplifying with (57), (259)
% 142.05/19.40 | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | (260) all_180_3 = elec_2
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | REDUCE: (258), (260) imply:
% 142.05/19.40 | | | | | | | | | | (261) $false
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | CLOSE: (261) is inconsistent.
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | (262) index(pendack, all_65_12) = all_180_0 &
% 142.05/19.40 | | | | | | | | | | index(pendack, all_65_12) = all_180_1 &
% 142.05/19.40 | | | | | | | | | | $i(all_180_0) & $i(all_180_1) & ~ leq(all_180_1,
% 142.05/19.40 | | | | | | | | | | all_180_0)
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | ALPHA: (262) implies:
% 142.05/19.40 | | | | | | | | | | (263) ~ leq(all_180_1, all_180_0)
% 142.05/19.40 | | | | | | | | | | (264) index(pendack, all_65_12) = all_180_1
% 142.05/19.40 | | | | | | | | | | (265) index(pendack, all_65_12) = all_180_0
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | BETA: splitting (77) gives:
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | Case 1:
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | (266) leq(all_65_12, all_65_12)
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | PRED_UNIFY: (248), (266) imply:
% 142.05/19.40 | | | | | | | | | | | (267) $false
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | (268) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ (v1
% 142.05/19.40 | | | | | | | | | | | = elec_2) & index(status, all_65_12) = v1 &
% 142.05/19.40 | | | | | | | | | | | $i(v1)) | ( ~ (v0 = elec_2) & index(status,
% 142.05/19.40 | | | | | | | | | | | all_65_12) = v0 & $i(v0)) | (index(pendack,
% 142.05/19.40 | | | | | | | | | | | all_65_12) = v2 & $i(v2) & leq(v2,
% 142.05/19.40 | | | | | | | | | | | all_65_12)))
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_189_0,
% 142.05/19.40 | | | | | | | | | | | all_189_1, all_189_2 gives:
% 142.05/19.40 | | | | | | | | | | | (269) ( ~ (all_189_1 = elec_2) & index(status,
% 142.05/19.40 | | | | | | | | | | | all_65_12) = all_189_1 & $i(all_189_1)) | ( ~
% 142.05/19.40 | | | | | | | | | | | (all_189_2 = elec_2) & index(status, all_65_12)
% 142.05/19.40 | | | | | | | | | | | = all_189_2 & $i(all_189_2)) | (index(pendack,
% 142.05/19.40 | | | | | | | | | | | all_65_12) = all_189_0 & $i(all_189_0) &
% 142.05/19.40 | | | | | | | | | | | leq(all_189_0, all_65_12))
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | BETA: splitting (269) gives:
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | Case 1:
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | (270) ~ (all_189_1 = elec_2) & index(status, all_65_12)
% 142.05/19.40 | | | | | | | | | | | | = all_189_1 & $i(all_189_1)
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | ALPHA: (270) implies:
% 142.05/19.40 | | | | | | | | | | | | (271) ~ (all_189_1 = elec_2)
% 142.05/19.40 | | | | | | | | | | | | (272) index(status, all_65_12) = all_189_1
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_189_1,
% 142.05/19.40 | | | | | | | | | | | | all_65_12, status, simplifying with (57), (272)
% 142.05/19.40 | | | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | | | (273) all_189_1 = elec_2
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | REDUCE: (271), (273) imply:
% 142.05/19.40 | | | | | | | | | | | | (274) $false
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | CLOSE: (274) is inconsistent.
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | (275) ( ~ (all_189_2 = elec_2) & index(status,
% 142.05/19.40 | | | | | | | | | | | | all_65_12) = all_189_2 & $i(all_189_2)) |
% 142.05/19.40 | | | | | | | | | | | | (index(pendack, all_65_12) = all_189_0 &
% 142.05/19.40 | | | | | | | | | | | | $i(all_189_0) & leq(all_189_0, all_65_12))
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | BETA: splitting (275) gives:
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | Case 1:
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | (276) ~ (all_189_2 = elec_2) & index(status, all_65_12)
% 142.05/19.40 | | | | | | | | | | | | | = all_189_2 & $i(all_189_2)
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | ALPHA: (276) implies:
% 142.05/19.40 | | | | | | | | | | | | | (277) ~ (all_189_2 = elec_2)
% 142.05/19.40 | | | | | | | | | | | | | (278) index(status, all_65_12) = all_189_2
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with elec_2, all_189_2,
% 142.05/19.40 | | | | | | | | | | | | | all_65_12, status, simplifying with (57), (278)
% 142.05/19.40 | | | | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | | | | (279) all_189_2 = elec_2
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | REDUCE: (277), (279) imply:
% 142.05/19.40 | | | | | | | | | | | | | (280) $false
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | CLOSE: (280) is inconsistent.
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | Case 2:
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | (281) index(pendack, all_65_12) = all_189_0 &
% 142.05/19.40 | | | | | | | | | | | | | $i(all_189_0) & leq(all_189_0, all_65_12)
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | ALPHA: (281) implies:
% 142.05/19.40 | | | | | | | | | | | | | (282) index(pendack, all_65_12) = all_189_0
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_65_5, all_180_0,
% 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (56), (265)
% 142.05/19.40 | | | | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | | | | (283) all_180_0 = all_65_5
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_180_0, all_189_0,
% 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (265), (282)
% 142.05/19.40 | | | | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | | | | (284) all_189_0 = all_180_0
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_180_1, all_189_0,
% 142.05/19.40 | | | | | | | | | | | | | all_65_12, pendack, simplifying with (264), (282)
% 142.05/19.40 | | | | | | | | | | | | | gives:
% 142.05/19.40 | | | | | | | | | | | | | (285) all_189_0 = all_180_1
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | COMBINE_EQS: (284), (285) imply:
% 142.05/19.40 | | | | | | | | | | | | | (286) all_180_0 = all_180_1
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | SIMP: (286) implies:
% 142.05/19.40 | | | | | | | | | | | | | (287) all_180_0 = all_180_1
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | COMBINE_EQS: (283), (287) imply:
% 142.05/19.40 | | | | | | | | | | | | | (288) all_180_1 = all_65_5
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | REDUCE: (263), (283), (288) imply:
% 142.05/19.40 | | | | | | | | | | | | | (289) ~ leq(all_65_5, all_65_5)
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | PRED_UNIFY: (179), (289) imply:
% 142.05/19.40 | | | | | | | | | | | | | (290) $false
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | | CLOSE: (290) is inconsistent.
% 142.05/19.40 | | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | | |
% 142.05/19.40 | | | | | | | | | End of split
% 142.05/19.40 | | | | | | | | |
% 142.05/19.40 | | | | | | | | End of split
% 142.05/19.40 | | | | | | | |
% 142.05/19.40 | | | | | | | End of split
% 142.05/19.40 | | | | | | |
% 142.05/19.40 | | | | | | End of split
% 142.05/19.40 | | | | | |
% 142.05/19.40 | | | | | End of split
% 142.05/19.40 | | | | |
% 142.05/19.40 | | | | End of split
% 142.05/19.40 | | | |
% 142.05/19.40 | | | End of split
% 142.05/19.40 | | |
% 142.05/19.40 | | End of split
% 142.05/19.40 | |
% 142.05/19.40 | Case 2:
% 142.05/19.40 | |
% 142.05/19.40 | | (291) queue(all_65_15) = all_97_1 & $i(all_97_1) & ~ elem(all_65_13,
% 142.05/19.40 | | all_97_1)
% 142.05/19.40 | |
% 142.05/19.40 | | ALPHA: (291) implies:
% 142.05/19.41 | | (292) ~ elem(all_65_13, all_97_1)
% 142.05/19.41 | | (293) queue(all_65_15) = all_97_1
% 142.05/19.41 | |
% 142.05/19.41 | | GROUND_INST: instantiating (13) with all_65_14, all_97_1, all_65_15,
% 142.05/19.41 | | simplifying with (41), (293) gives:
% 142.05/19.41 | | (294) all_97_1 = all_65_14
% 142.05/19.41 | |
% 142.05/19.41 | | REDUCE: (292), (294) imply:
% 142.05/19.41 | | (295) ~ elem(all_65_13, all_65_14)
% 142.05/19.41 | |
% 142.05/19.41 | | PRED_UNIFY: (90), (295) imply:
% 142.05/19.41 | | (296) $false
% 142.05/19.41 | |
% 142.05/19.41 | | CLOSE: (296) is inconsistent.
% 142.05/19.41 | |
% 142.05/19.41 | End of split
% 142.05/19.41 |
% 142.05/19.41 End of proof
% 142.05/19.41
% 142.05/19.41 Sub-proof #1 shows that the following formulas are inconsistent:
% 142.05/19.41 ----------------------------------------------------------------
% 142.05/19.41 (1) m_Ack(all_65_6, all_65_8) = all_65_11
% 142.05/19.41 (2) index(status, all_65_12) = elec_2
% 142.05/19.41 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~
% 142.05/19.41 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 142.05/19.41 (4) m_Halt(all_65_16) = all_65_13
% 142.05/19.41 (5) setIn(all_65_10, alive)
% 142.05/19.41 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 142.05/19.41 = v0 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) |
% 142.05/19.41 ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 142.05/19.41 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v1) = v2)
% 142.05/19.41 | ~ (m_Halt(v0) = v2) | ~ $i(v1) | ~ $i(v0))
% 142.05/19.41 (8) index(pendack, all_65_12) = all_65_5
% 142.05/19.41 (9) m_Ack(all_65_16, all_65_17) = all_65_11
% 142.05/19.41 (10) host(all_65_6) = all_65_12
% 142.05/19.41 (11) leq(all_65_12, all_65_12)
% 142.05/19.41 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 142.05/19.41 | ~ (host(v2) = v0))
% 142.05/19.41 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 142.05/19.41 [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) =
% 142.05/19.41 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~
% 142.05/19.41 setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 142.05/19.41 $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) &
% 142.05/19.41 index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr,
% 142.05/19.41 v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) =
% 142.05/19.41 v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 &
% 142.05/19.41 host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = v8 &
% 142.05/19.41 $i(v8) & ~ elem(v4, v8))))
% 142.05/19.41 (14) setIn(all_65_6, alive)
% 142.05/19.41 (15) $i(all_174_2)
% 142.05/19.41 (16) $i(all_65_6)
% 142.05/19.41 (17) queue(all_65_15) = all_65_14
% 142.05/19.41 (18) index(status, all_65_9) = norm
% 142.05/19.41 (19) host(all_65_17) = all_65_15
% 142.05/19.41 (20) $i(all_65_10)
% 142.05/19.41 (21) ( ~ (all_229_2 = elec_2) & index(status, all_65_9) = all_229_2 &
% 142.05/19.41 $i(all_229_2)) | ( ~ (all_229_3 = elec_2) & index(status, all_65_12) =
% 142.05/19.41 all_229_3 & $i(all_229_3)) | (index(pendack, all_65_9) = all_229_0 &
% 142.05/19.41 index(pendack, all_65_12) = all_229_1 & $i(all_229_0) & $i(all_229_1)
% 142.05/19.41 & ~ leq(all_229_1, all_229_0))
% 142.05/19.41 (22) host(all_65_10) = all_65_9
% 142.05/19.41 (23) ~ leq(all_65_15, all_65_9)
% 142.05/19.41 (24) host(all_65_8) = all_65_5
% 142.05/19.41 (25) index(ldr, all_65_9) = all_65_9
% 142.05/19.41 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1)
% 142.05/19.41 = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 142.05/19.41 ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) =
% 142.05/19.41 v4 & $i(v4) & ~ elem(v2, v4))))
% 142.05/19.41 (27) (all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13) | (all_174_1 =
% 142.05/19.41 all_65_13 & m_Halt(all_174_2) = all_65_13)
% 142.05/19.41 (28) $i(all_65_8)
% 142.05/19.41 (29) elem(all_65_13, all_65_14)
% 142.05/19.41 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1)
% 142.05/19.41 | ~ (queue(v2) = v0))
% 142.05/19.41 (31) $i(all_65_17)
% 142.05/19.41 (32) $i(all_65_16)
% 142.05/19.41 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.05/19.41 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 142.05/19.41 (34) all_65_8 = all_65_17
% 142.05/19.41
% 142.05/19.41 Begin of proof
% 142.05/19.41 |
% 142.05/19.41 | GROUND_INST: instantiating (6) with all_65_16, all_65_6, all_65_17, all_65_8,
% 142.05/19.41 | all_65_11, simplifying with (1), (9), (16), (28), (31), (32)
% 142.05/19.41 | gives:
% 142.05/19.41 | (35) all_65_6 = all_65_16
% 142.05/19.41 |
% 142.05/19.41 | REDUCE: (10), (35) imply:
% 142.05/19.41 | (36) host(all_65_16) = all_65_12
% 142.05/19.41 |
% 142.05/19.41 | REDUCE: (24), (34) imply:
% 142.05/19.41 | (37) host(all_65_17) = all_65_5
% 142.05/19.41 |
% 142.05/19.41 | REDUCE: (14), (35) imply:
% 142.05/19.41 | (38) setIn(all_65_16, alive)
% 142.05/19.41 |
% 142.05/19.41 | GROUND_INST: instantiating (12) with all_65_15, all_65_5, all_65_17,
% 142.05/19.41 | simplifying with (19), (37) gives:
% 142.05/19.41 | (39) all_65_5 = all_65_15
% 142.05/19.41 |
% 142.05/19.41 | REDUCE: (8), (39) imply:
% 142.05/19.41 | (40) index(pendack, all_65_12) = all_65_15
% 142.05/19.41 |
% 142.05/19.41 | BETA: splitting (27) gives:
% 142.05/19.41 |
% 142.05/19.41 | Case 1:
% 142.05/19.41 | |
% 142.05/19.41 | | (41) all_174_0 = all_65_13 & m_Down(all_174_2) = all_65_13
% 142.05/19.41 | |
% 142.05/19.41 | | ALPHA: (41) implies:
% 142.05/19.41 | | (42) m_Down(all_174_2) = all_65_13
% 142.05/19.41 | |
% 142.05/19.41 | | GROUND_INST: instantiating (3) with all_174_2, all_65_16, all_65_13,
% 142.05/19.41 | | simplifying with (4), (15), (32), (42) gives:
% 142.05/19.41 | | (43) $false
% 142.05/19.41 | |
% 142.05/19.41 | | CLOSE: (43) is inconsistent.
% 142.05/19.41 | |
% 142.05/19.41 | Case 2:
% 142.05/19.41 | |
% 142.05/19.41 | | (44) all_174_1 = all_65_13 & m_Halt(all_174_2) = all_65_13
% 142.05/19.41 | |
% 142.05/19.41 | | ALPHA: (44) implies:
% 142.05/19.41 | | (45) m_Halt(all_174_2) = all_65_13
% 142.05/19.41 | |
% 142.05/19.41 | | BETA: splitting (21) gives:
% 142.05/19.41 | |
% 142.05/19.41 | | Case 1:
% 142.05/19.41 | | |
% 142.05/19.41 | | | (46) ~ (all_229_2 = elec_2) & index(status, all_65_9) = all_229_2 &
% 142.05/19.41 | | | $i(all_229_2)
% 142.05/19.41 | | |
% 142.05/19.41 | | | ALPHA: (46) implies:
% 142.05/19.41 | | | (47) index(status, all_65_9) = all_229_2
% 142.05/19.41 | | |
% 142.05/19.41 | | | GROUND_INST: instantiating (33) with norm, all_229_2, all_65_9, status,
% 142.05/19.41 | | | simplifying with (18), (47) gives:
% 142.05/19.41 | | | (48) all_229_2 = norm
% 142.05/19.41 | | |
% 142.05/19.41 | | | GROUND_INST: instantiating (13) with all_65_10, all_65_17, all_65_16,
% 142.05/19.41 | | | all_65_9, all_65_13, all_65_15, simplifying with (4), (5),
% 142.05/19.41 | | | (19), (20), (22), (31), (32), (38) gives:
% 142.05/19.41 | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 142.05/19.41 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9)
% 142.05/19.41 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) =
% 142.05/19.41 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 &
% 142.05/19.41 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0)
% 142.05/19.41 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1,
% 142.05/19.41 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~
% 142.05/19.41 | | | elem(all_65_13, v2)))
% 142.05/19.41 | | |
% 142.05/19.41 | | | DELTA: instantiating (49) with fresh symbols all_800_0, all_800_1,
% 142.05/19.41 | | | all_800_2, all_800_3, all_800_4, all_800_5 gives:
% 142.05/19.42 | | | (50) ( ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 &
% 142.05/19.42 | | | $i(all_800_0)) | ( ~ (all_800_1 = all_65_9) & index(ldr,
% 142.05/19.42 | | | all_65_9) = all_800_1 & $i(all_800_1)) | ( ~ (all_800_2 =
% 142.05/19.42 | | | elec_2) & index(status, all_800_5) = all_800_2 &
% 142.05/19.42 | | | host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5)) |
% 142.05/19.42 | | | (index(pendack, all_800_5) = all_800_4 & host(all_65_16) =
% 142.05/19.42 | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4,
% 142.05/19.42 | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3) &
% 142.05/19.42 | | | ~ elem(all_65_13, all_800_3))
% 142.05/19.42 | | |
% 142.05/19.42 | | | BETA: splitting (50) gives:
% 142.05/19.42 | | |
% 142.05/19.42 | | | Case 1:
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | (51) ( ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 &
% 142.05/19.42 | | | | $i(all_800_0)) | ( ~ (all_800_1 = all_65_9) & index(ldr,
% 142.05/19.42 | | | | all_65_9) = all_800_1 & $i(all_800_1))
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | BETA: splitting (51) gives:
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | Case 1:
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | (52) ~ (all_800_0 = norm) & index(status, all_65_9) = all_800_0 &
% 142.05/19.42 | | | | | $i(all_800_0)
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | ALPHA: (52) implies:
% 142.05/19.42 | | | | | (53) ~ (all_800_0 = norm)
% 142.05/19.42 | | | | | (54) index(status, all_65_9) = all_800_0
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with norm, all_800_0, all_65_9,
% 142.05/19.42 | | | | | status, simplifying with (18), (54) gives:
% 142.05/19.42 | | | | | (55) all_800_0 = norm
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | REDUCE: (53), (55) imply:
% 142.05/19.42 | | | | | (56) $false
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | CLOSE: (56) is inconsistent.
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | Case 2:
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | (57) ~ (all_800_1 = all_65_9) & index(ldr, all_65_9) = all_800_1 &
% 142.05/19.42 | | | | | $i(all_800_1)
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | ALPHA: (57) implies:
% 142.05/19.42 | | | | | (58) ~ (all_800_1 = all_65_9)
% 142.05/19.42 | | | | | (59) index(ldr, all_65_9) = all_800_1
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with all_65_9, all_800_1, all_65_9,
% 142.05/19.42 | | | | | ldr, simplifying with (25), (59) gives:
% 142.05/19.42 | | | | | (60) all_800_1 = all_65_9
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | REDUCE: (58), (60) imply:
% 142.05/19.42 | | | | | (61) $false
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | CLOSE: (61) is inconsistent.
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | End of split
% 142.05/19.42 | | | |
% 142.05/19.42 | | | Case 2:
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | (62) ( ~ (all_800_2 = elec_2) & index(status, all_800_5) = all_800_2
% 142.05/19.42 | | | | & host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5))
% 142.05/19.42 | | | | | (index(pendack, all_800_5) = all_800_4 & host(all_65_16) =
% 142.05/19.42 | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4,
% 142.05/19.42 | | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3) &
% 142.05/19.42 | | | | ~ elem(all_65_13, all_800_3))
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | BETA: splitting (62) gives:
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | Case 1:
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | (63) ~ (all_800_2 = elec_2) & index(status, all_800_5) = all_800_2
% 142.05/19.42 | | | | | & host(all_65_16) = all_800_5 & $i(all_800_2) & $i(all_800_5)
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | ALPHA: (63) implies:
% 142.05/19.42 | | | | | (64) ~ (all_800_2 = elec_2)
% 142.05/19.42 | | | | | (65) host(all_65_16) = all_800_5
% 142.05/19.42 | | | | | (66) index(status, all_800_5) = all_800_2
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | GROUND_INST: instantiating (12) with all_65_12, all_800_5, all_65_16,
% 142.05/19.42 | | | | | simplifying with (36), (65) gives:
% 142.05/19.42 | | | | | (67) all_800_5 = all_65_12
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | REDUCE: (66), (67) imply:
% 142.05/19.42 | | | | | (68) index(status, all_65_12) = all_800_2
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | GROUND_INST: instantiating (33) with elec_2, all_800_2, all_65_12,
% 142.05/19.42 | | | | | status, simplifying with (2), (68) gives:
% 142.05/19.42 | | | | | (69) all_800_2 = elec_2
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | REDUCE: (64), (69) imply:
% 142.05/19.42 | | | | | (70) $false
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | CLOSE: (70) is inconsistent.
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | Case 2:
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | (71) (index(pendack, all_800_5) = all_800_4 & host(all_65_16) =
% 142.05/19.42 | | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4,
% 142.05/19.42 | | | | | all_65_9)) | (queue(all_65_15) = all_800_3 & $i(all_800_3)
% 142.05/19.42 | | | | | & ~ elem(all_65_13, all_800_3))
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | BETA: splitting (71) gives:
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | | Case 1:
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | (72) index(pendack, all_800_5) = all_800_4 & host(all_65_16) =
% 142.05/19.42 | | | | | | all_800_5 & $i(all_800_4) & $i(all_800_5) & leq(all_800_4,
% 142.05/19.42 | | | | | | all_65_9)
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | ALPHA: (72) implies:
% 142.05/19.42 | | | | | | (73) leq(all_800_4, all_65_9)
% 142.05/19.42 | | | | | | (74) host(all_65_16) = all_800_5
% 142.05/19.42 | | | | | | (75) index(pendack, all_800_5) = all_800_4
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_800_5,
% 142.05/19.42 | | | | | | all_65_16, simplifying with (36), (74) gives:
% 142.05/19.42 | | | | | | (76) all_800_5 = all_65_12
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | REDUCE: (75), (76) imply:
% 142.05/19.42 | | | | | | (77) index(pendack, all_65_12) = all_800_4
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | GROUND_INST: instantiating (33) with all_65_15, all_800_4,
% 142.05/19.42 | | | | | | all_65_12, pendack, simplifying with (40), (77) gives:
% 142.05/19.42 | | | | | | (78) all_800_4 = all_65_15
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | REDUCE: (73), (78) imply:
% 142.05/19.42 | | | | | | (79) leq(all_65_15, all_65_9)
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | PRED_UNIFY: (23), (79) imply:
% 142.05/19.42 | | | | | | (80) $false
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | CLOSE: (80) is inconsistent.
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | Case 2:
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | (81) queue(all_65_15) = all_800_3 & $i(all_800_3) & ~
% 142.05/19.42 | | | | | | elem(all_65_13, all_800_3)
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | ALPHA: (81) implies:
% 142.05/19.42 | | | | | | (82) ~ elem(all_65_13, all_800_3)
% 142.05/19.42 | | | | | | (83) queue(all_65_15) = all_800_3
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | GROUND_INST: instantiating (30) with all_65_14, all_800_3,
% 142.05/19.42 | | | | | | all_65_15, simplifying with (17), (83) gives:
% 142.05/19.42 | | | | | | (84) all_800_3 = all_65_14
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | REDUCE: (82), (84) imply:
% 142.05/19.42 | | | | | | (85) ~ elem(all_65_13, all_65_14)
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | PRED_UNIFY: (29), (85) imply:
% 142.05/19.42 | | | | | | (86) $false
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | | CLOSE: (86) is inconsistent.
% 142.05/19.42 | | | | | |
% 142.05/19.42 | | | | | End of split
% 142.05/19.42 | | | | |
% 142.05/19.42 | | | | End of split
% 142.05/19.42 | | | |
% 142.05/19.42 | | | End of split
% 142.05/19.42 | | |
% 142.05/19.42 | | Case 2:
% 142.05/19.42 | | |
% 142.05/19.42 | | | (87) ( ~ (all_229_3 = elec_2) & index(status, all_65_12) = all_229_3 &
% 142.05/19.42 | | | $i(all_229_3)) | (index(pendack, all_65_9) = all_229_0 &
% 142.05/19.42 | | | index(pendack, all_65_12) = all_229_1 & $i(all_229_0) &
% 142.05/19.42 | | | $i(all_229_1) & ~ leq(all_229_1, all_229_0))
% 142.05/19.42 | | |
% 142.05/19.42 | | | BETA: splitting (87) gives:
% 142.05/19.42 | | |
% 142.05/19.42 | | | Case 1:
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | (88) ~ (all_229_3 = elec_2) & index(status, all_65_12) = all_229_3 &
% 142.05/19.42 | | | | $i(all_229_3)
% 142.05/19.42 | | | |
% 142.05/19.42 | | | | ALPHA: (88) implies:
% 142.47/19.42 | | | | (89) ~ (all_229_3 = elec_2)
% 142.47/19.42 | | | | (90) index(status, all_65_12) = all_229_3
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | GROUND_INST: instantiating (33) with elec_2, all_229_3, all_65_12,
% 142.47/19.42 | | | | status, simplifying with (2), (90) gives:
% 142.47/19.42 | | | | (91) all_229_3 = elec_2
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | REDUCE: (89), (91) imply:
% 142.47/19.42 | | | | (92) $false
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | CLOSE: (92) is inconsistent.
% 142.47/19.42 | | | |
% 142.47/19.42 | | | Case 2:
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | (93) index(pendack, all_65_9) = all_229_0 & index(pendack, all_65_12)
% 142.47/19.42 | | | | = all_229_1 & $i(all_229_0) & $i(all_229_1) & ~ leq(all_229_1,
% 142.47/19.42 | | | | all_229_0)
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | ALPHA: (93) implies:
% 142.47/19.42 | | | | (94) index(pendack, all_65_12) = all_229_1
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | GROUND_INST: instantiating (33) with all_65_15, all_229_1, all_65_12,
% 142.47/19.42 | | | | pendack, simplifying with (40), (94) gives:
% 142.47/19.42 | | | | (95) all_229_1 = all_65_15
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | GROUND_INST: instantiating (13) with all_65_10, all_65_17, all_65_16,
% 142.47/19.42 | | | | all_65_9, all_65_13, all_65_15, simplifying with (4), (5),
% 142.47/19.42 | | | | (19), (20), (22), (31), (32), (38) gives:
% 142.47/19.42 | | | | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 142.47/19.42 | | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status,
% 142.47/19.42 | | | | all_65_9) = v5 & $i(v5)) | ( ~ (v4 = all_65_9) &
% 142.47/19.42 | | | | index(ldr, all_65_9) = v4 & $i(v4)) | ( ~ (v3 = elec_2) &
% 142.47/19.42 | | | | index(status, v0) = v3 & host(all_65_16) = v0 & $i(v3) &
% 142.47/19.42 | | | | $i(v0)) | (index(pendack, v0) = v1 & host(all_65_16) = v0 &
% 142.47/19.42 | | | | $i(v1) & $i(v0) & leq(v1, all_65_9)) | (queue(all_65_15) =
% 142.47/19.42 | | | | v2 & $i(v2) & ~ elem(all_65_13, v2)))
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | GROUND_INST: instantiating (26) with all_65_16, all_174_2, all_65_13,
% 142.47/19.42 | | | | all_65_12, simplifying with (15), (32), (36), (45) gives:
% 142.47/19.42 | | | | (97) ? [v0: $i] : ? [v1: $i] : ((host(all_174_2) = v1 & $i(v1) & ~
% 142.47/19.42 | | | | leq(all_65_12, v1)) | (queue(all_65_12) = v0 & $i(v0) & ~
% 142.47/19.42 | | | | elem(all_65_13, v0)))
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | GROUND_INST: instantiating (7) with all_65_16, all_174_2, all_65_13,
% 142.47/19.42 | | | | simplifying with (4), (15), (32), (45) gives:
% 142.47/19.42 | | | | (98) all_174_2 = all_65_16
% 142.47/19.42 | | | |
% 142.47/19.42 | | | | DELTA: instantiating (97) with fresh symbols all_773_0, all_773_1 gives:
% 142.47/19.43 | | | | (99) (host(all_174_2) = all_773_0 & $i(all_773_0) & ~ leq(all_65_12,
% 142.47/19.43 | | | | all_773_0)) | (queue(all_65_12) = all_773_1 & $i(all_773_1)
% 142.47/19.43 | | | | & ~ elem(all_65_13, all_773_1))
% 142.47/19.43 | | | |
% 142.47/19.43 | | | | DELTA: instantiating (96) with fresh symbols all_804_0, all_804_1,
% 142.47/19.43 | | | | all_804_2, all_804_3, all_804_4, all_804_5 gives:
% 142.47/19.43 | | | | (100) ( ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0 &
% 142.47/19.43 | | | | $i(all_804_0)) | ( ~ (all_804_1 = all_65_9) & index(ldr,
% 142.47/19.43 | | | | all_65_9) = all_804_1 & $i(all_804_1)) | ( ~ (all_804_2 =
% 142.47/19.43 | | | | elec_2) & index(status, all_804_5) = all_804_2 &
% 142.47/19.43 | | | | host(all_65_16) = all_804_5 & $i(all_804_2) & $i(all_804_5))
% 142.47/19.43 | | | | | (index(pendack, all_804_5) = all_804_4 & host(all_65_16) =
% 142.47/19.43 | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) & leq(all_804_4,
% 142.47/19.43 | | | | all_65_9)) | (queue(all_65_15) = all_804_3 & $i(all_804_3)
% 142.47/19.43 | | | | & ~ elem(all_65_13, all_804_3))
% 142.47/19.43 | | | |
% 142.47/19.43 | | | | BETA: splitting (100) gives:
% 142.47/19.43 | | | |
% 142.47/19.43 | | | | Case 1:
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | (101) ( ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0
% 142.47/19.43 | | | | | & $i(all_804_0)) | ( ~ (all_804_1 = all_65_9) & index(ldr,
% 142.47/19.43 | | | | | all_65_9) = all_804_1 & $i(all_804_1))
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | BETA: splitting (101) gives:
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | Case 1:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | (102) ~ (all_804_0 = norm) & index(status, all_65_9) = all_804_0
% 142.47/19.43 | | | | | | & $i(all_804_0)
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | ALPHA: (102) implies:
% 142.47/19.43 | | | | | | (103) ~ (all_804_0 = norm)
% 142.47/19.43 | | | | | | (104) index(status, all_65_9) = all_804_0
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | GROUND_INST: instantiating (33) with norm, all_804_0, all_65_9,
% 142.47/19.43 | | | | | | status, simplifying with (18), (104) gives:
% 142.47/19.43 | | | | | | (105) all_804_0 = norm
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | REDUCE: (103), (105) imply:
% 142.47/19.43 | | | | | | (106) $false
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | CLOSE: (106) is inconsistent.
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | Case 2:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | (107) ~ (all_804_1 = all_65_9) & index(ldr, all_65_9) =
% 142.47/19.43 | | | | | | all_804_1 & $i(all_804_1)
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | ALPHA: (107) implies:
% 142.47/19.43 | | | | | | (108) ~ (all_804_1 = all_65_9)
% 142.47/19.43 | | | | | | (109) index(ldr, all_65_9) = all_804_1
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | GROUND_INST: instantiating (33) with all_65_9, all_804_1, all_65_9,
% 142.47/19.43 | | | | | | ldr, simplifying with (25), (109) gives:
% 142.47/19.43 | | | | | | (110) all_804_1 = all_65_9
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | REDUCE: (108), (110) imply:
% 142.47/19.43 | | | | | | (111) $false
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | CLOSE: (111) is inconsistent.
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | End of split
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | Case 2:
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | (112) ( ~ (all_804_2 = elec_2) & index(status, all_804_5) =
% 142.47/19.43 | | | | | all_804_2 & host(all_65_16) = all_804_5 & $i(all_804_2) &
% 142.47/19.43 | | | | | $i(all_804_5)) | (index(pendack, all_804_5) = all_804_4 &
% 142.47/19.43 | | | | | host(all_65_16) = all_804_5 & $i(all_804_4) & $i(all_804_5)
% 142.47/19.43 | | | | | & leq(all_804_4, all_65_9)) | (queue(all_65_15) = all_804_3
% 142.47/19.43 | | | | | & $i(all_804_3) & ~ elem(all_65_13, all_804_3))
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | BETA: splitting (112) gives:
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | | Case 1:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | (113) ~ (all_804_2 = elec_2) & index(status, all_804_5) =
% 142.47/19.43 | | | | | | all_804_2 & host(all_65_16) = all_804_5 & $i(all_804_2) &
% 142.47/19.43 | | | | | | $i(all_804_5)
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | ALPHA: (113) implies:
% 142.47/19.43 | | | | | | (114) ~ (all_804_2 = elec_2)
% 142.47/19.43 | | | | | | (115) host(all_65_16) = all_804_5
% 142.47/19.43 | | | | | | (116) index(status, all_804_5) = all_804_2
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | BETA: splitting (99) gives:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | Case 1:
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | (117) host(all_174_2) = all_773_0 & $i(all_773_0) & ~
% 142.47/19.43 | | | | | | | leq(all_65_12, all_773_0)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | ALPHA: (117) implies:
% 142.47/19.43 | | | | | | | (118) ~ leq(all_65_12, all_773_0)
% 142.47/19.43 | | | | | | | (119) host(all_174_2) = all_773_0
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (98), (119) imply:
% 142.47/19.43 | | | | | | | (120) host(all_65_16) = all_773_0
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5,
% 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (115) gives:
% 142.47/19.43 | | | | | | | (121) all_804_5 = all_65_12
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_773_0, all_804_5,
% 142.47/19.43 | | | | | | | all_65_16, simplifying with (115), (120) gives:
% 142.47/19.43 | | | | | | | (122) all_804_5 = all_773_0
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | COMBINE_EQS: (121), (122) imply:
% 142.47/19.43 | | | | | | | (123) all_773_0 = all_65_12
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | SIMP: (123) implies:
% 142.47/19.43 | | | | | | | (124) all_773_0 = all_65_12
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (118), (124) imply:
% 142.47/19.43 | | | | | | | (125) ~ leq(all_65_12, all_65_12)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | PRED_UNIFY: (11), (125) imply:
% 142.47/19.43 | | | | | | | (126) $false
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | CLOSE: (126) is inconsistent.
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | Case 2:
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5,
% 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (115) gives:
% 142.47/19.43 | | | | | | | (127) all_804_5 = all_65_12
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (116), (127) imply:
% 142.47/19.43 | | | | | | | (128) index(status, all_65_12) = all_804_2
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (33) with elec_2, all_804_2, all_65_12,
% 142.47/19.43 | | | | | | | status, simplifying with (2), (128) gives:
% 142.47/19.43 | | | | | | | (129) all_804_2 = elec_2
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (114), (129) imply:
% 142.47/19.43 | | | | | | | (130) $false
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | CLOSE: (130) is inconsistent.
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | End of split
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | Case 2:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | (131) (index(pendack, all_804_5) = all_804_4 & host(all_65_16) =
% 142.47/19.43 | | | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) &
% 142.47/19.43 | | | | | | leq(all_804_4, all_65_9)) | (queue(all_65_15) = all_804_3
% 142.47/19.43 | | | | | | & $i(all_804_3) & ~ elem(all_65_13, all_804_3))
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | BETA: splitting (131) gives:
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | | Case 1:
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | (132) index(pendack, all_804_5) = all_804_4 & host(all_65_16) =
% 142.47/19.43 | | | | | | | all_804_5 & $i(all_804_4) & $i(all_804_5) &
% 142.47/19.43 | | | | | | | leq(all_804_4, all_65_9)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | ALPHA: (132) implies:
% 142.47/19.43 | | | | | | | (133) leq(all_804_4, all_65_9)
% 142.47/19.43 | | | | | | | (134) host(all_65_16) = all_804_5
% 142.47/19.43 | | | | | | | (135) index(pendack, all_804_5) = all_804_4
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (12) with all_65_12, all_804_5,
% 142.47/19.43 | | | | | | | all_65_16, simplifying with (36), (134) gives:
% 142.47/19.43 | | | | | | | (136) all_804_5 = all_65_12
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (135), (136) imply:
% 142.47/19.43 | | | | | | | (137) index(pendack, all_65_12) = all_804_4
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (33) with all_65_15, all_804_4,
% 142.47/19.43 | | | | | | | all_65_12, pendack, simplifying with (40), (137)
% 142.47/19.43 | | | | | | | gives:
% 142.47/19.43 | | | | | | | (138) all_804_4 = all_65_15
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (133), (138) imply:
% 142.47/19.43 | | | | | | | (139) leq(all_65_15, all_65_9)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | PRED_UNIFY: (23), (139) imply:
% 142.47/19.43 | | | | | | | (140) $false
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | CLOSE: (140) is inconsistent.
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | Case 2:
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | (141) queue(all_65_15) = all_804_3 & $i(all_804_3) & ~
% 142.47/19.43 | | | | | | | elem(all_65_13, all_804_3)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | ALPHA: (141) implies:
% 142.47/19.43 | | | | | | | (142) ~ elem(all_65_13, all_804_3)
% 142.47/19.43 | | | | | | | (143) queue(all_65_15) = all_804_3
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | GROUND_INST: instantiating (30) with all_65_14, all_804_3,
% 142.47/19.43 | | | | | | | all_65_15, simplifying with (17), (143) gives:
% 142.47/19.43 | | | | | | | (144) all_804_3 = all_65_14
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | REDUCE: (142), (144) imply:
% 142.47/19.43 | | | | | | | (145) ~ elem(all_65_13, all_65_14)
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | PRED_UNIFY: (29), (145) imply:
% 142.47/19.43 | | | | | | | (146) $false
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | | CLOSE: (146) is inconsistent.
% 142.47/19.43 | | | | | | |
% 142.47/19.43 | | | | | | End of split
% 142.47/19.43 | | | | | |
% 142.47/19.43 | | | | | End of split
% 142.47/19.43 | | | | |
% 142.47/19.43 | | | | End of split
% 142.47/19.43 | | | |
% 142.47/19.43 | | | End of split
% 142.47/19.43 | | |
% 142.47/19.43 | | End of split
% 142.47/19.43 | |
% 142.47/19.43 | End of split
% 142.47/19.43 |
% 142.47/19.43 End of proof
% 142.47/19.43
% 142.47/19.43 Sub-proof #2 shows that the following formulas are inconsistent:
% 142.47/19.43 ----------------------------------------------------------------
% 142.47/19.43 (1) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0 &
% 142.47/19.43 $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr, all_65_9) =
% 142.47/19.43 all_123_1 & $i(all_123_1)) | ( ~ (all_123_2 = all_65_9) &
% 142.47/19.43 host(all_65_7) = all_123_2 & $i(all_123_2)) | (queue(all_65_12) =
% 142.47/19.43 all_123_3 & $i(all_123_3) & ~ elem(all_65_3, all_123_3))
% 142.47/19.43 (2) host(all_65_7) = nbr_proc
% 142.47/19.43 (3) m_Ack(all_65_6, all_65_8) = all_65_0
% 142.47/19.43 (4) m_Ack(all_65_16, all_65_17) = all_65_11
% 142.47/19.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) |
% 142.47/19.43 ~ (host(v2) = v0))
% 142.47/19.43 (6) $i(all_65_7)
% 142.47/19.43 (7) ( ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 & $i(all_96_0)) |
% 142.47/19.43 (queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3,
% 142.47/19.43 all_96_1))
% 142.47/19.43 (8) all_65_9 = nbr_proc | leq(all_65_9, all_65_5)
% 142.47/19.43 (9) $i(all_65_6)
% 142.47/19.43 (10) queue(all_65_12) = all_65_2
% 142.47/19.43 (11) index(status, all_65_9) = norm
% 142.47/19.43 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v2)
% 142.47/19.43 = v3) | ~ (m_Ack(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 142.47/19.43 (13) host(all_65_17) = all_65_15
% 142.47/19.43 (14) all_128_7 = all_65_2
% 142.47/19.43 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 142.47/19.43 (v3 = v2 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3)
% 142.47/19.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 142.47/19.44 (16) ~ elem(all_65_0, all_128_7) | ~ elem(all_65_3, all_128_7)
% 142.47/19.44 (17) all_65_0 = all_65_11 | elem(all_65_0, all_65_2)
% 142.47/19.44 (18) ~ leq(all_65_9, all_65_15)
% 142.47/19.44 (19) all_65_3 = all_65_11 | elem(all_65_3, all_65_2)
% 142.47/19.44 (20) host(all_65_8) = all_65_5
% 142.47/19.44 (21) m_Down(all_65_7) = all_65_3
% 142.47/19.44 (22) index(ldr, all_65_9) = all_65_9
% 142.47/19.44 (23) $i(all_65_8)
% 142.47/19.44 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1)
% 142.47/19.44 | ~ (queue(v2) = v0))
% 142.47/19.44 (25) $i(all_65_17)
% 142.47/19.44 (26) $i(all_65_16)
% 142.47/19.44 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.47/19.44 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 142.47/19.44
% 142.47/19.44 Begin of proof
% 142.47/19.44 |
% 142.47/19.44 | BETA: splitting (19) gives:
% 142.47/19.44 |
% 142.47/19.44 | Case 1:
% 142.47/19.44 | |
% 142.47/19.44 | | (28) elem(all_65_3, all_65_2)
% 142.47/19.44 | |
% 142.47/19.44 | | BETA: splitting (16) gives:
% 142.47/19.44 | |
% 142.47/19.44 | | Case 1:
% 142.47/19.44 | | |
% 142.47/19.44 | | | (29) ~ elem(all_65_0, all_128_7)
% 142.47/19.44 | | |
% 142.47/19.44 | | | REDUCE: (14), (29) imply:
% 142.47/19.44 | | | (30) ~ elem(all_65_0, all_65_2)
% 142.47/19.44 | | |
% 142.47/19.44 | | | BETA: splitting (17) gives:
% 142.47/19.44 | | |
% 142.47/19.44 | | | Case 1:
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | (31) elem(all_65_0, all_65_2)
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | PRED_UNIFY: (30), (31) imply:
% 142.47/19.44 | | | | (32) $false
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | CLOSE: (32) is inconsistent.
% 142.47/19.44 | | | |
% 142.47/19.44 | | | Case 2:
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | (33) all_65_0 = all_65_11
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | REDUCE: (3), (33) imply:
% 142.47/19.44 | | | | (34) m_Ack(all_65_6, all_65_8) = all_65_11
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | BETA: splitting (7) gives:
% 142.47/19.44 | | | |
% 142.47/19.44 | | | | Case 1:
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | (35) ~ (all_96_0 = all_65_12) & host(all_65_7) = all_96_0 &
% 142.47/19.44 | | | | | $i(all_96_0)
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | ALPHA: (35) implies:
% 142.47/19.44 | | | | | (36) host(all_65_7) = all_96_0
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | BETA: splitting (1) gives:
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | Case 1:
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | (37) ( ~ (all_123_0 = norm) & index(status, all_65_9) = all_123_0
% 142.47/19.44 | | | | | | & $i(all_123_0)) | ( ~ (all_123_1 = all_65_9) & index(ldr,
% 142.47/19.44 | | | | | | all_65_9) = all_123_1 & $i(all_123_1))
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | BETA: splitting (37) gives:
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | Case 1:
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | (38) ~ (all_123_0 = norm) & index(status, all_65_9) =
% 142.47/19.44 | | | | | | | all_123_0 & $i(all_123_0)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | ALPHA: (38) implies:
% 142.47/19.44 | | | | | | | (39) ~ (all_123_0 = norm)
% 142.47/19.44 | | | | | | | (40) index(status, all_65_9) = all_123_0
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | GROUND_INST: instantiating (27) with norm, all_123_0, all_65_9,
% 142.47/19.44 | | | | | | | status, simplifying with (11), (40) gives:
% 142.47/19.44 | | | | | | | (41) all_123_0 = norm
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | REDUCE: (39), (41) imply:
% 142.47/19.44 | | | | | | | (42) $false
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | CLOSE: (42) is inconsistent.
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | Case 2:
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | (43) ~ (all_123_1 = all_65_9) & index(ldr, all_65_9) =
% 142.47/19.44 | | | | | | | all_123_1 & $i(all_123_1)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | ALPHA: (43) implies:
% 142.47/19.44 | | | | | | | (44) ~ (all_123_1 = all_65_9)
% 142.47/19.44 | | | | | | | (45) index(ldr, all_65_9) = all_123_1
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | GROUND_INST: instantiating (27) with all_65_9, all_123_1,
% 142.47/19.44 | | | | | | | all_65_9, ldr, simplifying with (22), (45) gives:
% 142.47/19.44 | | | | | | | (46) all_123_1 = all_65_9
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | REDUCE: (44), (46) imply:
% 142.47/19.44 | | | | | | | (47) $false
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | CLOSE: (47) is inconsistent.
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | End of split
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | Case 2:
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | (48) ( ~ (all_123_2 = all_65_9) & host(all_65_7) = all_123_2 &
% 142.47/19.44 | | | | | | $i(all_123_2)) | (queue(all_65_12) = all_123_3 &
% 142.47/19.44 | | | | | | $i(all_123_3) & ~ elem(all_65_3, all_123_3))
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | BETA: splitting (48) gives:
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | | Case 1:
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | (49) ~ (all_123_2 = all_65_9) & host(all_65_7) = all_123_2 &
% 142.47/19.44 | | | | | | | $i(all_123_2)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | ALPHA: (49) implies:
% 142.47/19.44 | | | | | | | (50) ~ (all_123_2 = all_65_9)
% 142.47/19.44 | | | | | | | (51) host(all_65_7) = all_123_2
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | GROUND_INST: instantiating (5) with nbr_proc, all_123_2, all_65_7,
% 142.47/19.44 | | | | | | | simplifying with (2), (51) gives:
% 142.47/19.44 | | | | | | | (52) all_123_2 = nbr_proc
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | GROUND_INST: instantiating (5) with all_96_0, all_123_2, all_65_7,
% 142.47/19.44 | | | | | | | simplifying with (36), (51) gives:
% 142.47/19.44 | | | | | | | (53) all_123_2 = all_96_0
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | COMBINE_EQS: (52), (53) imply:
% 142.47/19.44 | | | | | | | (54) all_96_0 = nbr_proc
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | REDUCE: (50), (52) imply:
% 142.47/19.44 | | | | | | | (55) ~ (all_65_9 = nbr_proc)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | SIMP: (55) implies:
% 142.47/19.44 | | | | | | | (56) ~ (all_65_9 = nbr_proc)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | BETA: splitting (8) gives:
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | Case 1:
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | (57) leq(all_65_9, all_65_5)
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | GROUND_INST: instantiating (15) with all_65_16, all_65_6,
% 142.47/19.44 | | | | | | | | all_65_17, all_65_8, all_65_11, simplifying with
% 142.47/19.44 | | | | | | | | (4), (9), (23), (25), (26), (34) gives:
% 142.47/19.44 | | | | | | | | (58) all_65_8 = all_65_17
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | REDUCE: (20), (58) imply:
% 142.47/19.44 | | | | | | | | (59) host(all_65_17) = all_65_5
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | GROUND_INST: instantiating (5) with all_65_15, all_65_5,
% 142.47/19.44 | | | | | | | | all_65_17, simplifying with (13), (59) gives:
% 142.47/19.44 | | | | | | | | (60) all_65_5 = all_65_15
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | REDUCE: (57), (60) imply:
% 142.47/19.44 | | | | | | | | (61) leq(all_65_9, all_65_15)
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | PRED_UNIFY: (18), (61) imply:
% 142.47/19.44 | | | | | | | | (62) $false
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | CLOSE: (62) is inconsistent.
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | Case 2:
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | (63) all_65_9 = nbr_proc
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | REDUCE: (56), (63) imply:
% 142.47/19.44 | | | | | | | | (64) $false
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | | CLOSE: (64) is inconsistent.
% 142.47/19.44 | | | | | | | |
% 142.47/19.44 | | | | | | | End of split
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | Case 2:
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | (65) queue(all_65_12) = all_123_3 & $i(all_123_3) & ~
% 142.47/19.44 | | | | | | | elem(all_65_3, all_123_3)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | ALPHA: (65) implies:
% 142.47/19.44 | | | | | | | (66) ~ elem(all_65_3, all_123_3)
% 142.47/19.44 | | | | | | | (67) queue(all_65_12) = all_123_3
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | GROUND_INST: instantiating (24) with all_65_2, all_123_3,
% 142.47/19.44 | | | | | | | all_65_12, simplifying with (10), (67) gives:
% 142.47/19.44 | | | | | | | (68) all_123_3 = all_65_2
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | REDUCE: (66), (68) imply:
% 142.47/19.44 | | | | | | | (69) ~ elem(all_65_3, all_65_2)
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | PRED_UNIFY: (28), (69) imply:
% 142.47/19.44 | | | | | | | (70) $false
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | | CLOSE: (70) is inconsistent.
% 142.47/19.44 | | | | | | |
% 142.47/19.44 | | | | | | End of split
% 142.47/19.44 | | | | | |
% 142.47/19.44 | | | | | End of split
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | Case 2:
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | (71) queue(all_65_12) = all_96_1 & $i(all_96_1) & ~ elem(all_65_3,
% 142.47/19.44 | | | | | all_96_1)
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | ALPHA: (71) implies:
% 142.47/19.44 | | | | | (72) ~ elem(all_65_3, all_96_1)
% 142.47/19.44 | | | | | (73) queue(all_65_12) = all_96_1
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | GROUND_INST: instantiating (24) with all_65_2, all_96_1, all_65_12,
% 142.47/19.44 | | | | | simplifying with (10), (73) gives:
% 142.47/19.44 | | | | | (74) all_96_1 = all_65_2
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | REDUCE: (72), (74) imply:
% 142.47/19.44 | | | | | (75) ~ elem(all_65_3, all_65_2)
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | PRED_UNIFY: (28), (75) imply:
% 142.47/19.44 | | | | | (76) $false
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | | CLOSE: (76) is inconsistent.
% 142.47/19.44 | | | | |
% 142.47/19.44 | | | | End of split
% 142.47/19.44 | | | |
% 142.47/19.44 | | | End of split
% 142.47/19.44 | | |
% 142.47/19.44 | | Case 2:
% 142.47/19.44 | | |
% 142.47/19.44 | | | (77) ~ elem(all_65_3, all_128_7)
% 142.47/19.44 | | |
% 142.47/19.44 | | | REDUCE: (14), (77) imply:
% 142.47/19.44 | | | (78) ~ elem(all_65_3, all_65_2)
% 142.47/19.44 | | |
% 142.47/19.44 | | | PRED_UNIFY: (28), (78) imply:
% 142.47/19.44 | | | (79) $false
% 142.47/19.44 | | |
% 142.47/19.44 | | | CLOSE: (79) is inconsistent.
% 142.47/19.44 | | |
% 142.47/19.44 | | End of split
% 142.47/19.44 | |
% 142.47/19.44 | Case 2:
% 142.47/19.44 | |
% 142.47/19.44 | | (80) all_65_3 = all_65_11
% 142.47/19.44 | |
% 142.47/19.44 | | REDUCE: (21), (80) imply:
% 142.47/19.44 | | (81) m_Down(all_65_7) = all_65_11
% 142.47/19.44 | |
% 142.47/19.44 | | GROUND_INST: instantiating (12) with all_65_16, all_65_17, all_65_7,
% 142.47/19.44 | | all_65_11, simplifying with (4), (6), (25), (26), (81) gives:
% 142.47/19.44 | | (82) $false
% 142.47/19.44 | |
% 142.47/19.44 | | CLOSE: (82) is inconsistent.
% 142.47/19.44 | |
% 142.47/19.44 | End of split
% 142.47/19.44 |
% 142.47/19.44 End of proof
% 142.47/19.44
% 142.47/19.44 Sub-proof #3 shows that the following formulas are inconsistent:
% 142.47/19.44 ----------------------------------------------------------------
% 142.47/19.44 (1) m_Ack(all_65_6, all_65_8) = all_65_11
% 142.47/19.44 (2) index(status, all_65_12) = elec_2
% 142.47/19.44 (3) m_Halt(all_65_16) = all_65_13
% 142.47/19.44 (4) setIn(all_65_10, alive)
% 142.47/19.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1
% 142.47/19.44 = v0 | ~ (m_Ack(v1, v3) = v4) | ~ (m_Ack(v0, v2) = v4) | ~ $i(v3) |
% 142.47/19.44 ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 142.47/19.44 (6) index(pendack, all_65_12) = all_65_5
% 142.47/19.44 (7) m_Ack(all_65_16, all_65_17) = all_65_11
% 142.47/19.44 (8) host(all_65_6) = all_65_12
% 142.47/19.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1) |
% 142.47/19.44 ~ (host(v2) = v0))
% 142.47/19.45 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 142.47/19.45 [v5: $i] : ( ~ (m_Halt(v2) = v4) | ~ (host(v1) = v5) | ~ (host(v0) =
% 142.47/19.45 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~
% 142.47/19.45 setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9:
% 142.47/19.45 $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v11 = norm) &
% 142.47/19.45 index(status, v3) = v11 & $i(v11)) | ( ~ (v10 = v3) & index(ldr,
% 142.47/19.45 v3) = v10 & $i(v10)) | ( ~ (v9 = elec_2) & index(status, v6) =
% 142.47/19.45 v9 & host(v2) = v6 & $i(v9) & $i(v6)) | (index(pendack, v6) = v7 &
% 142.47/19.45 host(v2) = v6 & $i(v7) & $i(v6) & leq(v7, v3)) | (queue(v5) = v8 &
% 142.47/19.45 $i(v8) & ~ elem(v4, v8))))
% 142.47/19.45 (11) setIn(all_65_6, alive)
% 142.47/19.45 (12) $i(all_65_6)
% 142.47/19.45 (13) queue(all_65_15) = all_65_14
% 142.47/19.45 (14) index(status, all_65_9) = norm
% 142.47/19.45 (15) ( ~ (all_254_2 = elec_2) & index(status, all_65_12) = all_254_2 &
% 142.47/19.45 $i(all_254_2)) | ( ~ (all_254_3 = elec_2) & index(status, all_65_9) =
% 142.47/19.45 all_254_3 & $i(all_254_3)) | (index(pendack, all_65_9) = all_254_1 &
% 142.47/19.45 index(pendack, all_65_12) = all_254_0 & $i(all_254_0) & $i(all_254_1)
% 142.47/19.45 & ~ leq(all_254_1, all_254_0))
% 142.47/19.45 (16) host(all_65_17) = all_65_15
% 142.47/19.45 (17) $i(all_65_10)
% 142.47/19.45 (18) host(all_65_10) = all_65_9
% 142.47/19.45 (19) ~ leq(all_65_15, all_65_9)
% 142.47/19.45 (20) host(all_65_8) = all_65_5
% 142.47/19.45 (21) index(ldr, all_65_9) = all_65_9
% 142.47/19.45 (22) $i(all_65_8)
% 142.47/19.45 (23) elem(all_65_13, all_65_14)
% 142.47/19.45 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1)
% 142.47/19.45 | ~ (queue(v2) = v0))
% 142.47/19.45 (25) $i(all_65_17)
% 142.47/19.45 (26) $i(all_65_16)
% 142.47/19.45 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.47/19.45 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 142.47/19.45 (28) all_65_8 = all_65_17
% 142.47/19.45
% 142.47/19.45 Begin of proof
% 142.47/19.45 |
% 142.47/19.45 | GROUND_INST: instantiating (5) with all_65_16, all_65_6, all_65_17, all_65_8,
% 142.47/19.45 | all_65_11, simplifying with (1), (7), (12), (22), (25), (26)
% 142.47/19.45 | gives:
% 142.47/19.45 | (29) all_65_6 = all_65_16
% 142.47/19.45 |
% 142.47/19.45 | REDUCE: (8), (29) imply:
% 142.47/19.45 | (30) host(all_65_16) = all_65_12
% 142.47/19.45 |
% 142.47/19.45 | REDUCE: (20), (28) imply:
% 142.47/19.45 | (31) host(all_65_17) = all_65_5
% 142.47/19.45 |
% 142.47/19.45 | REDUCE: (11), (29) imply:
% 142.47/19.45 | (32) setIn(all_65_16, alive)
% 142.47/19.45 |
% 142.47/19.45 | GROUND_INST: instantiating (9) with all_65_15, all_65_5, all_65_17,
% 142.47/19.45 | simplifying with (16), (31) gives:
% 142.47/19.45 | (33) all_65_5 = all_65_15
% 142.47/19.45 |
% 142.47/19.45 | REDUCE: (6), (33) imply:
% 142.47/19.45 | (34) index(pendack, all_65_12) = all_65_15
% 142.47/19.45 |
% 142.47/19.45 | BETA: splitting (15) gives:
% 142.47/19.45 |
% 142.47/19.45 | Case 1:
% 142.47/19.45 | |
% 142.47/19.45 | | (35) ~ (all_254_2 = elec_2) & index(status, all_65_12) = all_254_2 &
% 142.47/19.45 | | $i(all_254_2)
% 142.47/19.45 | |
% 142.47/19.45 | | ALPHA: (35) implies:
% 142.47/19.45 | | (36) ~ (all_254_2 = elec_2)
% 142.47/19.45 | | (37) index(status, all_65_12) = all_254_2
% 142.47/19.45 | |
% 142.47/19.45 | | GROUND_INST: instantiating (27) with elec_2, all_254_2, all_65_12, status,
% 142.47/19.45 | | simplifying with (2), (37) gives:
% 142.47/19.45 | | (38) all_254_2 = elec_2
% 142.47/19.45 | |
% 142.47/19.45 | | REDUCE: (36), (38) imply:
% 142.47/19.45 | | (39) $false
% 142.47/19.45 | |
% 142.47/19.45 | | CLOSE: (39) is inconsistent.
% 142.47/19.45 | |
% 142.47/19.45 | Case 2:
% 142.47/19.45 | |
% 142.47/19.45 | | (40) ( ~ (all_254_3 = elec_2) & index(status, all_65_9) = all_254_3 &
% 142.47/19.45 | | $i(all_254_3)) | (index(pendack, all_65_9) = all_254_1 &
% 142.47/19.45 | | index(pendack, all_65_12) = all_254_0 & $i(all_254_0) &
% 142.47/19.45 | | $i(all_254_1) & ~ leq(all_254_1, all_254_0))
% 142.47/19.45 | |
% 142.47/19.45 | | BETA: splitting (40) gives:
% 142.47/19.45 | |
% 142.47/19.45 | | Case 1:
% 142.47/19.45 | | |
% 142.47/19.45 | | | (41) ~ (all_254_3 = elec_2) & index(status, all_65_9) = all_254_3 &
% 142.47/19.45 | | | $i(all_254_3)
% 142.47/19.45 | | |
% 142.47/19.45 | | | ALPHA: (41) implies:
% 142.47/19.45 | | | (42) index(status, all_65_9) = all_254_3
% 142.47/19.45 | | |
% 142.47/19.45 | | | GROUND_INST: instantiating (27) with norm, all_254_3, all_65_9, status,
% 142.47/19.45 | | | simplifying with (14), (42) gives:
% 142.47/19.45 | | | (43) all_254_3 = norm
% 142.47/19.45 | | |
% 142.47/19.45 | | | GROUND_INST: instantiating (10) with all_65_10, all_65_17, all_65_16,
% 142.47/19.45 | | | all_65_9, all_65_13, all_65_15, simplifying with (3), (4),
% 142.47/19.45 | | | (16), (17), (18), (25), (26), (32) gives:
% 142.47/19.45 | | | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 142.47/19.45 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9)
% 142.47/19.45 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) =
% 142.47/19.45 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 &
% 142.47/19.45 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0)
% 142.47/19.45 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1,
% 142.47/19.45 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~
% 142.47/19.45 | | | elem(all_65_13, v2)))
% 142.47/19.45 | | |
% 142.47/19.45 | | | DELTA: instantiating (44) with fresh symbols all_801_0, all_801_1,
% 142.47/19.45 | | | all_801_2, all_801_3, all_801_4, all_801_5 gives:
% 142.47/19.45 | | | (45) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.45 | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr,
% 142.47/19.45 | | | all_65_9) = all_801_1 & $i(all_801_1)) | ( ~ (all_801_2 =
% 142.47/19.45 | | | elec_2) & index(status, all_801_5) = all_801_2 &
% 142.47/19.45 | | | host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) |
% 142.47/19.45 | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.45 | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.45 | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) &
% 142.47/19.45 | | | ~ elem(all_65_13, all_801_3))
% 142.47/19.45 | | |
% 142.47/19.45 | | | BETA: splitting (45) gives:
% 142.47/19.45 | | |
% 142.47/19.45 | | | Case 1:
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | (46) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.45 | | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr,
% 142.47/19.45 | | | | all_65_9) = all_801_1 & $i(all_801_1))
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | BETA: splitting (46) gives:
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | Case 1:
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | (47) ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.45 | | | | | $i(all_801_0)
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | ALPHA: (47) implies:
% 142.47/19.45 | | | | | (48) ~ (all_801_0 = norm)
% 142.47/19.45 | | | | | (49) index(status, all_65_9) = all_801_0
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with norm, all_801_0, all_65_9,
% 142.47/19.45 | | | | | status, simplifying with (14), (49) gives:
% 142.47/19.45 | | | | | (50) all_801_0 = norm
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | REDUCE: (48), (50) imply:
% 142.47/19.45 | | | | | (51) $false
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | CLOSE: (51) is inconsistent.
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | Case 2:
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | (52) ~ (all_801_1 = all_65_9) & index(ldr, all_65_9) = all_801_1 &
% 142.47/19.45 | | | | | $i(all_801_1)
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | ALPHA: (52) implies:
% 142.47/19.45 | | | | | (53) ~ (all_801_1 = all_65_9)
% 142.47/19.45 | | | | | (54) index(ldr, all_65_9) = all_801_1
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with all_65_9, all_801_1, all_65_9,
% 142.47/19.45 | | | | | ldr, simplifying with (21), (54) gives:
% 142.47/19.45 | | | | | (55) all_801_1 = all_65_9
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | REDUCE: (53), (55) imply:
% 142.47/19.45 | | | | | (56) $false
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | CLOSE: (56) is inconsistent.
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | End of split
% 142.47/19.45 | | | |
% 142.47/19.45 | | | Case 2:
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | (57) ( ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2
% 142.47/19.45 | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5))
% 142.47/19.45 | | | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.45 | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.45 | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) &
% 142.47/19.45 | | | | ~ elem(all_65_13, all_801_3))
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | BETA: splitting (57) gives:
% 142.47/19.45 | | | |
% 142.47/19.45 | | | | Case 1:
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | (58) ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2
% 142.47/19.45 | | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | ALPHA: (58) implies:
% 142.47/19.45 | | | | | (59) ~ (all_801_2 = elec_2)
% 142.47/19.45 | | | | | (60) host(all_65_16) = all_801_5
% 142.47/19.45 | | | | | (61) index(status, all_801_5) = all_801_2
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16,
% 142.47/19.45 | | | | | simplifying with (30), (60) gives:
% 142.47/19.45 | | | | | (62) all_801_5 = all_65_12
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | REDUCE: (61), (62) imply:
% 142.47/19.45 | | | | | (63) index(status, all_65_12) = all_801_2
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | GROUND_INST: instantiating (27) with elec_2, all_801_2, all_65_12,
% 142.47/19.45 | | | | | status, simplifying with (2), (63) gives:
% 142.47/19.45 | | | | | (64) all_801_2 = elec_2
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | REDUCE: (59), (64) imply:
% 142.47/19.45 | | | | | (65) $false
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | CLOSE: (65) is inconsistent.
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | Case 2:
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | (66) (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.45 | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.45 | | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3)
% 142.47/19.45 | | | | | & ~ elem(all_65_13, all_801_3))
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | BETA: splitting (66) gives:
% 142.47/19.45 | | | | |
% 142.47/19.45 | | | | | Case 1:
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | (67) index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.45 | | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.45 | | | | | | all_65_9)
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | ALPHA: (67) implies:
% 142.47/19.45 | | | | | | (68) leq(all_801_4, all_65_9)
% 142.47/19.45 | | | | | | (69) host(all_65_16) = all_801_5
% 142.47/19.45 | | | | | | (70) index(pendack, all_801_5) = all_801_4
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16,
% 142.47/19.45 | | | | | | simplifying with (30), (69) gives:
% 142.47/19.45 | | | | | | (71) all_801_5 = all_65_12
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | REDUCE: (70), (71) imply:
% 142.47/19.45 | | | | | | (72) index(pendack, all_65_12) = all_801_4
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | GROUND_INST: instantiating (27) with all_65_15, all_801_4,
% 142.47/19.45 | | | | | | all_65_12, pendack, simplifying with (34), (72) gives:
% 142.47/19.45 | | | | | | (73) all_801_4 = all_65_15
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | REDUCE: (68), (73) imply:
% 142.47/19.45 | | | | | | (74) leq(all_65_15, all_65_9)
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | PRED_UNIFY: (19), (74) imply:
% 142.47/19.45 | | | | | | (75) $false
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | | CLOSE: (75) is inconsistent.
% 142.47/19.45 | | | | | |
% 142.47/19.45 | | | | | Case 2:
% 142.47/19.45 | | | | | |
% 142.47/19.46 | | | | | | (76) queue(all_65_15) = all_801_3 & $i(all_801_3) & ~
% 142.47/19.46 | | | | | | elem(all_65_13, all_801_3)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | ALPHA: (76) implies:
% 142.47/19.46 | | | | | | (77) ~ elem(all_65_13, all_801_3)
% 142.47/19.46 | | | | | | (78) queue(all_65_15) = all_801_3
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | GROUND_INST: instantiating (24) with all_65_14, all_801_3,
% 142.47/19.46 | | | | | | all_65_15, simplifying with (13), (78) gives:
% 142.47/19.46 | | | | | | (79) all_801_3 = all_65_14
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | REDUCE: (77), (79) imply:
% 142.47/19.46 | | | | | | (80) ~ elem(all_65_13, all_65_14)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | PRED_UNIFY: (23), (80) imply:
% 142.47/19.46 | | | | | | (81) $false
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | CLOSE: (81) is inconsistent.
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | End of split
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | End of split
% 142.47/19.46 | | | |
% 142.47/19.46 | | | End of split
% 142.47/19.46 | | |
% 142.47/19.46 | | Case 2:
% 142.47/19.46 | | |
% 142.47/19.46 | | | (82) index(pendack, all_65_9) = all_254_1 & index(pendack, all_65_12) =
% 142.47/19.46 | | | all_254_0 & $i(all_254_0) & $i(all_254_1) & ~ leq(all_254_1,
% 142.47/19.46 | | | all_254_0)
% 142.47/19.46 | | |
% 142.47/19.46 | | | ALPHA: (82) implies:
% 142.47/19.46 | | | (83) index(pendack, all_65_12) = all_254_0
% 142.47/19.46 | | |
% 142.47/19.46 | | | GROUND_INST: instantiating (27) with all_65_15, all_254_0, all_65_12,
% 142.47/19.46 | | | pendack, simplifying with (34), (83) gives:
% 142.47/19.46 | | | (84) all_254_0 = all_65_15
% 142.47/19.46 | | |
% 142.47/19.46 | | | GROUND_INST: instantiating (10) with all_65_10, all_65_17, all_65_16,
% 142.47/19.46 | | | all_65_9, all_65_13, all_65_15, simplifying with (3), (4),
% 142.47/19.46 | | | (16), (17), (18), (25), (26), (32) gives:
% 142.47/19.46 | | | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 142.47/19.46 | | | any] : ? [v5: $i] : (( ~ (v5 = norm) & index(status, all_65_9)
% 142.47/19.46 | | | = v5 & $i(v5)) | ( ~ (v4 = all_65_9) & index(ldr, all_65_9) =
% 142.47/19.46 | | | v4 & $i(v4)) | ( ~ (v3 = elec_2) & index(status, v0) = v3 &
% 142.47/19.46 | | | host(all_65_16) = v0 & $i(v3) & $i(v0)) | (index(pendack, v0)
% 142.47/19.46 | | | = v1 & host(all_65_16) = v0 & $i(v1) & $i(v0) & leq(v1,
% 142.47/19.46 | | | all_65_9)) | (queue(all_65_15) = v2 & $i(v2) & ~
% 142.47/19.46 | | | elem(all_65_13, v2)))
% 142.47/19.46 | | |
% 142.47/19.46 | | | DELTA: instantiating (85) with fresh symbols all_801_0, all_801_1,
% 142.47/19.46 | | | all_801_2, all_801_3, all_801_4, all_801_5 gives:
% 142.47/19.46 | | | (86) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.46 | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr,
% 142.47/19.46 | | | all_65_9) = all_801_1 & $i(all_801_1)) | ( ~ (all_801_2 =
% 142.47/19.46 | | | elec_2) & index(status, all_801_5) = all_801_2 &
% 142.47/19.46 | | | host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)) |
% 142.47/19.46 | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.46 | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.46 | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) &
% 142.47/19.46 | | | ~ elem(all_65_13, all_801_3))
% 142.47/19.46 | | |
% 142.47/19.46 | | | BETA: splitting (86) gives:
% 142.47/19.46 | | |
% 142.47/19.46 | | | Case 1:
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | (87) ( ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.46 | | | | $i(all_801_0)) | ( ~ (all_801_1 = all_65_9) & index(ldr,
% 142.47/19.46 | | | | all_65_9) = all_801_1 & $i(all_801_1))
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | BETA: splitting (87) gives:
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | Case 1:
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | (88) ~ (all_801_0 = norm) & index(status, all_65_9) = all_801_0 &
% 142.47/19.46 | | | | | $i(all_801_0)
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | ALPHA: (88) implies:
% 142.47/19.46 | | | | | (89) ~ (all_801_0 = norm)
% 142.47/19.46 | | | | | (90) index(status, all_65_9) = all_801_0
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with norm, all_801_0, all_65_9,
% 142.47/19.46 | | | | | status, simplifying with (14), (90) gives:
% 142.47/19.46 | | | | | (91) all_801_0 = norm
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | REDUCE: (89), (91) imply:
% 142.47/19.46 | | | | | (92) $false
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | CLOSE: (92) is inconsistent.
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | Case 2:
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | (93) ~ (all_801_1 = all_65_9) & index(ldr, all_65_9) = all_801_1 &
% 142.47/19.46 | | | | | $i(all_801_1)
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | ALPHA: (93) implies:
% 142.47/19.46 | | | | | (94) ~ (all_801_1 = all_65_9)
% 142.47/19.46 | | | | | (95) index(ldr, all_65_9) = all_801_1
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with all_65_9, all_801_1, all_65_9,
% 142.47/19.46 | | | | | ldr, simplifying with (21), (95) gives:
% 142.47/19.46 | | | | | (96) all_801_1 = all_65_9
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | REDUCE: (94), (96) imply:
% 142.47/19.46 | | | | | (97) $false
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | CLOSE: (97) is inconsistent.
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | End of split
% 142.47/19.46 | | | |
% 142.47/19.46 | | | Case 2:
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | (98) ( ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2
% 142.47/19.46 | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5))
% 142.47/19.46 | | | | | (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.46 | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.46 | | | | all_65_9)) | (queue(all_65_15) = all_801_3 & $i(all_801_3) &
% 142.47/19.46 | | | | ~ elem(all_65_13, all_801_3))
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | BETA: splitting (98) gives:
% 142.47/19.46 | | | |
% 142.47/19.46 | | | | Case 1:
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | (99) ~ (all_801_2 = elec_2) & index(status, all_801_5) = all_801_2
% 142.47/19.46 | | | | | & host(all_65_16) = all_801_5 & $i(all_801_2) & $i(all_801_5)
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | ALPHA: (99) implies:
% 142.47/19.46 | | | | | (100) ~ (all_801_2 = elec_2)
% 142.47/19.46 | | | | | (101) host(all_65_16) = all_801_5
% 142.47/19.46 | | | | | (102) index(status, all_801_5) = all_801_2
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16,
% 142.47/19.46 | | | | | simplifying with (30), (101) gives:
% 142.47/19.46 | | | | | (103) all_801_5 = all_65_12
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | REDUCE: (102), (103) imply:
% 142.47/19.46 | | | | | (104) index(status, all_65_12) = all_801_2
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | GROUND_INST: instantiating (27) with elec_2, all_801_2, all_65_12,
% 142.47/19.46 | | | | | status, simplifying with (2), (104) gives:
% 142.47/19.46 | | | | | (105) all_801_2 = elec_2
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | REDUCE: (100), (105) imply:
% 142.47/19.46 | | | | | (106) $false
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | CLOSE: (106) is inconsistent.
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | Case 2:
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | (107) (index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.46 | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.46 | | | | | all_65_9)) | (queue(all_65_15) = all_801_3 &
% 142.47/19.46 | | | | | $i(all_801_3) & ~ elem(all_65_13, all_801_3))
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | BETA: splitting (107) gives:
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | | Case 1:
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | (108) index(pendack, all_801_5) = all_801_4 & host(all_65_16) =
% 142.47/19.46 | | | | | | all_801_5 & $i(all_801_4) & $i(all_801_5) & leq(all_801_4,
% 142.47/19.46 | | | | | | all_65_9)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | ALPHA: (108) implies:
% 142.47/19.46 | | | | | | (109) leq(all_801_4, all_65_9)
% 142.47/19.46 | | | | | | (110) host(all_65_16) = all_801_5
% 142.47/19.46 | | | | | | (111) index(pendack, all_801_5) = all_801_4
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | GROUND_INST: instantiating (9) with all_65_12, all_801_5, all_65_16,
% 142.47/19.46 | | | | | | simplifying with (30), (110) gives:
% 142.47/19.46 | | | | | | (112) all_801_5 = all_65_12
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | REDUCE: (111), (112) imply:
% 142.47/19.46 | | | | | | (113) index(pendack, all_65_12) = all_801_4
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | GROUND_INST: instantiating (27) with all_65_15, all_801_4,
% 142.47/19.46 | | | | | | all_65_12, pendack, simplifying with (34), (113) gives:
% 142.47/19.46 | | | | | | (114) all_801_4 = all_65_15
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | REDUCE: (109), (114) imply:
% 142.47/19.46 | | | | | | (115) leq(all_65_15, all_65_9)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | PRED_UNIFY: (19), (115) imply:
% 142.47/19.46 | | | | | | (116) $false
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | CLOSE: (116) is inconsistent.
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | Case 2:
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | (117) queue(all_65_15) = all_801_3 & $i(all_801_3) & ~
% 142.47/19.46 | | | | | | elem(all_65_13, all_801_3)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | ALPHA: (117) implies:
% 142.47/19.46 | | | | | | (118) ~ elem(all_65_13, all_801_3)
% 142.47/19.46 | | | | | | (119) queue(all_65_15) = all_801_3
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | GROUND_INST: instantiating (24) with all_65_14, all_801_3,
% 142.47/19.46 | | | | | | all_65_15, simplifying with (13), (119) gives:
% 142.47/19.46 | | | | | | (120) all_801_3 = all_65_14
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | REDUCE: (118), (120) imply:
% 142.47/19.46 | | | | | | (121) ~ elem(all_65_13, all_65_14)
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | PRED_UNIFY: (23), (121) imply:
% 142.47/19.46 | | | | | | (122) $false
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | | CLOSE: (122) is inconsistent.
% 142.47/19.46 | | | | | |
% 142.47/19.46 | | | | | End of split
% 142.47/19.46 | | | | |
% 142.47/19.46 | | | | End of split
% 142.47/19.46 | | | |
% 142.47/19.46 | | | End of split
% 142.47/19.46 | | |
% 142.47/19.46 | | End of split
% 142.47/19.46 | |
% 142.47/19.46 | End of split
% 142.47/19.46 |
% 142.47/19.46 End of proof
% 142.47/19.46
% 142.47/19.46 Sub-proof #4 shows that the following formulas are inconsistent:
% 142.47/19.46 ----------------------------------------------------------------
% 142.47/19.46 (1) $i(all_65_15)
% 142.47/19.46 (2) $i(all_65_9)
% 142.47/19.46 (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v1,
% 142.47/19.46 v0) | ~ leq(v0, v1))
% 142.47/19.46 (4) ~ (all_65_9 = all_65_15)
% 142.47/19.46 (5) leq(all_65_9, all_65_15)
% 142.47/19.46 (6) leq(all_65_15, all_65_9)
% 142.47/19.46
% 142.47/19.46 Begin of proof
% 142.47/19.46 |
% 142.47/19.46 | GROUND_INST: instantiating (3) with all_65_15, all_65_9, simplifying with (1),
% 142.47/19.46 | (2), (5), (6) gives:
% 142.47/19.46 | (7) all_65_9 = all_65_15
% 142.47/19.46 |
% 142.47/19.46 | REDUCE: (4), (7) imply:
% 142.47/19.46 | (8) $false
% 142.47/19.46 |
% 142.47/19.46 | CLOSE: (8) is inconsistent.
% 142.47/19.46 |
% 142.47/19.46 End of proof
% 142.47/19.46 % SZS output end Proof for theBenchmark
% 142.47/19.46
% 142.47/19.46 18852ms
%------------------------------------------------------------------------------