TSTP Solution File: SWV472+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV472+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 : n025.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 22:56:38 EDT 2023
% Result : Theorem 53.88s 7.87s
% Output : Proof 77.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV472+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 03:14:54 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ________ _____
% 0.18/0.58 ___ __ \_________(_)________________________________
% 0.18/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.58 (2023-06-19)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2023
% 0.18/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.58 Amanda Stjerna.
% 0.18/0.58 Free software under BSD-3-Clause.
% 0.18/0.58
% 0.18/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.48/1.22 Prover 4: Preprocessing ...
% 3.48/1.23 Prover 1: Preprocessing ...
% 3.89/1.28 Prover 2: Preprocessing ...
% 3.89/1.28 Prover 5: Preprocessing ...
% 3.89/1.28 Prover 0: Preprocessing ...
% 3.89/1.28 Prover 3: Preprocessing ...
% 3.89/1.28 Prover 6: Preprocessing ...
% 10.04/2.12 Prover 3: Constructing countermodel ...
% 10.04/2.15 Prover 1: Constructing countermodel ...
% 10.04/2.16 Prover 6: Proving ...
% 10.62/2.27 Prover 5: Proving ...
% 11.35/2.30 Prover 2: Proving ...
% 11.58/2.41 Prover 4: Constructing countermodel ...
% 12.26/2.45 Prover 0: Proving ...
% 13.53/2.71 Prover 3: gave up
% 13.53/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.73/2.82 Prover 7: Preprocessing ...
% 18.39/3.30 Prover 7: Warning: ignoring some quantifiers
% 18.39/3.35 Prover 7: Constructing countermodel ...
% 21.06/3.65 Prover 1: gave up
% 21.45/3.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.45/3.71 Prover 8: Preprocessing ...
% 22.90/3.91 Prover 8: Warning: ignoring some quantifiers
% 22.90/3.92 Prover 8: Constructing countermodel ...
% 28.76/4.67 Prover 8: gave up
% 28.76/4.67 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 29.54/4.73 Prover 9: Preprocessing ...
% 32.60/5.15 Prover 9: Constructing countermodel ...
% 53.88/7.87 Prover 2: proved (7238ms)
% 53.88/7.87
% 53.88/7.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.88/7.87
% 53.88/7.87 Prover 9: stopped
% 53.88/7.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 53.88/7.87 Prover 5: stopped
% 53.88/7.87 Prover 6: stopped
% 53.99/7.88 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 53.99/7.88 Prover 0: stopped
% 53.99/7.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 53.99/7.89 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 53.99/7.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 54.50/7.96 Prover 10: Preprocessing ...
% 54.50/7.97 Prover 11: Preprocessing ...
% 54.50/7.98 Prover 16: Preprocessing ...
% 54.50/7.98 Prover 13: Preprocessing ...
% 54.50/7.99 Prover 19: Preprocessing ...
% 55.17/8.05 Prover 10: Warning: ignoring some quantifiers
% 55.17/8.05 Prover 10: Constructing countermodel ...
% 55.58/8.11 Prover 16: Warning: ignoring some quantifiers
% 55.58/8.12 Prover 16: Constructing countermodel ...
% 56.24/8.21 Prover 19: Warning: ignoring some quantifiers
% 56.24/8.22 Prover 13: Warning: ignoring some quantifiers
% 56.24/8.23 Prover 19: Constructing countermodel ...
% 56.24/8.24 Prover 13: Constructing countermodel ...
% 56.24/8.25 Prover 11: Constructing countermodel ...
% 77.53/10.94 Prover 16: Found proof (size 101)
% 77.53/10.94 Prover 16: proved (3045ms)
% 77.53/10.94 Prover 11: stopped
% 77.53/10.94 Prover 7: stopped
% 77.53/10.94 Prover 13: stopped
% 77.53/10.94 Prover 19: stopped
% 77.53/10.94 Prover 10: stopped
% 77.53/10.94 Prover 4: stopped
% 77.53/10.94
% 77.53/10.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 77.53/10.94
% 77.53/10.95 % SZS output start Proof for theBenchmark
% 77.53/10.95 Assumptions after simplification:
% 77.53/10.95 ---------------------------------
% 77.53/10.95
% 77.53/10.95 (axiom_01)
% 77.53/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) =
% 77.53/10.98 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v2) & s(v2) = v3 &
% 77.53/10.98 $i(v3)))
% 77.53/10.98
% 77.53/10.98 (axiom_03)
% 77.53/10.98 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0,
% 77.53/10.98 nbr_proc))
% 77.53/10.98
% 77.53/10.98 (axiom_17)
% 77.53/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (m_Down(v0) = v2) | ~
% 77.53/10.98 (m_Halt(v1) = v2) | ~ $i(v1) | ~ $i(v0))
% 77.53/10.98
% 77.53/10.98 (axiom_46)
% 77.53/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.53/10.98 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 77.53/10.98 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 77.53/10.98 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 77.53/10.98 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 77.53/10.98 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 77.53/10.98
% 77.53/10.98 (axiom_47)
% 77.53/11.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.53/11.01 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 77.53/11.01 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 77.53/11.01 (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 77.53/11.01 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (snoc(v1, v0)
% 77.53/11.01 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 77.53/11.01
% 77.53/11.01 (conj)
% 77.53/11.03 $i(pendack) & $i(down) & $i(ldr) & $i(elid) & $i(status) & $i(alive) &
% 77.53/11.03 $i(norm) & $i(wait) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ?
% 77.53/11.03 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 77.53/11.03 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 77.53/11.03 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ?
% 77.53/11.03 [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: $i] : ( ~ (v5 = nbr_proc) &
% 77.53/11.03 index(pendack, v5) = v8 & index(down, nbr_proc) = v15 & index(elid, v5) = v2
% 77.53/11.03 & index(status, v5) = elec_2 & index(status, nbr_proc) = elec_1 & snoc(v1,
% 77.53/11.03 v9) = v10 & cons(v7, v1) = v6 & m_Down(v13) = v17 & m_Down(v12) = v19 &
% 77.53/11.03 m_Halt(v3) = v9 & s(v8) = v5 & s(zero) = v0 & m_Ack(v2, v4) = v7 & host(v14)
% 77.53/11.03 = nbr_proc & host(v13) = v16 & host(v12) = nbr_proc & host(v11) = v5 &
% 77.53/11.03 host(v4) = v8 & host(v3) = v5 & queue(v5) = v6 & queue(nbr_proc) = v18 &
% 77.53/11.03 $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) &
% 77.53/11.03 $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 77.53/11.03 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & setIn(v11, alive) & setIn(v3,
% 77.53/11.03 alive) & elem(v19, v10) & elem(v17, v18) & ~ leq(nbr_proc, v8) & ! [v20:
% 77.53/11.03 $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25:
% 77.53/11.03 $i] : ! [v26: $i] : ! [v27: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) |
% 77.53/11.03 ~ (m_Down(v21) = v27) | ~ (host(v22) = v24) | ~ (host(v20) = v25) | ~
% 77.53/11.03 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 77.53/11.03 setIn(v20, alive) | ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31:
% 77.53/11.03 $i] : (( ~ (v29 = v24) & host(v23) = v29 & $i(v29)) | ( ~ (v28 = v25) &
% 77.53/11.03 host(v21) = v28 & $i(v28)) | (queue(v25) = v30 & $i(v30) & ~
% 77.53/11.03 elem(v26, v30)) | (queue(v24) = v31 & $i(v31) & ~ elem(v27, v31)))) &
% 77.53/11.03 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] :
% 77.53/11.03 ! [v25: $i] : ! [v26: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~
% 77.53/11.03 (host(v22) = v24) | ~ (host(v21) = v25) | ~ (host(v20) = v25) | ~
% 77.53/11.03 $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 77.53/11.03 setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v27
% 77.53/11.03 = v24) & host(v23) = v27 & $i(v27)) | (index(down, v24) = v29 &
% 77.53/11.03 $i(v29) & ~ setIn(v25, v29)) | (queue(v25) = v28 & $i(v28) & ~
% 77.53/11.03 elem(v26, v28)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 77.53/11.03 [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i] : ( ~ (m_Down(v22) =
% 77.53/11.03 v24) | ~ (m_Down(v21) = v25) | ~ (host(v23) = nbr_proc) | ~
% 77.53/11.03 (host(v20) = v26) | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~
% 77.53/11.03 setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30:
% 77.53/11.03 $i] : ? [v31: $i] : ? [v32: $i] : ($i(v32) & ((v29 = v18 & ~
% 77.53/11.03 elem(v24, v18)) | (v27 = v15 & ~ (v32 = v28) & host(v22) = v28 &
% 77.53/11.03 $i(v28) & leq(v0, v32) & ~ leq(nbr_proc, v32) & ~ setIn(v32, v15))
% 77.53/11.03 | ( ~ (v30 = nbr_proc) & host(v21) = v30 & $i(v30)) | (queue(v26) =
% 77.53/11.03 v31 & $i(v31) & ~ elem(v25, v31))))) & ! [v20: $i] : ! [v21: $i]
% 77.53/11.03 : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : (v24 = v23 |
% 77.53/11.03 ~ (m_Down(v20) = v25) | ~ (host(v22) = v23) | ~ (host(v21) = v24) | ~
% 77.53/11.03 $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ? [v26: $i] :
% 77.53/11.03 ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : (( ~ (v29 =
% 77.53/11.03 v24) & index(elid, v23) = v28 & host(v28) = v29 & $i(v29) & $i(v28))
% 77.53/11.03 | ( ~ (v27 = wait) & index(status, v23) = v27 & $i(v27)) | ( ~ (v26 =
% 77.53/11.03 v23) & host(v20) = v26 & $i(v26)) | (queue(v24) = v30 & $i(v30) & ~
% 77.53/11.03 elem(v25, v30)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 77.53/11.03 [v23: $i] : ! [v24: $i] : ! [v25: $i] : (v24 = v23 | ~ (m_Down(v20) =
% 77.53/11.03 v25) | ~ (host(v22) = v23) | ~ (host(v21) = v24) | ~ $i(v22) | ~
% 77.53/11.03 $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ? [v26: $i] : ? [v27: $i]
% 77.53/11.03 : ? [v28: $i] : ? [v29: $i] : (( ~ (v28 = v24) & index(ldr, v23) = v28 &
% 77.53/11.03 $i(v28)) | ( ~ (v27 = norm) & index(status, v23) = v27 & $i(v27)) | (
% 77.53/11.03 ~ (v26 = v23) & host(v20) = v26 & $i(v26)) | (queue(v24) = v29 &
% 77.53/11.03 $i(v29) & ~ elem(v25, v29)))) & ! [v20: $i] : ! [v21: $i] : !
% 77.53/11.03 [v22: $i] : ! [v23: $i] : ( ~ (m_Ldr(v21) = v22) | ~ (host(v20) = v23) |
% 77.53/11.03 ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) = v25 &
% 77.53/11.03 $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24) & ~
% 77.53/11.03 elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 77.53/11.03 [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23) | ~ $i(v21) | ~
% 77.53/11.03 $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25 = v23) & host(v21) = v25
% 77.53/11.03 & $i(v25)) | (queue(v23) = v24 & $i(v24) & ~ elem(v22, v24)))) & !
% 77.53/11.03 [v20: $i] : ! [v21: $i] : ! [v22: $i] : (v21 = v20 | ~ (host(v21) = v22)
% 77.53/11.03 | ~ (host(v20) = v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) |
% 77.53/11.03 ~ setIn(v20, alive)) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~
% 77.53/11.03 (m_NotNorm(v20) = v22) | ~ (host(v21) = nbr_proc) | ~ $i(v21) | ~
% 77.53/11.03 $i(v20) | ~ elem(v22, v18)) & ! [v20: $i] : ! [v21: $i] : ( ~
% 77.53/11.03 (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) | ? [v22: $i] : ?
% 77.53/11.03 [v23: $i] : ((v23 = v20 & index(elid, v21) = v20) | ( ~ (v22 = elec_1) &
% 77.53/11.03 ~ (v22 = elec_2) & index(status, v21) = v22 & $i(v22)))) & ! [v20:
% 77.53/11.03 $i] : (v20 = v16 | ~ $i(v20) | ~ leq(v0, v20) | leq(nbr_proc, v20) |
% 77.53/11.03 setIn(v20, v15)))
% 77.53/11.03
% 77.53/11.03 (function-axioms)
% 77.53/11.03 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.53/11.03 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 77.53/11.03 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 77.53/11.03 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 77.53/11.03 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 77.53/11.03 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 77.53/11.03 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 77.53/11.03 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 77.53/11.03 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 77.53/11.03 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 77.53/11.03 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 77.53/11.03 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 77.53/11.03 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 77.53/11.03 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 77.53/11.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 77.53/11.03 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.53/11.03 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 77.53/11.03 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 77.53/11.03 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 77.53/11.03 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.53/11.03 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 77.53/11.03 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 77.53/11.03 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 77.53/11.03
% 77.53/11.03 Further assumptions not needed in the proof:
% 77.53/11.03 --------------------------------------------
% 77.53/11.03 axiom, axiom_02, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08, axiom_09,
% 77.53/11.03 axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16, axiom_18,
% 77.53/11.03 axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25, axiom_26,
% 77.53/11.03 axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, axiom_32, axiom_33, axiom_34,
% 77.53/11.03 axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41, axiom_42,
% 77.53/11.03 axiom_43, axiom_44, axiom_45, axiom_48, axiom_49, axiom_50, axiom_51, axiom_52,
% 77.53/11.03 axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_58, axiom_59, axiom_60,
% 77.53/11.03 axiom_61, axiom_62, axiom_63, axiom_64, axiom_65
% 77.53/11.03
% 77.53/11.03 Those formulas are unsatisfiable:
% 77.53/11.03 ---------------------------------
% 77.53/11.03
% 77.53/11.03 Begin of proof
% 77.53/11.03 |
% 77.53/11.03 | ALPHA: (axiom_03) implies:
% 77.53/11.03 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc))
% 77.53/11.03 |
% 77.53/11.03 | ALPHA: (axiom_46) implies:
% 77.53/11.04 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v1,
% 77.53/11.04 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 77.53/11.04 | elem(v0, v3))
% 77.53/11.04 |
% 77.53/11.04 | ALPHA: (axiom_47) implies:
% 77.53/11.04 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.53/11.04 | (snoc(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0,
% 77.53/11.04 | v3) | elem(v0, v2))
% 77.53/11.04 |
% 77.53/11.04 | ALPHA: (conj) implies:
% 77.53/11.04 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 77.53/11.04 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 77.53/11.04 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 77.53/11.04 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19:
% 77.53/11.04 | $i] : ( ~ (v5 = nbr_proc) & index(pendack, v5) = v8 & index(down,
% 77.53/11.04 | nbr_proc) = v15 & index(elid, v5) = v2 & index(status, v5) = elec_2
% 77.53/11.04 | & index(status, nbr_proc) = elec_1 & snoc(v1, v9) = v10 & cons(v7,
% 77.53/11.04 | v1) = v6 & m_Down(v13) = v17 & m_Down(v12) = v19 & m_Halt(v3) = v9
% 77.53/11.04 | & s(v8) = v5 & s(zero) = v0 & m_Ack(v2, v4) = v7 & host(v14) =
% 77.53/11.04 | nbr_proc & host(v13) = v16 & host(v12) = nbr_proc & host(v11) = v5 &
% 77.53/11.04 | host(v4) = v8 & host(v3) = v5 & queue(v5) = v6 & queue(nbr_proc) =
% 77.53/11.04 | v18 & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) &
% 77.53/11.04 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 77.53/11.04 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 77.53/11.04 | setIn(v11, alive) & setIn(v3, alive) & elem(v19, v10) & elem(v17,
% 77.53/11.04 | v18) & ~ leq(nbr_proc, v8) & ! [v20: $i] : ! [v21: $i] : !
% 77.53/11.04 | [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26: $i]
% 77.53/11.04 | : ! [v27: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~
% 77.53/11.04 | (m_Down(v21) = v27) | ~ (host(v22) = v24) | ~ (host(v20) = v25) |
% 77.53/11.04 | ~ $i(v23) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22,
% 77.53/11.04 | alive) | ~ setIn(v20, alive) | ? [v28: $i] : ? [v29: $i] : ?
% 77.53/11.04 | [v30: $i] : ? [v31: $i] : (( ~ (v29 = v24) & host(v23) = v29 &
% 77.53/11.04 | $i(v29)) | ( ~ (v28 = v25) & host(v21) = v28 & $i(v28)) |
% 77.53/11.04 | (queue(v25) = v30 & $i(v30) & ~ elem(v26, v30)) | (queue(v24) =
% 77.53/11.04 | v31 & $i(v31) & ~ elem(v27, v31)))) & ! [v20: $i] : ! [v21:
% 77.53/11.04 | $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] :
% 77.53/11.04 | ! [v26: $i] : (v25 = v24 | ~ (m_Down(v23) = v26) | ~ (host(v22) =
% 77.53/11.04 | v24) | ~ (host(v21) = v25) | ~ (host(v20) = v25) | ~ $i(v23) |
% 77.53/11.04 | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ~
% 77.53/11.04 | setIn(v20, alive) | ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : ((
% 77.53/11.04 | ~ (v27 = v24) & host(v23) = v27 & $i(v27)) | (index(down, v24)
% 77.53/11.04 | = v29 & $i(v29) & ~ setIn(v25, v29)) | (queue(v25) = v28 &
% 77.53/11.04 | $i(v28) & ~ elem(v26, v28)))) & ! [v20: $i] : ! [v21: $i] :
% 77.53/11.04 | ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : ! [v26:
% 77.53/11.04 | $i] : ( ~ (m_Down(v22) = v24) | ~ (m_Down(v21) = v25) | ~
% 77.53/11.04 | (host(v23) = nbr_proc) | ~ (host(v20) = v26) | ~ $i(v23) | ~
% 77.53/11.04 | $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v20, alive) | ? [v27:
% 77.53/11.05 | $i] : ? [v28: $i] : ? [v29: $i] : ? [v30: $i] : ? [v31: $i] :
% 77.53/11.05 | ? [v32: $i] : ($i(v32) & ((v29 = v18 & ~ elem(v24, v18)) | (v27 =
% 77.53/11.05 | v15 & ~ (v32 = v28) & host(v22) = v28 & $i(v28) & leq(v0,
% 77.53/11.05 | v32) & ~ leq(nbr_proc, v32) & ~ setIn(v32, v15)) | ( ~
% 77.53/11.05 | (v30 = nbr_proc) & host(v21) = v30 & $i(v30)) | (queue(v26) =
% 77.53/11.05 | v31 & $i(v31) & ~ elem(v25, v31))))) & ! [v20: $i] : !
% 77.53/11.05 | [v21: $i] : ! [v22: $i] : ! [v23: $i] : ! [v24: $i] : ! [v25: $i]
% 77.53/11.05 | : (v24 = v23 | ~ (m_Down(v20) = v25) | ~ (host(v22) = v23) | ~
% 77.53/11.05 | (host(v21) = v24) | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~
% 77.53/11.05 | setIn(v22, alive) | ? [v26: $i] : ? [v27: $i] : ? [v28: $i] : ?
% 77.53/11.05 | [v29: $i] : ? [v30: $i] : (( ~ (v29 = v24) & index(elid, v23) =
% 77.53/11.05 | v28 & host(v28) = v29 & $i(v29) & $i(v28)) | ( ~ (v27 = wait) &
% 77.53/11.05 | index(status, v23) = v27 & $i(v27)) | ( ~ (v26 = v23) &
% 77.53/11.05 | host(v20) = v26 & $i(v26)) | (queue(v24) = v30 & $i(v30) & ~
% 77.53/11.05 | elem(v25, v30)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 77.53/11.05 | : ! [v23: $i] : ! [v24: $i] : ! [v25: $i] : (v24 = v23 | ~
% 77.53/11.05 | (m_Down(v20) = v25) | ~ (host(v22) = v23) | ~ (host(v21) = v24) |
% 77.53/11.05 | ~ $i(v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v22, alive) | ?
% 77.53/11.05 | [v26: $i] : ? [v27: $i] : ? [v28: $i] : ? [v29: $i] : (( ~ (v28
% 77.53/11.05 | = v24) & index(ldr, v23) = v28 & $i(v28)) | ( ~ (v27 = norm)
% 77.53/11.05 | & index(status, v23) = v27 & $i(v27)) | ( ~ (v26 = v23) &
% 77.53/11.05 | host(v20) = v26 & $i(v26)) | (queue(v24) = v29 & $i(v29) & ~
% 77.53/11.05 | elem(v25, v29)))) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i]
% 77.53/11.05 | : ! [v23: $i] : ( ~ (m_Ldr(v21) = v22) | ~ (host(v20) = v23) | ~
% 77.53/11.05 | $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : ((host(v21) =
% 77.53/11.05 | v25 & $i(v25) & ~ leq(v23, v25)) | (queue(v23) = v24 & $i(v24)
% 77.53/11.05 | & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] : ! [v22:
% 77.53/11.05 | $i] : ! [v23: $i] : ( ~ (m_Down(v21) = v22) | ~ (host(v20) = v23)
% 77.53/11.05 | | ~ $i(v21) | ~ $i(v20) | ? [v24: $i] : ? [v25: $i] : (( ~ (v25
% 77.53/11.05 | = v23) & host(v21) = v25 & $i(v25)) | (queue(v23) = v24 &
% 77.53/11.05 | $i(v24) & ~ elem(v22, v24)))) & ! [v20: $i] : ! [v21: $i] :
% 77.53/11.05 | ! [v22: $i] : (v21 = v20 | ~ (host(v21) = v22) | ~ (host(v20) =
% 77.53/11.05 | v22) | ~ $i(v21) | ~ $i(v20) | ~ setIn(v21, alive) | ~
% 77.53/11.05 | setIn(v20, alive)) & ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (
% 77.53/11.05 | ~ (m_NotNorm(v20) = v22) | ~ (host(v21) = nbr_proc) | ~ $i(v21) |
% 77.53/11.05 | ~ $i(v20) | ~ elem(v22, v18)) & ! [v20: $i] : ! [v21: $i] : ( ~
% 77.53/11.05 | (host(v20) = v21) | ~ $i(v20) | ~ setIn(v20, alive) | ? [v22:
% 77.53/11.05 | $i] : ? [v23: $i] : ((v23 = v20 & index(elid, v21) = v20) | ( ~
% 77.53/11.05 | (v22 = elec_1) & ~ (v22 = elec_2) & index(status, v21) = v22 &
% 77.53/11.05 | $i(v22)))) & ! [v20: $i] : (v20 = v16 | ~ $i(v20) | ~
% 77.53/11.05 | leq(v0, v20) | leq(nbr_proc, v20) | setIn(v20, v15)))
% 77.53/11.05 |
% 77.53/11.05 | ALPHA: (function-axioms) implies:
% 77.98/11.05 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 77.98/11.05 | v1) | ~ (queue(v2) = v0))
% 77.98/11.05 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 77.98/11.05 | | ~ (host(v2) = v0))
% 77.98/11.05 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) |
% 77.98/11.05 | ~ (s(v2) = v0))
% 77.98/11.05 |
% 77.98/11.05 | DELTA: instantiating (1) with fresh symbol all_50_0 gives:
% 77.98/11.05 | (8) s(zero) = all_50_0 & $i(all_50_0) & leq(all_50_0, nbr_proc)
% 77.98/11.05 |
% 77.98/11.05 | ALPHA: (8) implies:
% 77.98/11.05 | (9) s(zero) = all_50_0
% 77.98/11.05 |
% 77.98/11.05 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1, all_65_2,
% 77.98/11.05 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 77.98/11.05 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 77.98/11.05 | all_65_16, all_65_17, all_65_18, all_65_19 gives:
% 77.98/11.06 | (10) ~ (all_65_14 = nbr_proc) & index(pendack, all_65_14) = all_65_11 &
% 77.98/11.06 | index(down, nbr_proc) = all_65_4 & index(elid, all_65_14) = all_65_17
% 77.98/11.06 | & index(status, all_65_14) = elec_2 & index(status, nbr_proc) = elec_1
% 77.98/11.06 | & snoc(all_65_18, all_65_10) = all_65_9 & cons(all_65_12, all_65_18) =
% 77.98/11.06 | all_65_13 & m_Down(all_65_6) = all_65_2 & m_Down(all_65_7) = all_65_0
% 77.98/11.06 | & m_Halt(all_65_16) = all_65_10 & s(all_65_11) = all_65_14 & s(zero) =
% 77.98/11.06 | all_65_19 & m_Ack(all_65_17, all_65_15) = all_65_12 & host(all_65_5) =
% 77.98/11.06 | nbr_proc & host(all_65_6) = all_65_3 & host(all_65_7) = nbr_proc &
% 77.98/11.06 | host(all_65_8) = all_65_14 & host(all_65_15) = all_65_11 &
% 77.98/11.06 | host(all_65_16) = all_65_14 & queue(all_65_14) = all_65_13 &
% 77.98/11.06 | queue(nbr_proc) = all_65_1 & $i(all_65_0) & $i(all_65_1) &
% 77.98/11.06 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) &
% 77.98/11.06 | $i(all_65_6) & $i(all_65_7) & $i(all_65_8) & $i(all_65_9) &
% 77.98/11.06 | $i(all_65_10) & $i(all_65_11) & $i(all_65_12) & $i(all_65_13) &
% 77.98/11.06 | $i(all_65_14) & $i(all_65_15) & $i(all_65_16) & $i(all_65_17) &
% 77.98/11.06 | $i(all_65_18) & $i(all_65_19) & setIn(all_65_8, alive) &
% 77.98/11.06 | setIn(all_65_16, alive) & elem(all_65_0, all_65_9) & elem(all_65_2,
% 77.98/11.06 | all_65_1) & ~ leq(nbr_proc, all_65_11) & ! [v0: $i] : ! [v1: $i]
% 77.98/11.06 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 77.98/11.06 | : ! [v7: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~ (m_Down(v1) = v7)
% 77.98/11.06 | | ~ (host(v2) = v4) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) |
% 77.98/11.06 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) |
% 77.98/11.06 | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : (( ~ (v9 =
% 77.98/11.06 | v4) & host(v3) = v9 & $i(v9)) | ( ~ (v8 = v5) & host(v1) = v8
% 77.98/11.06 | & $i(v8)) | (queue(v5) = v10 & $i(v10) & ~ elem(v6, v10)) |
% 77.98/11.06 | (queue(v4) = v11 & $i(v11) & ~ elem(v7, v11)))) & ! [v0: $i] :
% 77.98/11.06 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 77.98/11.06 | ! [v6: $i] : (v5 = v4 | ~ (m_Down(v3) = v6) | ~ (host(v2) = v4) | ~
% 77.98/11.06 | (host(v1) = v5) | ~ (host(v0) = v5) | ~ $i(v3) | ~ $i(v2) | ~
% 77.98/11.06 | $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ?
% 77.98/11.06 | [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v7 = v4) & host(v3) =
% 77.98/11.06 | v7 & $i(v7)) | (index(down, v4) = v9 & $i(v9) & ~ setIn(v5,
% 77.98/11.06 | v9)) | (queue(v5) = v8 & $i(v8) & ~ elem(v6, v8)))) & ! [v0:
% 77.98/11.06 | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 77.98/11.06 | [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v4) | ~ (m_Down(v1) = v5)
% 77.98/11.06 | | ~ (host(v3) = nbr_proc) | ~ (host(v0) = v6) | ~ $i(v3) | ~
% 77.98/11.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v7: int]
% 77.98/11.06 | : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] : ?
% 77.98/11.06 | [v12: $i] : ($i(v12) & ((v9 = all_65_1 & ~ elem(v4, all_65_1)) |
% 77.98/11.06 | (v7 = all_65_4 & ~ (v12 = v8) & host(v2) = v8 & $i(v8) &
% 77.98/11.06 | leq(all_65_19, v12) & ~ leq(nbr_proc, v12) & ~ setIn(v12,
% 77.98/11.06 | all_65_4)) | ( ~ (v10 = nbr_proc) & host(v1) = v10 &
% 77.98/11.06 | $i(v10)) | (queue(v6) = v11 & $i(v11) & ~ elem(v5, v11))))) &
% 77.98/11.06 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.98/11.06 | ! [v5: $i] : (v4 = v3 | ~ (m_Down(v0) = v5) | ~ (host(v2) = v3) | ~
% 77.98/11.06 | (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2,
% 77.98/11.06 | alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 77.98/11.06 | ? [v10: $i] : (( ~ (v9 = v4) & index(elid, v3) = v8 & host(v8) = v9
% 77.98/11.06 | & $i(v9) & $i(v8)) | ( ~ (v7 = wait) & index(status, v3) = v7 &
% 77.98/11.06 | $i(v7)) | ( ~ (v6 = v3) & host(v0) = v6 & $i(v6)) | (queue(v4) =
% 77.98/11.06 | v10 & $i(v10) & ~ elem(v5, v10)))) & ! [v0: $i] : ! [v1: $i]
% 77.98/11.06 | : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 |
% 77.98/11.06 | ~ (m_Down(v0) = v5) | ~ (host(v2) = v3) | ~ (host(v1) = v4) | ~
% 77.98/11.06 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ? [v6: $i] :
% 77.98/11.06 | ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~ (v8 = v4) &
% 77.98/11.06 | index(ldr, v3) = v8 & $i(v8)) | ( ~ (v7 = norm) & index(status,
% 77.98/11.06 | v3) = v7 & $i(v7)) | ( ~ (v6 = v3) & host(v0) = v6 & $i(v6)) |
% 77.98/11.06 | (queue(v4) = v9 & $i(v9) & ~ elem(v5, v9)))) & ! [v0: $i] : !
% 77.98/11.06 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Ldr(v1) = v2) | ~
% 77.98/11.06 | (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i]
% 77.98/11.06 | : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3) = v4 &
% 77.98/11.06 | $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] : !
% 77.98/11.06 | [v2: $i] : ! [v3: $i] : ( ~ (m_Down(v1) = v2) | ~ (host(v0) = v3) |
% 77.98/11.06 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) &
% 77.98/11.06 | host(v1) = v5 & $i(v5)) | (queue(v3) = v4 & $i(v4) & ~ elem(v2,
% 77.98/11.06 | v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 77.98/11.06 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 77.98/11.06 | setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: $i] : ! [v1: $i]
% 77.98/11.06 | : ! [v2: $i] : ( ~ (m_NotNorm(v0) = v2) | ~ (host(v1) = nbr_proc) |
% 77.98/11.06 | ~ $i(v1) | ~ $i(v0) | ~ elem(v2, all_65_1)) & ! [v0: $i] : !
% 77.98/11.06 | [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ?
% 77.98/11.06 | [v2: $i] : ? [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2
% 77.98/11.06 | = elec_1) & ~ (v2 = elec_2) & index(status, v1) = v2 &
% 77.98/11.06 | $i(v2)))) & ! [v0: any] : (v0 = all_65_3 | ~ $i(v0) | ~
% 77.98/11.06 | leq(all_65_19, v0) | leq(nbr_proc, v0) | setIn(v0, all_65_4))
% 77.98/11.06 |
% 77.98/11.06 | ALPHA: (10) implies:
% 77.98/11.06 | (11) elem(all_65_2, all_65_1)
% 77.98/11.06 | (12) elem(all_65_0, all_65_9)
% 77.98/11.06 | (13) setIn(all_65_16, alive)
% 77.98/11.06 | (14) $i(all_65_18)
% 77.98/11.06 | (15) $i(all_65_16)
% 77.98/11.06 | (16) $i(all_65_15)
% 77.98/11.06 | (17) $i(all_65_12)
% 77.98/11.06 | (18) $i(all_65_10)
% 77.98/11.06 | (19) $i(all_65_7)
% 77.98/11.06 | (20) $i(all_65_6)
% 77.98/11.06 | (21) $i(all_65_0)
% 77.98/11.06 | (22) queue(nbr_proc) = all_65_1
% 77.98/11.06 | (23) queue(all_65_14) = all_65_13
% 77.98/11.06 | (24) host(all_65_16) = all_65_14
% 77.98/11.06 | (25) host(all_65_15) = all_65_11
% 77.98/11.06 | (26) host(all_65_7) = nbr_proc
% 77.98/11.06 | (27) host(all_65_6) = all_65_3
% 77.98/11.06 | (28) s(zero) = all_65_19
% 77.98/11.06 | (29) s(all_65_11) = all_65_14
% 77.98/11.06 | (30) m_Halt(all_65_16) = all_65_10
% 77.98/11.06 | (31) m_Down(all_65_7) = all_65_0
% 77.98/11.06 | (32) m_Down(all_65_6) = all_65_2
% 77.98/11.06 | (33) cons(all_65_12, all_65_18) = all_65_13
% 77.98/11.06 | (34) snoc(all_65_18, all_65_10) = all_65_9
% 77.98/11.06 | (35) ! [v0: any] : (v0 = all_65_3 | ~ $i(v0) | ~ leq(all_65_19, v0) |
% 77.98/11.06 | leq(nbr_proc, v0) | setIn(v0, all_65_4))
% 77.98/11.07 | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 77.98/11.07 | (m_Down(v1) = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 77.98/11.07 | [v4: $i] : ? [v5: $i] : (( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) |
% 77.98/11.07 | (queue(v3) = v4 & $i(v4) & ~ elem(v2, v4))))
% 77.98/11.07 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.98/11.07 | ! [v5: $i] : (v4 = v3 | ~ (m_Down(v0) = v5) | ~ (host(v2) = v3) | ~
% 77.98/11.07 | (host(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2,
% 77.98/11.07 | alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 77.98/11.07 | ? [v10: $i] : (( ~ (v9 = v4) & index(elid, v3) = v8 & host(v8) = v9
% 77.98/11.07 | & $i(v9) & $i(v8)) | ( ~ (v7 = wait) & index(status, v3) = v7 &
% 77.98/11.07 | $i(v7)) | ( ~ (v6 = v3) & host(v0) = v6 & $i(v6)) | (queue(v4) =
% 77.98/11.07 | v10 & $i(v10) & ~ elem(v5, v10))))
% 77.98/11.07 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.98/11.07 | ! [v5: $i] : ! [v6: $i] : ( ~ (m_Down(v2) = v4) | ~ (m_Down(v1) =
% 77.98/11.07 | v5) | ~ (host(v3) = nbr_proc) | ~ (host(v0) = v6) | ~ $i(v3) |
% 77.98/11.07 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v7:
% 77.98/11.07 | int] : ? [v8: $i] : ? [v9: int] : ? [v10: $i] : ? [v11: $i] :
% 77.98/11.07 | ? [v12: $i] : ($i(v12) & ((v9 = all_65_1 & ~ elem(v4, all_65_1)) |
% 77.98/11.07 | (v7 = all_65_4 & ~ (v12 = v8) & host(v2) = v8 & $i(v8) &
% 77.98/11.07 | leq(all_65_19, v12) & ~ leq(nbr_proc, v12) & ~ setIn(v12,
% 77.98/11.07 | all_65_4)) | ( ~ (v10 = nbr_proc) & host(v1) = v10 &
% 77.98/11.07 | $i(v10)) | (queue(v6) = v11 & $i(v11) & ~ elem(v5, v11)))))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (7) with all_50_0, all_65_19, zero, simplifying
% 77.98/11.07 | with (9), (28) gives:
% 77.98/11.07 | (39) all_65_19 = all_50_0
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (axiom_01) with all_65_15, all_65_15, all_65_11,
% 77.98/11.07 | simplifying with (16), (25) gives:
% 77.98/11.07 | (40) ? [v0: any] : ( ~ (v0 = all_65_11) & s(all_65_11) = v0 & $i(v0))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (36) with all_65_7, all_65_7, all_65_0, nbr_proc,
% 77.98/11.07 | simplifying with (19), (26), (31) gives:
% 77.98/11.07 | (41) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = nbr_proc) & host(all_65_7) = v1
% 77.98/11.07 | & $i(v1)) | (queue(nbr_proc) = v0 & $i(v0) & ~ elem(all_65_0,
% 77.98/11.07 | v0)))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (37) with all_65_7, all_65_15, all_65_16,
% 77.98/11.07 | all_65_14, all_65_11, all_65_0, simplifying with (13), (15),
% 77.98/11.07 | (16), (19), (24), (25), (31) gives:
% 77.98/11.07 | (42) all_65_11 = all_65_14 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ?
% 77.98/11.07 | [v3: any] : ? [v4: $i] : (( ~ (v3 = all_65_11) & index(elid,
% 77.98/11.07 | all_65_14) = v2 & host(v2) = v3 & $i(v3) & $i(v2)) | ( ~ (v1 =
% 77.98/11.07 | wait) & index(status, all_65_14) = v1 & $i(v1)) | ( ~ (v0 =
% 77.98/11.07 | all_65_14) & host(all_65_7) = v0 & $i(v0)) | (queue(all_65_11) =
% 77.98/11.07 | v4 & $i(v4) & ~ elem(all_65_0, v4)))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (axiom_17) with all_65_7, all_65_16, all_65_10,
% 77.98/11.07 | simplifying with (15), (19), (30) gives:
% 77.98/11.07 | (43) ~ (m_Down(all_65_7) = all_65_10)
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (38) with all_65_16, all_65_7, all_65_6, all_65_7,
% 77.98/11.07 | all_65_2, all_65_0, all_65_14, simplifying with (13), (15), (19),
% 77.98/11.07 | (20), (24), (26), (31), (32) gives:
% 77.98/11.07 | (44) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i] : ? [v4: $i]
% 77.98/11.07 | : ? [v5: $i] : ($i(v5) & ((v2 = all_65_1 & ~ elem(all_65_2,
% 77.98/11.07 | all_65_1)) | (v0 = all_65_4 & ~ (v5 = v1) & host(all_65_6) =
% 77.98/11.07 | v1 & $i(v1) & leq(all_65_19, v5) & ~ leq(nbr_proc, v5) & ~
% 77.98/11.07 | setIn(v5, all_65_4)) | ( ~ (v3 = nbr_proc) & host(all_65_7) = v3
% 77.98/11.07 | & $i(v3)) | (queue(all_65_14) = v4 & $i(v4) & ~ elem(all_65_0,
% 77.98/11.07 | v4))))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (36) with all_65_6, all_65_6, all_65_2, all_65_3,
% 77.98/11.07 | simplifying with (20), (27), (32) gives:
% 77.98/11.07 | (45) ? [v0: $i] : ? [v1: any] : (( ~ (v1 = all_65_3) & host(all_65_6) =
% 77.98/11.07 | v1 & $i(v1)) | (queue(all_65_3) = v0 & $i(v0) & ~ elem(all_65_2,
% 77.98/11.07 | v0)))
% 77.98/11.07 |
% 77.98/11.07 | GROUND_INST: instantiating (36) with all_65_7, all_65_6, all_65_2, nbr_proc,
% 77.98/11.07 | simplifying with (19), (20), (26), (32) gives:
% 77.98/11.07 | (46) ? [v0: $i] : ? [v1: $i] : (( ~ (v1 = nbr_proc) & host(all_65_6) = v1
% 77.98/11.07 | & $i(v1)) | (queue(nbr_proc) = v0 & $i(v0) & ~ elem(all_65_2,
% 77.98/11.07 | v0)))
% 77.98/11.07 |
% 77.98/11.08 | GROUND_INST: instantiating (2) with all_65_0, all_65_12, all_65_18, all_65_13,
% 77.98/11.08 | simplifying with (14), (17), (21), (33) gives:
% 77.98/11.08 | (47) ~ elem(all_65_0, all_65_18) | elem(all_65_0, all_65_13)
% 77.98/11.08 |
% 77.98/11.08 | GROUND_INST: instantiating (3) with all_65_0, all_65_10, all_65_18, all_65_9,
% 77.98/11.08 | simplifying with (12), (14), (18), (21), (34) gives:
% 77.98/11.08 | (48) all_65_0 = all_65_10 | elem(all_65_0, all_65_18)
% 77.98/11.08 |
% 77.98/11.08 | DELTA: instantiating (40) with fresh symbol all_84_0 gives:
% 77.98/11.08 | (49) ~ (all_84_0 = all_65_11) & s(all_65_11) = all_84_0 & $i(all_84_0)
% 77.98/11.08 |
% 77.98/11.08 | ALPHA: (49) implies:
% 77.98/11.08 | (50) ~ (all_84_0 = all_65_11)
% 77.98/11.08 | (51) s(all_65_11) = all_84_0
% 77.98/11.08 |
% 77.98/11.08 | DELTA: instantiating (46) with fresh symbols all_88_0, all_88_1 gives:
% 77.98/11.08 | (52) ( ~ (all_88_0 = nbr_proc) & host(all_65_6) = all_88_0 & $i(all_88_0))
% 77.98/11.08 | | (queue(nbr_proc) = all_88_1 & $i(all_88_1) & ~ elem(all_65_2,
% 77.98/11.08 | all_88_1))
% 77.98/11.08 |
% 77.98/11.08 | DELTA: instantiating (45) with fresh symbols all_93_0, all_93_1 gives:
% 77.98/11.08 | (53) ( ~ (all_93_0 = all_65_3) & host(all_65_6) = all_93_0 & $i(all_93_0))
% 77.98/11.08 | | (queue(all_65_3) = all_93_1 & $i(all_93_1) & ~ elem(all_65_2,
% 77.98/11.08 | all_93_1))
% 77.98/11.08 |
% 77.98/11.08 | DELTA: instantiating (41) with fresh symbols all_94_0, all_94_1 gives:
% 77.98/11.08 | (54) ( ~ (all_94_0 = nbr_proc) & host(all_65_7) = all_94_0 & $i(all_94_0))
% 77.98/11.08 | | (queue(nbr_proc) = all_94_1 & $i(all_94_1) & ~ elem(all_65_0,
% 77.98/11.08 | all_94_1))
% 77.98/11.08 |
% 77.98/11.08 | DELTA: instantiating (44) with fresh symbols all_102_0, all_102_1, all_102_2,
% 77.98/11.08 | all_102_3, all_102_4, all_102_5 gives:
% 77.98/11.08 | (55) $i(all_102_0) & ((all_102_3 = all_65_1 & ~ elem(all_65_2, all_65_1))
% 77.98/11.08 | | (all_102_5 = all_65_4 & ~ (all_102_0 = all_102_4) &
% 77.98/11.08 | host(all_65_6) = all_102_4 & $i(all_102_4) & leq(all_65_19,
% 77.98/11.08 | all_102_0) & ~ leq(nbr_proc, all_102_0) & ~ setIn(all_102_0,
% 77.98/11.08 | all_65_4)) | ( ~ (all_102_2 = nbr_proc) & host(all_65_7) =
% 77.98/11.08 | all_102_2 & $i(all_102_2)) | (queue(all_65_14) = all_102_1 &
% 77.98/11.08 | $i(all_102_1) & ~ elem(all_65_0, all_102_1)))
% 77.98/11.08 |
% 77.98/11.08 | ALPHA: (55) implies:
% 77.98/11.08 | (56) $i(all_102_0)
% 77.98/11.08 | (57) (all_102_3 = all_65_1 & ~ elem(all_65_2, all_65_1)) | (all_102_5 =
% 77.98/11.08 | all_65_4 & ~ (all_102_0 = all_102_4) & host(all_65_6) = all_102_4 &
% 77.98/11.08 | $i(all_102_4) & leq(all_65_19, all_102_0) & ~ leq(nbr_proc,
% 77.98/11.08 | all_102_0) & ~ setIn(all_102_0, all_65_4)) | ( ~ (all_102_2 =
% 77.98/11.08 | nbr_proc) & host(all_65_7) = all_102_2 & $i(all_102_2)) |
% 77.98/11.08 | (queue(all_65_14) = all_102_1 & $i(all_102_1) & ~ elem(all_65_0,
% 77.98/11.08 | all_102_1))
% 77.98/11.08 |
% 77.98/11.08 | BETA: splitting (54) gives:
% 77.98/11.08 |
% 77.98/11.08 | Case 1:
% 77.98/11.08 | |
% 77.98/11.08 | | (58) ~ (all_94_0 = nbr_proc) & host(all_65_7) = all_94_0 & $i(all_94_0)
% 77.98/11.08 | |
% 77.98/11.08 | | ALPHA: (58) implies:
% 77.98/11.08 | | (59) ~ (all_94_0 = nbr_proc)
% 77.98/11.08 | | (60) host(all_65_7) = all_94_0
% 77.98/11.08 | |
% 77.98/11.08 | | GROUND_INST: instantiating (6) with nbr_proc, all_94_0, all_65_7,
% 77.98/11.08 | | simplifying with (26), (60) gives:
% 77.98/11.08 | | (61) all_94_0 = nbr_proc
% 77.98/11.08 | |
% 77.98/11.08 | | REDUCE: (59), (61) imply:
% 77.98/11.08 | | (62) $false
% 77.98/11.08 | |
% 77.98/11.08 | | CLOSE: (62) is inconsistent.
% 77.98/11.08 | |
% 77.98/11.08 | Case 2:
% 77.98/11.08 | |
% 77.98/11.08 | | (63) queue(nbr_proc) = all_94_1 & $i(all_94_1) & ~ elem(all_65_0,
% 77.98/11.08 | | all_94_1)
% 77.98/11.08 | |
% 77.98/11.08 | | ALPHA: (63) implies:
% 77.98/11.08 | | (64) queue(nbr_proc) = all_94_1
% 77.98/11.08 | |
% 77.98/11.08 | | BETA: splitting (53) gives:
% 77.98/11.08 | |
% 77.98/11.08 | | Case 1:
% 77.98/11.08 | | |
% 77.98/11.08 | | | (65) ~ (all_93_0 = all_65_3) & host(all_65_6) = all_93_0 &
% 77.98/11.08 | | | $i(all_93_0)
% 77.98/11.08 | | |
% 77.98/11.08 | | | ALPHA: (65) implies:
% 77.98/11.08 | | | (66) ~ (all_93_0 = all_65_3)
% 77.98/11.08 | | | (67) host(all_65_6) = all_93_0
% 77.98/11.08 | | |
% 77.98/11.08 | | | GROUND_INST: instantiating (6) with all_65_3, all_93_0, all_65_6,
% 77.98/11.08 | | | simplifying with (27), (67) gives:
% 77.98/11.08 | | | (68) all_93_0 = all_65_3
% 77.98/11.08 | | |
% 77.98/11.08 | | | REDUCE: (66), (68) imply:
% 77.98/11.08 | | | (69) $false
% 77.98/11.08 | | |
% 77.98/11.08 | | | CLOSE: (69) is inconsistent.
% 77.98/11.08 | | |
% 77.98/11.08 | | Case 2:
% 77.98/11.08 | | |
% 77.98/11.08 | | |
% 77.98/11.08 | | | GROUND_INST: instantiating (5) with all_65_1, all_94_1, nbr_proc,
% 77.98/11.08 | | | simplifying with (22), (64) gives:
% 77.98/11.08 | | | (70) all_94_1 = all_65_1
% 77.98/11.08 | | |
% 77.98/11.08 | | | GROUND_INST: instantiating (7) with all_65_14, all_84_0, all_65_11,
% 77.98/11.08 | | | simplifying with (29), (51) gives:
% 77.98/11.08 | | | (71) all_84_0 = all_65_14
% 77.98/11.08 | | |
% 77.98/11.08 | | | PRED_UNIFY: (31), (43) imply:
% 77.98/11.08 | | | (72) ~ (all_65_0 = all_65_10)
% 77.98/11.08 | | |
% 77.98/11.08 | | | REDUCE: (50), (71) imply:
% 77.98/11.08 | | | (73) ~ (all_65_11 = all_65_14)
% 77.98/11.08 | | |
% 77.98/11.08 | | | SIMP: (73) implies:
% 77.98/11.08 | | | (74) ~ (all_65_11 = all_65_14)
% 77.98/11.08 | | |
% 77.98/11.08 | | | BETA: splitting (52) gives:
% 77.98/11.08 | | |
% 77.98/11.08 | | | Case 1:
% 77.98/11.08 | | | |
% 77.98/11.08 | | | | (75) ~ (all_88_0 = nbr_proc) & host(all_65_6) = all_88_0 &
% 77.98/11.08 | | | | $i(all_88_0)
% 77.98/11.08 | | | |
% 77.98/11.08 | | | | ALPHA: (75) implies:
% 77.98/11.08 | | | | (76) host(all_65_6) = all_88_0
% 77.98/11.08 | | | |
% 77.98/11.08 | | | | BETA: splitting (48) gives:
% 77.98/11.08 | | | |
% 77.98/11.08 | | | | Case 1:
% 77.98/11.08 | | | | |
% 77.98/11.08 | | | | | (77) elem(all_65_0, all_65_18)
% 77.98/11.08 | | | | |
% 77.98/11.08 | | | | | BETA: splitting (47) gives:
% 77.98/11.08 | | | | |
% 77.98/11.08 | | | | | Case 1:
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | (78) ~ elem(all_65_0, all_65_18)
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | PRED_UNIFY: (77), (78) imply:
% 77.98/11.08 | | | | | | (79) $false
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | CLOSE: (79) is inconsistent.
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | Case 2:
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | (80) elem(all_65_0, all_65_13)
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | BETA: splitting (57) gives:
% 77.98/11.08 | | | | | |
% 77.98/11.08 | | | | | | Case 1:
% 77.98/11.08 | | | | | | |
% 77.98/11.08 | | | | | | | (81) (all_102_3 = all_65_1 & ~ elem(all_65_2, all_65_1)) |
% 77.98/11.08 | | | | | | | (all_102_5 = all_65_4 & ~ (all_102_0 = all_102_4) &
% 77.98/11.08 | | | | | | | host(all_65_6) = all_102_4 & $i(all_102_4) &
% 77.98/11.08 | | | | | | | leq(all_65_19, all_102_0) & ~ leq(nbr_proc, all_102_0)
% 77.98/11.08 | | | | | | | & ~ setIn(all_102_0, all_65_4))
% 77.98/11.08 | | | | | | |
% 77.98/11.08 | | | | | | | BETA: splitting (81) gives:
% 77.98/11.08 | | | | | | |
% 77.98/11.08 | | | | | | | Case 1:
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | (82) all_102_3 = all_65_1 & ~ elem(all_65_2, all_65_1)
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | ALPHA: (82) implies:
% 77.98/11.08 | | | | | | | | (83) ~ elem(all_65_2, all_65_1)
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | PRED_UNIFY: (11), (83) imply:
% 77.98/11.08 | | | | | | | | (84) $false
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | CLOSE: (84) is inconsistent.
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | Case 2:
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | (85) all_102_5 = all_65_4 & ~ (all_102_0 = all_102_4) &
% 77.98/11.08 | | | | | | | | host(all_65_6) = all_102_4 & $i(all_102_4) &
% 77.98/11.08 | | | | | | | | leq(all_65_19, all_102_0) & ~ leq(nbr_proc, all_102_0)
% 77.98/11.08 | | | | | | | | & ~ setIn(all_102_0, all_65_4)
% 77.98/11.08 | | | | | | | |
% 77.98/11.08 | | | | | | | | ALPHA: (85) implies:
% 77.98/11.09 | | | | | | | | (86) ~ (all_102_0 = all_102_4)
% 77.98/11.09 | | | | | | | | (87) ~ setIn(all_102_0, all_65_4)
% 77.98/11.09 | | | | | | | | (88) ~ leq(nbr_proc, all_102_0)
% 77.98/11.09 | | | | | | | | (89) leq(all_65_19, all_102_0)
% 77.98/11.09 | | | | | | | | (90) host(all_65_6) = all_102_4
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | REDUCE: (39), (89) imply:
% 77.98/11.09 | | | | | | | | (91) leq(all_50_0, all_102_0)
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | BETA: splitting (42) gives:
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | Case 1:
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | (92) all_65_11 = all_65_14
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | REDUCE: (74), (92) imply:
% 77.98/11.09 | | | | | | | | | (93) $false
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | CLOSE: (93) is inconsistent.
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | Case 2:
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | GROUND_INST: instantiating (6) with all_65_3, all_102_4,
% 77.98/11.09 | | | | | | | | | all_65_6, simplifying with (27), (90) gives:
% 77.98/11.09 | | | | | | | | | (94) all_102_4 = all_65_3
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | GROUND_INST: instantiating (6) with all_88_0, all_102_4,
% 77.98/11.09 | | | | | | | | | all_65_6, simplifying with (76), (90) gives:
% 77.98/11.09 | | | | | | | | | (95) all_102_4 = all_88_0
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | COMBINE_EQS: (94), (95) imply:
% 77.98/11.09 | | | | | | | | | (96) all_88_0 = all_65_3
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | REDUCE: (86), (94) imply:
% 77.98/11.09 | | | | | | | | | (97) ~ (all_102_0 = all_65_3)
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | GROUND_INST: instantiating (35) with all_102_0, simplifying
% 77.98/11.09 | | | | | | | | | with (56), (87), (88) gives:
% 77.98/11.09 | | | | | | | | | (98) all_102_0 = all_65_3 | ~ leq(all_65_19, all_102_0)
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | BETA: splitting (98) gives:
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | | Case 1:
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | (99) ~ leq(all_65_19, all_102_0)
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | REDUCE: (39), (99) imply:
% 77.98/11.09 | | | | | | | | | | (100) ~ leq(all_50_0, all_102_0)
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | PRED_UNIFY: (91), (100) imply:
% 77.98/11.09 | | | | | | | | | | (101) $false
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | CLOSE: (101) is inconsistent.
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | Case 2:
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | (102) all_102_0 = all_65_3
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | REDUCE: (97), (102) imply:
% 77.98/11.09 | | | | | | | | | | (103) $false
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | | CLOSE: (103) is inconsistent.
% 77.98/11.09 | | | | | | | | | |
% 77.98/11.09 | | | | | | | | | End of split
% 77.98/11.09 | | | | | | | | |
% 77.98/11.09 | | | | | | | | End of split
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | End of split
% 77.98/11.09 | | | | | | |
% 77.98/11.09 | | | | | | Case 2:
% 77.98/11.09 | | | | | | |
% 77.98/11.09 | | | | | | | (104) ( ~ (all_102_2 = nbr_proc) & host(all_65_7) = all_102_2 &
% 77.98/11.09 | | | | | | | $i(all_102_2)) | (queue(all_65_14) = all_102_1 &
% 77.98/11.09 | | | | | | | $i(all_102_1) & ~ elem(all_65_0, all_102_1))
% 77.98/11.09 | | | | | | |
% 77.98/11.09 | | | | | | | BETA: splitting (104) gives:
% 77.98/11.09 | | | | | | |
% 77.98/11.09 | | | | | | | Case 1:
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | (105) ~ (all_102_2 = nbr_proc) & host(all_65_7) = all_102_2
% 77.98/11.09 | | | | | | | | & $i(all_102_2)
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | ALPHA: (105) implies:
% 77.98/11.09 | | | | | | | | (106) ~ (all_102_2 = nbr_proc)
% 77.98/11.09 | | | | | | | | (107) host(all_65_7) = all_102_2
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | GROUND_INST: instantiating (6) with nbr_proc, all_102_2,
% 77.98/11.09 | | | | | | | | all_65_7, simplifying with (26), (107) gives:
% 77.98/11.09 | | | | | | | | (108) all_102_2 = nbr_proc
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | REDUCE: (106), (108) imply:
% 77.98/11.09 | | | | | | | | (109) $false
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | CLOSE: (109) is inconsistent.
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | Case 2:
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | (110) queue(all_65_14) = all_102_1 & $i(all_102_1) & ~
% 77.98/11.09 | | | | | | | | elem(all_65_0, all_102_1)
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | ALPHA: (110) implies:
% 77.98/11.09 | | | | | | | | (111) ~ elem(all_65_0, all_102_1)
% 77.98/11.09 | | | | | | | | (112) queue(all_65_14) = all_102_1
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | GROUND_INST: instantiating (5) with all_65_13, all_102_1,
% 77.98/11.09 | | | | | | | | all_65_14, simplifying with (23), (112) gives:
% 77.98/11.09 | | | | | | | | (113) all_102_1 = all_65_13
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | PRED_UNIFY: (80), (111) imply:
% 77.98/11.09 | | | | | | | | (114) ~ (all_102_1 = all_65_13)
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | REDUCE: (113), (114) imply:
% 77.98/11.09 | | | | | | | | (115) $false
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | | CLOSE: (115) is inconsistent.
% 77.98/11.09 | | | | | | | |
% 77.98/11.09 | | | | | | | End of split
% 77.98/11.09 | | | | | | |
% 77.98/11.09 | | | | | | End of split
% 77.98/11.09 | | | | | |
% 77.98/11.09 | | | | | End of split
% 77.98/11.09 | | | | |
% 77.98/11.09 | | | | Case 2:
% 77.98/11.09 | | | | |
% 77.98/11.09 | | | | | (116) all_65_0 = all_65_10
% 77.98/11.09 | | | | |
% 77.98/11.09 | | | | | REDUCE: (72), (116) imply:
% 77.98/11.09 | | | | | (117) $false
% 77.98/11.09 | | | | |
% 77.98/11.09 | | | | | CLOSE: (117) is inconsistent.
% 77.98/11.09 | | | | |
% 77.98/11.09 | | | | End of split
% 77.98/11.09 | | | |
% 77.98/11.09 | | | Case 2:
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | (118) queue(nbr_proc) = all_88_1 & $i(all_88_1) & ~ elem(all_65_2,
% 77.98/11.09 | | | | all_88_1)
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | ALPHA: (118) implies:
% 77.98/11.09 | | | | (119) ~ elem(all_65_2, all_88_1)
% 77.98/11.09 | | | | (120) queue(nbr_proc) = all_88_1
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | GROUND_INST: instantiating (5) with all_65_1, all_88_1, nbr_proc,
% 77.98/11.09 | | | | simplifying with (22), (120) gives:
% 77.98/11.09 | | | | (121) all_88_1 = all_65_1
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | PRED_UNIFY: (11), (119) imply:
% 77.98/11.09 | | | | (122) ~ (all_88_1 = all_65_1)
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | REDUCE: (121), (122) imply:
% 77.98/11.09 | | | | (123) $false
% 77.98/11.09 | | | |
% 77.98/11.09 | | | | CLOSE: (123) is inconsistent.
% 77.98/11.09 | | | |
% 77.98/11.09 | | | End of split
% 77.98/11.09 | | |
% 77.98/11.09 | | End of split
% 77.98/11.09 | |
% 77.98/11.09 | End of split
% 77.98/11.09 |
% 77.98/11.09 End of proof
% 77.98/11.09 % SZS output end Proof for theBenchmark
% 77.98/11.09
% 77.98/11.09 10506ms
%------------------------------------------------------------------------------