TSTP Solution File: SWV460+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV460+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 : n006.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 22:56:34 EDT 2023
% Result : Theorem 36.17s 5.42s
% Output : Proof 48.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV460+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 04:06:06 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Running up to 7 provers in parallel.
% 0.70/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.70/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.70/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.70/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.70/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.70/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.70/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.44/1.25 Prover 1: Preprocessing ...
% 3.44/1.25 Prover 4: Preprocessing ...
% 3.44/1.30 Prover 0: Preprocessing ...
% 3.44/1.30 Prover 3: Preprocessing ...
% 4.37/1.31 Prover 5: Preprocessing ...
% 4.37/1.31 Prover 2: Preprocessing ...
% 4.37/1.31 Prover 6: Preprocessing ...
% 10.58/2.14 Prover 1: Constructing countermodel ...
% 10.58/2.14 Prover 3: Constructing countermodel ...
% 10.58/2.17 Prover 6: Proving ...
% 10.58/2.19 Prover 5: Proving ...
% 11.30/2.21 Prover 2: Proving ...
% 11.30/2.22 Prover 4: Constructing countermodel ...
% 11.93/2.33 Prover 0: Proving ...
% 15.84/2.87 Prover 3: gave up
% 15.84/2.87 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.60/2.96 Prover 7: Preprocessing ...
% 19.08/3.25 Prover 7: Warning: ignoring some quantifiers
% 19.08/3.29 Prover 7: Constructing countermodel ...
% 28.57/4.51 Prover 1: gave up
% 29.11/4.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 29.53/4.58 Prover 8: Preprocessing ...
% 30.92/4.75 Prover 8: Warning: ignoring some quantifiers
% 30.92/4.76 Prover 8: Constructing countermodel ...
% 36.17/5.42 Prover 0: proved (4755ms)
% 36.17/5.42
% 36.17/5.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.17/5.42
% 36.17/5.42 Prover 2: stopped
% 36.17/5.42 Prover 6: stopped
% 36.17/5.42 Prover 5: stopped
% 36.17/5.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 36.17/5.43 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 36.17/5.43 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 36.17/5.45 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 36.55/5.47 Prover 10: Preprocessing ...
% 36.55/5.49 Prover 13: Preprocessing ...
% 36.55/5.50 Prover 11: Preprocessing ...
% 36.55/5.51 Prover 16: Preprocessing ...
% 37.90/5.64 Prover 10: Warning: ignoring some quantifiers
% 37.90/5.65 Prover 10: Constructing countermodel ...
% 37.90/5.67 Prover 8: gave up
% 37.90/5.68 Prover 16: Warning: ignoring some quantifiers
% 37.90/5.68 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 37.90/5.69 Prover 13: Warning: ignoring some quantifiers
% 37.90/5.69 Prover 16: Constructing countermodel ...
% 38.30/5.71 Prover 13: Constructing countermodel ...
% 38.30/5.74 Prover 19: Preprocessing ...
% 39.18/5.83 Prover 11: Constructing countermodel ...
% 40.28/5.96 Prover 19: Warning: ignoring some quantifiers
% 40.28/5.97 Prover 19: Constructing countermodel ...
% 47.80/6.93 Prover 10: Found proof (size 121)
% 47.80/6.93 Prover 10: proved (1510ms)
% 47.80/6.93 Prover 16: stopped
% 47.80/6.93 Prover 7: stopped
% 47.80/6.93 Prover 19: stopped
% 47.80/6.93 Prover 11: stopped
% 47.80/6.93 Prover 4: stopped
% 48.04/6.94 Prover 13: stopped
% 48.04/6.94
% 48.04/6.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.04/6.94
% 48.04/6.95 % SZS output start Proof for theBenchmark
% 48.04/6.95 Assumptions after simplification:
% 48.04/6.95 ---------------------------------
% 48.04/6.95
% 48.04/6.95 (axiom_02)
% 48.04/6.97 $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 48.04/6.97 ( ~ (host(v1) = v2) | ~ $i(v1) | leq(v0, v2)))
% 48.04/6.97
% 48.04/6.97 (axiom_03)
% 48.04/6.97 $i(nbr_proc) & $i(zero) & ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0,
% 48.04/6.97 nbr_proc))
% 48.04/6.97
% 48.04/6.97 (axiom_46)
% 48.04/6.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 48.04/6.98 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v3) |
% 48.04/6.98 elem(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 48.04/6.98 (cons(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ elem(v0, v2) |
% 48.04/6.98 elem(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1)
% 48.04/6.98 = v2) | ~ $i(v1) | ~ $i(v0) | elem(v0, v2))
% 48.04/6.98
% 48.04/6.98 (axiom_58)
% 48.04/6.98 ! [v0: $i] : ! [v1: $i] : ( ~ (s(v0) = v1) | ~ $i(v0) | ~ leq(v1, v0))
% 48.04/6.98
% 48.04/6.98 (axiom_62)
% 48.04/6.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 48.04/6.98 ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 48.04/6.98
% 48.04/6.98 (conj)
% 48.04/6.99 $i(ldr) & $i(down) & $i(elid) & $i(pendack) & $i(status) & $i(alive) &
% 48.04/6.99 $i(norm) & $i(wait) & $i(elec_1) & $i(elec_2) & $i(nbr_proc) & $i(zero) & ?
% 48.04/6.99 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i]
% 48.04/6.99 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ?
% 48.04/6.99 [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : ? [v15: $i] : ?
% 48.04/6.99 [v16: $i] : ? [v17: $i] : ( ~ (v16 = v5) & index(down, v5) = v12 &
% 48.04/6.99 index(pendack, v16) = v17 & index(status, v16) = elec_2 & index(status, v5)
% 48.04/6.99 = elec_1 & cons(v7, v1) = v6 & m_Down(v4) = v7 & s(v5) = v13 & s(zero) = v0
% 48.04/6.99 & host(v15) = v16 & host(v14) = v5 & host(v4) = v8 & host(v3) = v5 &
% 48.04/6.99 queue(v5) = v6 & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 48.04/6.99 $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 48.04/6.99 $i(v0) & leq(v13, v17) & setIn(v15, alive) & setIn(v14, alive) & setIn(v3,
% 48.04/6.99 alive) & ~ leq(v5, v16) & ~ leq(v5, v8) & ~ leq(nbr_proc, v5) & !
% 48.04/6.99 [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : !
% 48.04/6.99 [v23: $i] : ( ~ (m_Down(v19) = v23) | ~ (host(v20) = v21) | ~ (host(v18) =
% 48.04/6.99 v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~
% 48.04/6.99 setIn(v18, alive) | leq(v21, v22) | ? [v24: $i] : ? [v25: $i] : ? [v26:
% 48.04/6.99 $i] : (( ~ (v25 = elec_2) & index(status, v21) = v25 & $i(v25)) | ( ~
% 48.04/6.99 (v24 = v21) & host(v19) = v24 & $i(v24)) | (queue(v22) = v26 & $i(v26)
% 48.04/6.99 & ~ elem(v23, v26)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] :
% 48.04/6.99 ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v19) = v21) | ~
% 48.04/6.99 (host(v20) = v23) | ~ (host(v18) = v22) | ~ $i(v20) | ~ $i(v19) | ~
% 48.04/6.99 $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive) | ? [v24: $i] : ?
% 48.04/6.99 [v25: $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v26 = elec_2) &
% 48.04/6.99 index(status, v23) = v26 & $i(v26)) | ( ~ (v25 = v23) & host(v19) =
% 48.04/6.99 v25 & $i(v25)) | (index(pendack, v23) = v27 & $i(v27) & leq(v27, v22))
% 48.04/6.99 | (queue(v22) = v24 & $i(v24) & ~ elem(v21, v24)))) & ! [v18: $i] : !
% 48.04/6.99 [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v20,
% 48.04/6.99 v18) = v21) | ~ (host(v19) = v22) | ~ $i(v20) | ~ $i(v19) | ~
% 48.04/6.99 $i(v18) | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ((host(v20) = v25 &
% 48.04/6.99 host(v18) = v24 & $i(v25) & $i(v24) & ~ leq(v24, v25)) | (queue(v22)
% 48.04/6.99 = v23 & $i(v23) & ~ elem(v21, v23)))) & ! [v18: $i] : ! [v19: $i] :
% 48.04/6.99 ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v18, v19) = v22) |
% 48.04/6.99 ~ (host(v20) = v21) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20,
% 48.04/6.99 alive) | ~ setIn(v18, alive) | ? [v23: $i] : ? [v24: $i] : ? [v25:
% 48.04/6.99 $i] : ? [v26: $i] : ? [v27: $i] : (( ~ (v26 = elec_2) & index(status,
% 48.04/6.99 v21) = v26 & $i(v26)) | ( ~ (v25 = elec_2) & index(status, v24) =
% 48.04/6.99 v25 & host(v18) = v24 & $i(v25) & $i(v24)) | ( ~ (v23 = v21) &
% 48.04/6.99 host(v19) = v23 & $i(v23)) | (host(v18) = v24 & queue(v24) = v27 &
% 48.04/6.99 $i(v27) & $i(v24) & ~ elem(v22, v27)))) & ! [v18: $i] : ! [v19: $i]
% 48.04/6.99 : ! [v20: $i] : ! [v21: $i] : ( ~ (m_Halt(v19) = v20) | ~ (host(v18) =
% 48.04/6.99 v21) | ~ $i(v19) | ~ $i(v18) | ? [v22: $i] : ? [v23: $i] :
% 48.04/6.99 ((host(v19) = v23 & $i(v23) & ~ leq(v21, v23)) | (queue(v21) = v22 &
% 48.04/6.99 $i(v22) & ~ elem(v20, v22)))) & ! [v18: $i] : ! [v19: $i] : !
% 48.04/6.99 [v20: $i] : ! [v21: $i] : ( ~ (host(v19) = v21) | ~ (host(v18) = v20) | ~
% 48.04/6.99 $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive) |
% 48.04/6.99 leq(v20, v21) | ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : ? [v25: $i]
% 48.04/6.99 : (( ~ (v23 = elec_2) & index(status, v21) = v23 & $i(v23)) | ( ~ (v22 =
% 48.04/6.99 elec_2) & index(status, v20) = v22 & $i(v22)) | (index(pendack, v21)
% 48.04/6.99 = v25 & index(pendack, v20) = v24 & $i(v25) & $i(v24) & ~ leq(v24,
% 48.04/6.99 v25)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i]
% 48.04/6.99 : ( ~ (host(v19) = v21) | ~ (host(v18) = v20) | ~ $i(v19) | ~ $i(v18) |
% 48.04/6.99 ~ setIn(v19, alive) | ~ setIn(v18, alive) | leq(v20, v21) | ? [v22: $i]
% 48.04/6.99 : ? [v23: $i] : ? [v24: $i] : (( ~ (v23 = elec_2) & index(status, v21) =
% 48.04/6.99 v23 & $i(v23)) | ( ~ (v22 = elec_2) & index(status, v20) = v22 &
% 48.04/6.99 $i(v22)) | (index(pendack, v21) = v24 & $i(v24) & leq(v24, v20)))) &
% 48.04/6.99 ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (host(v19) =
% 48.04/6.99 v20) | ~ (host(v18) = v21) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19,
% 48.04/6.99 alive) | ~ setIn(v18, alive) | ? [v22: $i] : ? [v23: $i] : ? [v24:
% 48.04/6.99 $i] : (( ~ (v23 = elec_2) & index(status, v20) = v23 & $i(v23)) |
% 48.04/6.99 (index(down, v21) = v22 & $i(v22) & ~ setIn(v20, v22)) |
% 48.04/6.99 (index(pendack, v20) = v24 & $i(v24) & leq(v24, v21)))) & ! [v18: $i] :
% 48.04/6.99 ! [v19: $i] : ! [v20: $i] : (v19 = v18 | ~ (host(v19) = v20) | ~
% 48.04/6.99 (host(v18) = v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) | ~
% 48.04/6.99 setIn(v18, alive)) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~
% 48.04/6.99 (m_Ack(v18, v19) = v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) |
% 48.04/6.99 ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : (( ~ (v22 =
% 48.04/6.99 elec_2) & index(status, v21) = v22 & host(v19) = v21 & $i(v22) &
% 48.04/6.99 $i(v21)) | (host(v18) = v23 & queue(v23) = v24 & $i(v24) & $i(v23) &
% 48.04/6.99 ~ elem(v20, v24)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (host(v18) =
% 48.04/6.99 v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v20: $i] : ? [v21: $i] :
% 48.04/6.99 ((v21 = v18 & index(elid, v19) = v18) | ( ~ (v20 = elec_1) & ~ (v20 =
% 48.04/6.99 elec_2) & index(status, v19) = v20 & $i(v20)))) & ! [v18: $i] : !
% 48.04/6.99 [v19: $i] : ( ~ (host(v18) = v19) | ~ $i(v18) | ? [v20: $i] : ? [v21: $i]
% 48.04/6.99 : (( ~ (v20 = elec_2) & index(status, v19) = v20 & $i(v20)) |
% 48.04/6.99 (index(pendack, v19) = v21 & $i(v21) & ~ leq(v21, v19)))) & ! [v18:
% 48.04/6.99 $i] : (v18 = v8 | ~ $i(v18) | ~ leq(v0, v18) | leq(v5, v18) | setIn(v18,
% 48.04/6.99 v12)) & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & index(ldr, v5) = v9 &
% 48.04/6.99 $i(v9))) & ( ~ (wait = elec_1) | ( ~ (v11 = v8) & index(elid, v5) = v10
% 48.04/6.99 & host(v10) = v11 & $i(v11) & $i(v10))))
% 48.04/6.99
% 48.04/6.99 (function-axioms)
% 48.04/7.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 48.04/7.00 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 48.04/7.00 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (snoc(v3, v2) = v1) | ~ (snoc(v3,
% 48.04/7.00 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 48.04/7.00 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : !
% 48.04/7.00 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m_Ack(v3, v2) = v1) | ~
% 48.04/7.00 (m_Ack(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 48.04/7.00 ~ (pidMsg(v2) = v1) | ~ (pidMsg(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 48.04/7.00 ! [v2: $i] : (v1 = v0 | ~ (init(v2) = v1) | ~ (init(v2) = v0)) & ! [v0: $i]
% 48.04/7.00 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (last(v2) = v1) | ~ (last(v2) =
% 48.04/7.00 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tail(v2) =
% 48.04/7.00 v1) | ~ (tail(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 48.04/7.00 = v0 | ~ (head(v2) = v1) | ~ (head(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 48.04/7.00 : ! [v2: $i] : (v1 = v0 | ~ (m_NormQ(v2) = v1) | ~ (m_NormQ(v2) = v0)) & !
% 48.04/7.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Ldr(v2) = v1) | ~
% 48.04/7.00 (m_Ldr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.04/7.00 (m_NotNorm(v2) = v1) | ~ (m_NotNorm(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 48.04/7.00 : ! [v2: $i] : (v1 = v0 | ~ (m_Down(v2) = v1) | ~ (m_Down(v2) = v0)) & !
% 48.04/7.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (m_Halt(v2) = v1) | ~
% 48.04/7.00 (m_Halt(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.04/7.00 (s(v2) = v1) | ~ (s(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 48.04/7.00 (v1 = v0 | ~ (host(v2) = v1) | ~ (host(v2) = v0)) & ! [v0: $i] : ! [v1:
% 48.04/7.00 $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1) | ~ (queue(v2) = v0))
% 48.04/7.00
% 48.04/7.00 Further assumptions not needed in the proof:
% 48.04/7.00 --------------------------------------------
% 48.04/7.00 axiom, axiom_01, axiom_04, axiom_05, axiom_06, axiom_07, axiom_08, axiom_09,
% 48.04/7.00 axiom_10, axiom_11, axiom_12, axiom_13, axiom_14, axiom_15, axiom_16, axiom_17,
% 48.04/7.00 axiom_18, axiom_19, axiom_20, axiom_21, axiom_22, axiom_23, axiom_24, axiom_25,
% 48.04/7.00 axiom_26, axiom_27, axiom_28, axiom_29, axiom_30, axiom_31, axiom_32, axiom_33,
% 48.04/7.00 axiom_34, axiom_35, axiom_36, axiom_37, axiom_38, axiom_39, axiom_40, axiom_41,
% 48.04/7.00 axiom_42, axiom_43, axiom_44, axiom_45, axiom_47, axiom_48, axiom_49, axiom_50,
% 48.04/7.00 axiom_51, axiom_52, axiom_53, axiom_54, axiom_55, axiom_56, axiom_57, axiom_59,
% 48.04/7.00 axiom_60, axiom_61, axiom_63, axiom_64, axiom_65
% 48.04/7.00
% 48.04/7.00 Those formulas are unsatisfiable:
% 48.04/7.00 ---------------------------------
% 48.04/7.00
% 48.04/7.00 Begin of proof
% 48.04/7.00 |
% 48.04/7.00 | ALPHA: (axiom_02) implies:
% 48.04/7.00 | (1) ? [v0: $i] : (s(zero) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 48.04/7.00 | (host(v1) = v2) | ~ $i(v1) | leq(v0, v2)))
% 48.04/7.00 |
% 48.04/7.00 | ALPHA: (axiom_03) implies:
% 48.04/7.00 | (2) ? [v0: $i] : (s(zero) = v0 & $i(v0) & leq(v0, nbr_proc))
% 48.04/7.00 |
% 48.04/7.00 | ALPHA: (axiom_46) implies:
% 48.04/7.00 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0, v1) = v2) | ~
% 48.04/7.00 | $i(v1) | ~ $i(v0) | elem(v0, v2))
% 48.04/7.00 |
% 48.04/7.00 | ALPHA: (conj) implies:
% 48.04/7.01 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 48.04/7.01 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 48.04/7.01 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 48.04/7.01 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ( ~ (v16 = v5) &
% 48.04/7.01 | index(down, v5) = v12 & index(pendack, v16) = v17 & index(status,
% 48.04/7.01 | v16) = elec_2 & index(status, v5) = elec_1 & cons(v7, v1) = v6 &
% 48.04/7.01 | m_Down(v4) = v7 & s(v5) = v13 & s(zero) = v0 & host(v15) = v16 &
% 48.04/7.01 | host(v14) = v5 & host(v4) = v8 & host(v3) = v5 & queue(v5) = v6 &
% 48.04/7.01 | $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v8) &
% 48.04/7.01 | $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 48.04/7.01 | & leq(v13, v17) & setIn(v15, alive) & setIn(v14, alive) & setIn(v3,
% 48.04/7.01 | alive) & ~ leq(v5, v16) & ~ leq(v5, v8) & ~ leq(nbr_proc, v5) &
% 48.04/7.01 | ! [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22:
% 48.04/7.01 | $i] : ! [v23: $i] : ( ~ (m_Down(v19) = v23) | ~ (host(v20) = v21)
% 48.04/7.01 | | ~ (host(v18) = v22) | ~ $i(v20) | ~ $i(v19) | ~ $i(v18) | ~
% 48.04/7.01 | setIn(v20, alive) | ~ setIn(v18, alive) | leq(v21, v22) | ? [v24:
% 48.04/7.01 | $i] : ? [v25: $i] : ? [v26: $i] : (( ~ (v25 = elec_2) &
% 48.04/7.01 | index(status, v21) = v25 & $i(v25)) | ( ~ (v24 = v21) &
% 48.04/7.01 | host(v19) = v24 & $i(v24)) | (queue(v22) = v26 & $i(v26) & ~
% 48.04/7.01 | elem(v23, v26)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i]
% 48.04/7.01 | : ! [v21: $i] : ! [v22: $i] : ! [v23: $i] : ( ~ (m_Down(v19) =
% 48.04/7.01 | v21) | ~ (host(v20) = v23) | ~ (host(v18) = v22) | ~ $i(v20) |
% 48.04/7.01 | ~ $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18,
% 48.04/7.01 | alive) | ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ? [v27:
% 48.04/7.01 | $i] : (( ~ (v26 = elec_2) & index(status, v23) = v26 & $i(v26)) |
% 48.04/7.01 | ( ~ (v25 = v23) & host(v19) = v25 & $i(v25)) | (index(pendack,
% 48.04/7.01 | v23) = v27 & $i(v27) & leq(v27, v22)) | (queue(v22) = v24 &
% 48.04/7.01 | $i(v24) & ~ elem(v21, v24)))) & ! [v18: $i] : ! [v19: $i] :
% 48.04/7.01 | ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : ( ~ (m_Ack(v20, v18) =
% 48.04/7.01 | v21) | ~ (host(v19) = v22) | ~ $i(v20) | ~ $i(v19) | ~
% 48.04/7.01 | $i(v18) | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ((host(v20)
% 48.04/7.01 | = v25 & host(v18) = v24 & $i(v25) & $i(v24) & ~ leq(v24, v25))
% 48.04/7.01 | | (queue(v22) = v23 & $i(v23) & ~ elem(v21, v23)))) & ! [v18:
% 48.04/7.01 | $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ! [v22: $i] : (
% 48.04/7.01 | ~ (m_Ack(v18, v19) = v22) | ~ (host(v20) = v21) | ~ $i(v20) | ~
% 48.04/7.01 | $i(v19) | ~ $i(v18) | ~ setIn(v20, alive) | ~ setIn(v18, alive)
% 48.04/7.01 | | ? [v23: $i] : ? [v24: $i] : ? [v25: $i] : ? [v26: $i] : ?
% 48.04/7.01 | [v27: $i] : (( ~ (v26 = elec_2) & index(status, v21) = v26 &
% 48.04/7.01 | $i(v26)) | ( ~ (v25 = elec_2) & index(status, v24) = v25 &
% 48.04/7.01 | host(v18) = v24 & $i(v25) & $i(v24)) | ( ~ (v23 = v21) &
% 48.04/7.01 | host(v19) = v23 & $i(v23)) | (host(v18) = v24 & queue(v24) =
% 48.04/7.01 | v27 & $i(v27) & $i(v24) & ~ elem(v22, v27)))) & ! [v18: $i] :
% 48.04/7.01 | ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (m_Halt(v19) = v20)
% 48.04/7.01 | | ~ (host(v18) = v21) | ~ $i(v19) | ~ $i(v18) | ? [v22: $i] :
% 48.04/7.01 | ? [v23: $i] : ((host(v19) = v23 & $i(v23) & ~ leq(v21, v23)) |
% 48.04/7.01 | (queue(v21) = v22 & $i(v22) & ~ elem(v20, v22)))) & ! [v18: $i]
% 48.04/7.01 | : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~ (host(v19) = v21)
% 48.04/7.01 | | ~ (host(v18) = v20) | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19,
% 48.04/7.01 | alive) | ~ setIn(v18, alive) | leq(v20, v21) | ? [v22: $i] : ?
% 48.04/7.01 | [v23: $i] : ? [v24: $i] : ? [v25: $i] : (( ~ (v23 = elec_2) &
% 48.04/7.01 | index(status, v21) = v23 & $i(v23)) | ( ~ (v22 = elec_2) &
% 48.04/7.01 | index(status, v20) = v22 & $i(v22)) | (index(pendack, v21) =
% 48.04/7.01 | v25 & index(pendack, v20) = v24 & $i(v25) & $i(v24) & ~
% 48.04/7.01 | leq(v24, v25)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] :
% 48.04/7.01 | ! [v21: $i] : ( ~ (host(v19) = v21) | ~ (host(v18) = v20) | ~
% 48.04/7.01 | $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive)
% 48.04/7.01 | | leq(v20, v21) | ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : (( ~
% 48.04/7.01 | (v23 = elec_2) & index(status, v21) = v23 & $i(v23)) | ( ~ (v22
% 48.04/7.01 | = elec_2) & index(status, v20) = v22 & $i(v22)) |
% 48.04/7.01 | (index(pendack, v21) = v24 & $i(v24) & leq(v24, v20)))) & !
% 48.04/7.01 | [v18: $i] : ! [v19: $i] : ! [v20: $i] : ! [v21: $i] : ( ~
% 48.04/7.01 | (host(v19) = v20) | ~ (host(v18) = v21) | ~ $i(v19) | ~ $i(v18)
% 48.04/7.01 | | ~ setIn(v19, alive) | ~ setIn(v18, alive) | ? [v22: $i] : ?
% 48.04/7.01 | [v23: $i] : ? [v24: $i] : (( ~ (v23 = elec_2) & index(status, v20)
% 48.04/7.01 | = v23 & $i(v23)) | (index(down, v21) = v22 & $i(v22) & ~
% 48.04/7.01 | setIn(v20, v22)) | (index(pendack, v20) = v24 & $i(v24) &
% 48.04/7.01 | leq(v24, v21)))) & ! [v18: $i] : ! [v19: $i] : ! [v20: $i] :
% 48.04/7.01 | (v19 = v18 | ~ (host(v19) = v20) | ~ (host(v18) = v20) | ~ $i(v19)
% 48.04/7.01 | | ~ $i(v18) | ~ setIn(v19, alive) | ~ setIn(v18, alive)) & !
% 48.04/7.01 | [v18: $i] : ! [v19: $i] : ! [v20: $i] : ( ~ (m_Ack(v18, v19) = v20)
% 48.04/7.01 | | ~ $i(v19) | ~ $i(v18) | ~ setIn(v19, alive) | ? [v21: $i] :
% 48.04/7.01 | ? [v22: $i] : ? [v23: $i] : ? [v24: $i] : (( ~ (v22 = elec_2) &
% 48.04/7.01 | index(status, v21) = v22 & host(v19) = v21 & $i(v22) & $i(v21))
% 48.04/7.01 | | (host(v18) = v23 & queue(v23) = v24 & $i(v24) & $i(v23) & ~
% 48.04/7.01 | elem(v20, v24)))) & ! [v18: $i] : ! [v19: $i] : ( ~
% 48.04/7.01 | (host(v18) = v19) | ~ $i(v18) | ~ setIn(v18, alive) | ? [v20:
% 48.04/7.01 | $i] : ? [v21: $i] : ((v21 = v18 & index(elid, v19) = v18) | ( ~
% 48.04/7.01 | (v20 = elec_1) & ~ (v20 = elec_2) & index(status, v19) = v20 &
% 48.04/7.01 | $i(v20)))) & ! [v18: $i] : ! [v19: $i] : ( ~ (host(v18) =
% 48.04/7.01 | v19) | ~ $i(v18) | ? [v20: $i] : ? [v21: $i] : (( ~ (v20 =
% 48.04/7.01 | elec_2) & index(status, v19) = v20 & $i(v20)) |
% 48.04/7.01 | (index(pendack, v19) = v21 & $i(v21) & ~ leq(v21, v19)))) & !
% 48.04/7.01 | [v18: $i] : (v18 = v8 | ~ $i(v18) | ~ leq(v0, v18) | leq(v5, v18) |
% 48.04/7.01 | setIn(v18, v12)) & ( ~ (norm = elec_1) | ( ~ (v9 = v8) & index(ldr,
% 48.04/7.01 | v5) = v9 & $i(v9))) & ( ~ (wait = elec_1) | ( ~ (v11 = v8) &
% 48.04/7.02 | index(elid, v5) = v10 & host(v10) = v11 & $i(v11) & $i(v10))))
% 48.04/7.02 |
% 48.04/7.02 | ALPHA: (function-axioms) implies:
% 48.04/7.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) =
% 48.04/7.02 | v1) | ~ (queue(v2) = v0))
% 48.04/7.02 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (host(v2) = v1)
% 48.04/7.02 | | ~ (host(v2) = v0))
% 48.04/7.02 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) |
% 48.04/7.02 | ~ (s(v2) = v0))
% 48.04/7.02 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 48.04/7.02 | (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 48.04/7.02 |
% 48.04/7.02 | DELTA: instantiating (2) with fresh symbol all_59_0 gives:
% 48.04/7.02 | (9) s(zero) = all_59_0 & $i(all_59_0) & leq(all_59_0, nbr_proc)
% 48.04/7.02 |
% 48.04/7.02 | ALPHA: (9) implies:
% 48.04/7.02 | (10) s(zero) = all_59_0
% 48.04/7.02 |
% 48.04/7.02 | DELTA: instantiating (1) with fresh symbol all_62_0 gives:
% 48.04/7.02 | (11) s(zero) = all_62_0 & $i(all_62_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 48.04/7.02 | (host(v0) = v1) | ~ $i(v0) | leq(all_62_0, v1))
% 48.04/7.02 |
% 48.04/7.02 | ALPHA: (11) implies:
% 48.04/7.02 | (12) s(zero) = all_62_0
% 48.04/7.02 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) |
% 48.04/7.02 | leq(all_62_0, v1))
% 48.04/7.02 |
% 48.04/7.02 | DELTA: instantiating (4) with fresh symbols all_65_0, all_65_1, all_65_2,
% 48.04/7.02 | all_65_3, all_65_4, all_65_5, all_65_6, all_65_7, all_65_8, all_65_9,
% 48.04/7.02 | all_65_10, all_65_11, all_65_12, all_65_13, all_65_14, all_65_15,
% 48.04/7.02 | all_65_16, all_65_17 gives:
% 48.48/7.03 | (14) ~ (all_65_1 = all_65_12) & index(down, all_65_12) = all_65_5 &
% 48.48/7.03 | index(pendack, all_65_1) = all_65_0 & index(status, all_65_1) = elec_2
% 48.48/7.03 | & index(status, all_65_12) = elec_1 & cons(all_65_10, all_65_16) =
% 48.48/7.03 | all_65_11 & m_Down(all_65_13) = all_65_10 & s(all_65_12) = all_65_4 &
% 48.48/7.03 | s(zero) = all_65_17 & host(all_65_2) = all_65_1 & host(all_65_3) =
% 48.48/7.03 | all_65_12 & host(all_65_13) = all_65_9 & host(all_65_14) = all_65_12 &
% 48.48/7.03 | queue(all_65_12) = all_65_11 & $i(all_65_0) & $i(all_65_1) &
% 48.48/7.03 | $i(all_65_2) & $i(all_65_3) & $i(all_65_4) & $i(all_65_5) &
% 48.48/7.03 | $i(all_65_9) & $i(all_65_10) & $i(all_65_11) & $i(all_65_12) &
% 48.48/7.03 | $i(all_65_13) & $i(all_65_14) & $i(all_65_15) & $i(all_65_16) &
% 48.48/7.03 | $i(all_65_17) & leq(all_65_4, all_65_0) & setIn(all_65_2, alive) &
% 48.48/7.03 | setIn(all_65_3, alive) & setIn(all_65_14, alive) & ~ leq(all_65_12,
% 48.48/7.03 | all_65_1) & ~ leq(all_65_12, all_65_9) & ~ leq(nbr_proc,
% 48.48/7.03 | all_65_12) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 48.48/7.03 | ! [v4: $i] : ! [v5: $i] : ( ~ (m_Down(v1) = v5) | ~ (host(v2) = v3)
% 48.48/7.03 | | ~ (host(v0) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 48.48/7.03 | setIn(v2, alive) | ~ setIn(v0, alive) | leq(v3, v4) | ? [v6: $i] :
% 48.48/7.03 | ? [v7: $i] : ? [v8: $i] : (( ~ (v7 = elec_2) & index(status, v3) =
% 48.48/7.03 | v7 & $i(v7)) | ( ~ (v6 = v3) & host(v1) = v6 & $i(v6)) |
% 48.48/7.03 | (queue(v4) = v8 & $i(v8) & ~ elem(v5, v8)))) & ! [v0: $i] : !
% 48.48/7.03 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 48.48/7.03 | (m_Down(v1) = v3) | ~ (host(v2) = v5) | ~ (host(v0) = v4) | ~
% 48.48/7.03 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0,
% 48.48/7.03 | alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 48.48/7.03 | (( ~ (v8 = elec_2) & index(status, v5) = v8 & $i(v8)) | ( ~ (v7 =
% 48.48/7.03 | v5) & host(v1) = v7 & $i(v7)) | (index(pendack, v5) = v9 &
% 48.48/7.03 | $i(v9) & leq(v9, v4)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3,
% 48.48/7.03 | v6)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 48.48/7.03 | : ! [v4: $i] : ( ~ (m_Ack(v2, v0) = v3) | ~ (host(v1) = v4) | ~
% 48.48/7.03 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7:
% 48.48/7.03 | $i] : ((host(v2) = v7 & host(v0) = v6 & $i(v7) & $i(v6) & ~
% 48.48/7.03 | leq(v6, v7)) | (queue(v4) = v5 & $i(v5) & ~ elem(v3, v5)))) &
% 48.48/7.03 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 48.48/7.03 | ~ (m_Ack(v0, v1) = v4) | ~ (host(v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 48.48/7.03 | | ~ $i(v0) | ~ setIn(v2, alive) | ~ setIn(v0, alive) | ? [v5:
% 48.48/7.03 | $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (( ~
% 48.48/7.03 | (v8 = elec_2) & index(status, v3) = v8 & $i(v8)) | ( ~ (v7 =
% 48.48/7.03 | elec_2) & index(status, v6) = v7 & host(v0) = v6 & $i(v7) &
% 48.48/7.03 | $i(v6)) | ( ~ (v5 = v3) & host(v1) = v5 & $i(v5)) | (host(v0) =
% 48.48/7.03 | v6 & queue(v6) = v9 & $i(v9) & $i(v6) & ~ elem(v4, v9)))) & !
% 48.48/7.03 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (m_Halt(v1) =
% 48.48/7.03 | v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 48.48/7.03 | ? [v5: $i] : ((host(v1) = v5 & $i(v5) & ~ leq(v3, v5)) | (queue(v3)
% 48.48/7.03 | = v4 & $i(v4) & ~ elem(v2, v4)))) & ! [v0: $i] : ! [v1: $i] :
% 48.48/7.03 | ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1) = v3) | ~ (host(v0) = v2) |
% 48.48/7.03 | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive) |
% 48.48/7.03 | leq(v2, v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 48.48/7.03 | : (( ~ (v5 = elec_2) & index(status, v3) = v5 & $i(v5)) | ( ~ (v4 =
% 48.48/7.03 | elec_2) & index(status, v2) = v4 & $i(v4)) | (index(pendack,
% 48.48/7.03 | v3) = v7 & index(pendack, v2) = v6 & $i(v7) & $i(v6) & ~
% 48.48/7.03 | leq(v6, v7)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 48.48/7.03 | [v3: $i] : ( ~ (host(v1) = v3) | ~ (host(v0) = v2) | ~ $i(v1) | ~
% 48.48/7.03 | $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive) | leq(v2, v3) |
% 48.48/7.03 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (( ~ (v5 = elec_2) &
% 48.48/7.03 | index(status, v3) = v5 & $i(v5)) | ( ~ (v4 = elec_2) &
% 48.48/7.03 | index(status, v2) = v4 & $i(v4)) | (index(pendack, v3) = v6 &
% 48.48/7.03 | $i(v6) & leq(v6, v2)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 48.48/7.03 | $i] : ! [v3: $i] : ( ~ (host(v1) = v2) | ~ (host(v0) = v3) | ~
% 48.48/7.03 | $i(v1) | ~ $i(v0) | ~ setIn(v1, alive) | ~ setIn(v0, alive) | ?
% 48.48/7.03 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (( ~ (v5 = elec_2) &
% 48.48/7.03 | index(status, v2) = v5 & $i(v5)) | (index(down, v3) = v4 &
% 48.48/7.03 | $i(v4) & ~ setIn(v2, v4)) | (index(pendack, v2) = v6 & $i(v6) &
% 48.48/7.03 | leq(v6, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 48.48/7.03 | v0 | ~ (host(v1) = v2) | ~ (host(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 48.48/7.03 | | ~ setIn(v1, alive) | ~ setIn(v0, alive)) & ! [v0: $i] : ! [v1:
% 48.48/7.03 | $i] : ! [v2: $i] : ( ~ (m_Ack(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 48.48/7.03 | | ~ setIn(v1, alive) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 48.48/7.03 | [v6: $i] : (( ~ (v4 = elec_2) & index(status, v3) = v4 & host(v1) =
% 48.48/7.03 | v3 & $i(v4) & $i(v3)) | (host(v0) = v5 & queue(v5) = v6 & $i(v6)
% 48.48/7.03 | & $i(v5) & ~ elem(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 48.48/7.03 | (host(v0) = v1) | ~ $i(v0) | ~ setIn(v0, alive) | ? [v2: $i] : ?
% 48.48/7.03 | [v3: $i] : ((v3 = v0 & index(elid, v1) = v0) | ( ~ (v2 = elec_1) &
% 48.48/7.03 | ~ (v2 = elec_2) & index(status, v1) = v2 & $i(v2)))) & ! [v0:
% 48.48/7.03 | $i] : ! [v1: $i] : ( ~ (host(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 48.48/7.03 | ? [v3: $i] : (( ~ (v2 = elec_2) & index(status, v1) = v2 & $i(v2)) |
% 48.48/7.03 | (index(pendack, v1) = v3 & $i(v3) & ~ leq(v3, v1)))) & ! [v0:
% 48.48/7.03 | any] : (v0 = all_65_9 | ~ $i(v0) | ~ leq(all_65_17, v0) |
% 48.48/7.03 | leq(all_65_12, v0) | setIn(v0, all_65_5)) & ( ~ (norm = elec_1) | (
% 48.48/7.03 | ~ (all_65_8 = all_65_9) & index(ldr, all_65_12) = all_65_8 &
% 48.48/7.03 | $i(all_65_8))) & ( ~ (wait = elec_1) | ( ~ (all_65_6 = all_65_9) &
% 48.48/7.03 | index(elid, all_65_12) = all_65_7 & host(all_65_7) = all_65_6 &
% 48.48/7.03 | $i(all_65_6) & $i(all_65_7)))
% 48.48/7.03 |
% 48.48/7.03 | ALPHA: (14) implies:
% 48.48/7.03 | (15) ~ leq(all_65_12, all_65_1)
% 48.48/7.03 | (16) setIn(all_65_14, alive)
% 48.48/7.03 | (17) setIn(all_65_2, alive)
% 48.48/7.03 | (18) leq(all_65_4, all_65_0)
% 48.48/7.03 | (19) $i(all_65_16)
% 48.48/7.03 | (20) $i(all_65_14)
% 48.48/7.03 | (21) $i(all_65_13)
% 48.48/7.03 | (22) $i(all_65_12)
% 48.48/7.04 | (23) $i(all_65_10)
% 48.48/7.04 | (24) $i(all_65_4)
% 48.48/7.04 | (25) $i(all_65_2)
% 48.48/7.04 | (26) $i(all_65_1)
% 48.48/7.04 | (27) queue(all_65_12) = all_65_11
% 48.48/7.04 | (28) host(all_65_14) = all_65_12
% 48.48/7.04 | (29) host(all_65_13) = all_65_9
% 48.48/7.04 | (30) host(all_65_2) = all_65_1
% 48.48/7.04 | (31) s(zero) = all_65_17
% 48.48/7.04 | (32) s(all_65_12) = all_65_4
% 48.48/7.04 | (33) m_Down(all_65_13) = all_65_10
% 48.48/7.04 | (34) cons(all_65_10, all_65_16) = all_65_11
% 48.48/7.04 | (35) index(status, all_65_1) = elec_2
% 48.48/7.04 | (36) index(pendack, all_65_1) = all_65_0
% 48.48/7.04 | (37) index(down, all_65_12) = all_65_5
% 48.48/7.04 | (38) ! [v0: any] : (v0 = all_65_9 | ~ $i(v0) | ~ leq(all_65_17, v0) |
% 48.48/7.04 | leq(all_65_12, v0) | setIn(v0, all_65_5))
% 48.48/7.04 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (host(v1)
% 48.48/7.04 | = v2) | ~ (host(v0) = v3) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v1,
% 48.48/7.04 | alive) | ~ setIn(v0, alive) | ? [v4: $i] : ? [v5: $i] : ? [v6:
% 48.48/7.04 | $i] : (( ~ (v5 = elec_2) & index(status, v2) = v5 & $i(v5)) |
% 48.48/7.04 | (index(down, v3) = v4 & $i(v4) & ~ setIn(v2, v4)) |
% 48.48/7.04 | (index(pendack, v2) = v6 & $i(v6) & leq(v6, v3))))
% 48.48/7.04 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 48.48/7.04 | ! [v5: $i] : ( ~ (m_Down(v1) = v3) | ~ (host(v2) = v5) | ~ (host(v0)
% 48.48/7.04 | = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ setIn(v2, alive) |
% 48.48/7.04 | ~ setIn(v0, alive) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 48.48/7.04 | [v9: $i] : (( ~ (v8 = elec_2) & index(status, v5) = v8 & $i(v8)) | (
% 48.48/7.04 | ~ (v7 = v5) & host(v1) = v7 & $i(v7)) | (index(pendack, v5) = v9
% 48.48/7.04 | & $i(v9) & leq(v9, v4)) | (queue(v4) = v6 & $i(v6) & ~ elem(v3,
% 48.48/7.04 | v6))))
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (7) with all_62_0, all_65_17, zero, simplifying
% 48.48/7.04 | with (12), (31) gives:
% 48.48/7.04 | (41) all_65_17 = all_62_0
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (7) with all_59_0, all_65_17, zero, simplifying
% 48.48/7.04 | with (10), (31) gives:
% 48.48/7.04 | (42) all_65_17 = all_59_0
% 48.48/7.04 |
% 48.48/7.04 | COMBINE_EQS: (41), (42) imply:
% 48.48/7.04 | (43) all_62_0 = all_59_0
% 48.48/7.04 |
% 48.48/7.04 | SIMP: (43) implies:
% 48.48/7.04 | (44) all_62_0 = all_59_0
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (39) with all_65_14, all_65_2, all_65_1, all_65_12,
% 48.48/7.04 | simplifying with (16), (17), (20), (25), (28), (30) gives:
% 48.48/7.04 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (( ~ (v1 = elec_2) &
% 48.48/7.04 | index(status, all_65_1) = v1 & $i(v1)) | (index(down, all_65_12) =
% 48.48/7.04 | v0 & $i(v0) & ~ setIn(all_65_1, v0)) | (index(pendack, all_65_1)
% 48.48/7.04 | = v2 & $i(v2) & leq(v2, all_65_12)))
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (13) with all_65_2, all_65_1, simplifying with
% 48.48/7.04 | (25), (30) gives:
% 48.48/7.04 | (46) leq(all_62_0, all_65_1)
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (40) with all_65_14, all_65_13, all_65_2,
% 48.48/7.04 | all_65_10, all_65_12, all_65_1, simplifying with (16), (17),
% 48.48/7.04 | (20), (21), (25), (28), (30), (33) gives:
% 48.48/7.04 | (47) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : (( ~ (v2 =
% 48.48/7.04 | elec_2) & index(status, all_65_1) = v2 & $i(v2)) | ( ~ (v1 =
% 48.48/7.04 | all_65_1) & host(all_65_13) = v1 & $i(v1)) | (index(pendack,
% 48.48/7.04 | all_65_1) = v3 & $i(v3) & leq(v3, all_65_12)) |
% 48.48/7.04 | (queue(all_65_12) = v0 & $i(v0) & ~ elem(all_65_10, v0)))
% 48.48/7.04 |
% 48.48/7.04 | GROUND_INST: instantiating (3) with all_65_10, all_65_16, all_65_11,
% 48.48/7.04 | simplifying with (19), (23), (34) gives:
% 48.48/7.04 | (48) elem(all_65_10, all_65_11)
% 48.48/7.04 |
% 48.48/7.04 | DELTA: instantiating (45) with fresh symbols all_95_0, all_95_1, all_95_2
% 48.48/7.04 | gives:
% 48.48/7.05 | (49) ( ~ (all_95_1 = elec_2) & index(status, all_65_1) = all_95_1 &
% 48.48/7.05 | $i(all_95_1)) | (index(down, all_65_12) = all_95_2 & $i(all_95_2) &
% 48.48/7.05 | ~ setIn(all_65_1, all_95_2)) | (index(pendack, all_65_1) = all_95_0
% 48.48/7.05 | & $i(all_95_0) & leq(all_95_0, all_65_12))
% 48.48/7.05 |
% 48.48/7.05 | DELTA: instantiating (47) with fresh symbols all_97_0, all_97_1, all_97_2,
% 48.48/7.05 | all_97_3 gives:
% 48.48/7.05 | (50) ( ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.05 | $i(all_97_1)) | ( ~ (all_97_2 = all_65_1) & host(all_65_13) =
% 48.48/7.05 | all_97_2 & $i(all_97_2)) | (index(pendack, all_65_1) = all_97_0 &
% 48.48/7.05 | $i(all_97_0) & leq(all_97_0, all_65_12)) | (queue(all_65_12) =
% 48.48/7.05 | all_97_3 & $i(all_97_3) & ~ elem(all_65_10, all_97_3))
% 48.48/7.05 |
% 48.48/7.05 | REDUCE: (44), (46) imply:
% 48.48/7.05 | (51) leq(all_59_0, all_65_1)
% 48.48/7.05 |
% 48.48/7.05 | BETA: splitting (49) gives:
% 48.48/7.05 |
% 48.48/7.05 | Case 1:
% 48.48/7.05 | |
% 48.48/7.05 | | (52) ~ (all_95_1 = elec_2) & index(status, all_65_1) = all_95_1 &
% 48.48/7.05 | | $i(all_95_1)
% 48.48/7.05 | |
% 48.48/7.05 | | ALPHA: (52) implies:
% 48.48/7.05 | | (53) ~ (all_95_1 = elec_2)
% 48.48/7.05 | | (54) index(status, all_65_1) = all_95_1
% 48.48/7.05 | |
% 48.48/7.05 | | GROUND_INST: instantiating (8) with elec_2, all_95_1, all_65_1, status,
% 48.48/7.05 | | simplifying with (35), (54) gives:
% 48.48/7.05 | | (55) all_95_1 = elec_2
% 48.48/7.05 | |
% 48.48/7.05 | | REDUCE: (53), (55) imply:
% 48.48/7.05 | | (56) $false
% 48.48/7.05 | |
% 48.48/7.05 | | CLOSE: (56) is inconsistent.
% 48.48/7.05 | |
% 48.48/7.05 | Case 2:
% 48.48/7.05 | |
% 48.48/7.05 | | (57) (index(down, all_65_12) = all_95_2 & $i(all_95_2) & ~
% 48.48/7.05 | | setIn(all_65_1, all_95_2)) | (index(pendack, all_65_1) = all_95_0
% 48.48/7.05 | | & $i(all_95_0) & leq(all_95_0, all_65_12))
% 48.48/7.05 | |
% 48.48/7.05 | | BETA: splitting (57) gives:
% 48.48/7.05 | |
% 48.48/7.05 | | Case 1:
% 48.48/7.05 | | |
% 48.48/7.05 | | | (58) index(down, all_65_12) = all_95_2 & $i(all_95_2) & ~
% 48.48/7.05 | | | setIn(all_65_1, all_95_2)
% 48.48/7.05 | | |
% 48.48/7.05 | | | ALPHA: (58) implies:
% 48.48/7.05 | | | (59) ~ setIn(all_65_1, all_95_2)
% 48.48/7.05 | | | (60) index(down, all_65_12) = all_95_2
% 48.48/7.05 | | |
% 48.48/7.05 | | | GROUND_INST: instantiating (8) with all_65_5, all_95_2, all_65_12, down,
% 48.48/7.05 | | | simplifying with (37), (60) gives:
% 48.48/7.05 | | | (61) all_95_2 = all_65_5
% 48.48/7.05 | | |
% 48.48/7.05 | | | REDUCE: (59), (61) imply:
% 48.48/7.05 | | | (62) ~ setIn(all_65_1, all_65_5)
% 48.48/7.05 | | |
% 48.48/7.05 | | | BETA: splitting (50) gives:
% 48.48/7.05 | | |
% 48.48/7.05 | | | Case 1:
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | (63) ( ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.05 | | | | $i(all_97_1)) | ( ~ (all_97_2 = all_65_1) & host(all_65_13) =
% 48.48/7.05 | | | | all_97_2 & $i(all_97_2))
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | BETA: splitting (63) gives:
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | Case 1:
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | (64) ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.05 | | | | | $i(all_97_1)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | ALPHA: (64) implies:
% 48.48/7.05 | | | | | (65) ~ (all_97_1 = elec_2)
% 48.48/7.05 | | | | | (66) index(status, all_65_1) = all_97_1
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | GROUND_INST: instantiating (8) with elec_2, all_97_1, all_65_1,
% 48.48/7.05 | | | | | status, simplifying with (35), (66) gives:
% 48.48/7.05 | | | | | (67) all_97_1 = elec_2
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | REDUCE: (65), (67) imply:
% 48.48/7.05 | | | | | (68) $false
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | CLOSE: (68) is inconsistent.
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | Case 2:
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | (69) ~ (all_97_2 = all_65_1) & host(all_65_13) = all_97_2 &
% 48.48/7.05 | | | | | $i(all_97_2)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | ALPHA: (69) implies:
% 48.48/7.05 | | | | | (70) ~ (all_97_2 = all_65_1)
% 48.48/7.05 | | | | | (71) host(all_65_13) = all_97_2
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | GROUND_INST: instantiating (6) with all_65_9, all_97_2, all_65_13,
% 48.48/7.05 | | | | | simplifying with (29), (71) gives:
% 48.48/7.05 | | | | | (72) all_97_2 = all_65_9
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | REDUCE: (70), (72) imply:
% 48.48/7.05 | | | | | (73) ~ (all_65_1 = all_65_9)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | SIMP: (73) implies:
% 48.48/7.05 | | | | | (74) ~ (all_65_1 = all_65_9)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | GROUND_INST: instantiating (38) with all_65_1, simplifying with (15),
% 48.48/7.05 | | | | | (26), (62) gives:
% 48.48/7.05 | | | | | (75) all_65_1 = all_65_9 | ~ leq(all_65_17, all_65_1)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | BETA: splitting (75) gives:
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | Case 1:
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | (76) ~ leq(all_65_17, all_65_1)
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | REDUCE: (42), (76) imply:
% 48.48/7.05 | | | | | | (77) ~ leq(all_59_0, all_65_1)
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | PRED_UNIFY: (51), (77) imply:
% 48.48/7.05 | | | | | | (78) $false
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | CLOSE: (78) is inconsistent.
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | Case 2:
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | (79) all_65_1 = all_65_9
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | REDUCE: (74), (79) imply:
% 48.48/7.05 | | | | | | (80) $false
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | | CLOSE: (80) is inconsistent.
% 48.48/7.05 | | | | | |
% 48.48/7.05 | | | | | End of split
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | End of split
% 48.48/7.05 | | | |
% 48.48/7.05 | | | Case 2:
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | (81) (index(pendack, all_65_1) = all_97_0 & $i(all_97_0) &
% 48.48/7.05 | | | | leq(all_97_0, all_65_12)) | (queue(all_65_12) = all_97_3 &
% 48.48/7.05 | | | | $i(all_97_3) & ~ elem(all_65_10, all_97_3))
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | BETA: splitting (81) gives:
% 48.48/7.05 | | | |
% 48.48/7.05 | | | | Case 1:
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | (82) index(pendack, all_65_1) = all_97_0 & $i(all_97_0) &
% 48.48/7.05 | | | | | leq(all_97_0, all_65_12)
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | ALPHA: (82) implies:
% 48.48/7.05 | | | | | (83) leq(all_97_0, all_65_12)
% 48.48/7.05 | | | | | (84) $i(all_97_0)
% 48.48/7.05 | | | | | (85) index(pendack, all_65_1) = all_97_0
% 48.48/7.05 | | | | |
% 48.48/7.05 | | | | | GROUND_INST: instantiating (8) with all_65_0, all_97_0, all_65_1,
% 48.48/7.05 | | | | | pendack, simplifying with (36), (85) gives:
% 48.48/7.06 | | | | | (86) all_97_0 = all_65_0
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | | REDUCE: (84), (86) imply:
% 48.48/7.06 | | | | | (87) $i(all_65_0)
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | | REDUCE: (83), (86) imply:
% 48.48/7.06 | | | | | (88) leq(all_65_0, all_65_12)
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | | REF_CLOSE: (5), (8), (18), (22), (24), (27), (32), (35), (36), (48),
% 48.48/7.06 | | | | | (50), (87), (88), (axiom_58), (axiom_62) are inconsistent
% 48.48/7.06 | | | | | by sub-proof #1.
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | Case 2:
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | | (89) queue(all_65_12) = all_97_3 & $i(all_97_3) & ~
% 48.48/7.06 | | | | | elem(all_65_10, all_97_3)
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | | REF_CLOSE: (5), (27), (48), (89) are inconsistent by sub-proof #2.
% 48.48/7.06 | | | | |
% 48.48/7.06 | | | | End of split
% 48.48/7.06 | | | |
% 48.48/7.06 | | | End of split
% 48.48/7.06 | | |
% 48.48/7.06 | | Case 2:
% 48.48/7.06 | | |
% 48.48/7.06 | | | (90) index(pendack, all_65_1) = all_95_0 & $i(all_95_0) & leq(all_95_0,
% 48.48/7.06 | | | all_65_12)
% 48.48/7.06 | | |
% 48.48/7.06 | | | ALPHA: (90) implies:
% 48.48/7.06 | | | (91) leq(all_95_0, all_65_12)
% 48.48/7.06 | | | (92) $i(all_95_0)
% 48.48/7.06 | | | (93) index(pendack, all_65_1) = all_95_0
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (8) with all_65_0, all_95_0, all_65_1, pendack,
% 48.48/7.06 | | | simplifying with (36), (93) gives:
% 48.48/7.06 | | | (94) all_95_0 = all_65_0
% 48.48/7.06 | | |
% 48.48/7.06 | | | REDUCE: (92), (94) imply:
% 48.48/7.06 | | | (95) $i(all_65_0)
% 48.48/7.06 | | |
% 48.48/7.06 | | | REDUCE: (91), (94) imply:
% 48.48/7.06 | | | (96) leq(all_65_0, all_65_12)
% 48.48/7.06 | | |
% 48.48/7.06 | | | REF_CLOSE: (5), (8), (18), (22), (24), (27), (32), (35), (36), (48), (50),
% 48.48/7.06 | | | (95), (96), (axiom_58), (axiom_62) are inconsistent by
% 48.48/7.06 | | | sub-proof #1.
% 48.48/7.06 | | |
% 48.48/7.06 | | End of split
% 48.48/7.06 | |
% 48.48/7.06 | End of split
% 48.48/7.06 |
% 48.48/7.06 End of proof
% 48.48/7.06
% 48.48/7.06 Sub-proof #1 shows that the following formulas are inconsistent:
% 48.48/7.06 ----------------------------------------------------------------
% 48.48/7.06 (1) $i(all_65_12)
% 48.48/7.06 (2) ! [v0: $i] : ! [v1: $i] : ( ~ (s(v0) = v1) | ~ $i(v0) | ~ leq(v1,
% 48.48/7.06 v0))
% 48.48/7.06 (3) $i(all_65_4)
% 48.48/7.06 (4) $i(all_65_0)
% 48.48/7.06 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1)
% 48.48/7.06 | ~ (queue(v2) = v0))
% 48.48/7.06 (6) leq(all_65_0, all_65_12)
% 48.48/7.06 (7) ( ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.06 $i(all_97_1)) | ( ~ (all_97_2 = all_65_1) & host(all_65_13) = all_97_2
% 48.48/7.06 & $i(all_97_2)) | (index(pendack, all_65_1) = all_97_0 & $i(all_97_0) &
% 48.48/7.06 leq(all_97_0, all_65_12)) | (queue(all_65_12) = all_97_3 & $i(all_97_3)
% 48.48/7.06 & ~ elem(all_65_10, all_97_3))
% 48.48/7.06 (8) queue(all_65_12) = all_65_11
% 48.48/7.06 (9) elem(all_65_10, all_65_11)
% 48.48/7.06 (10) s(all_65_12) = all_65_4
% 48.48/7.06 (11) index(pendack, all_65_1) = all_65_0
% 48.48/7.06 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 48.48/7.06 $i(v0) | ~ leq(v1, v2) | ~ leq(v0, v1) | leq(v0, v2))
% 48.48/7.06 (13) leq(all_65_4, all_65_0)
% 48.48/7.06 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 48.48/7.06 (index(v3, v2) = v1) | ~ (index(v3, v2) = v0))
% 48.48/7.06 (15) index(status, all_65_1) = elec_2
% 48.48/7.06
% 48.48/7.06 Begin of proof
% 48.48/7.06 |
% 48.48/7.06 | BETA: splitting (7) gives:
% 48.48/7.06 |
% 48.48/7.06 | Case 1:
% 48.48/7.06 | |
% 48.48/7.06 | | (16) ( ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.06 | | $i(all_97_1)) | ( ~ (all_97_2 = all_65_1) & host(all_65_13) =
% 48.48/7.06 | | all_97_2 & $i(all_97_2))
% 48.48/7.06 | |
% 48.48/7.06 | | BETA: splitting (16) gives:
% 48.48/7.06 | |
% 48.48/7.06 | | Case 1:
% 48.48/7.06 | | |
% 48.48/7.06 | | | (17) ~ (all_97_1 = elec_2) & index(status, all_65_1) = all_97_1 &
% 48.48/7.06 | | | $i(all_97_1)
% 48.48/7.06 | | |
% 48.48/7.06 | | | ALPHA: (17) implies:
% 48.48/7.06 | | | (18) ~ (all_97_1 = elec_2)
% 48.48/7.06 | | | (19) index(status, all_65_1) = all_97_1
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (14) with elec_2, all_97_1, all_65_1, status,
% 48.48/7.06 | | | simplifying with (15), (19) gives:
% 48.48/7.06 | | | (20) all_97_1 = elec_2
% 48.48/7.06 | | |
% 48.48/7.06 | | | REDUCE: (18), (20) imply:
% 48.48/7.06 | | | (21) $false
% 48.48/7.06 | | |
% 48.48/7.06 | | | CLOSE: (21) is inconsistent.
% 48.48/7.06 | | |
% 48.48/7.06 | | Case 2:
% 48.48/7.06 | | |
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (12) with all_65_4, all_65_0, all_65_12,
% 48.48/7.06 | | | simplifying with (1), (3), (4), (6), (13) gives:
% 48.48/7.06 | | | (22) leq(all_65_4, all_65_12)
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (2) with all_65_12, all_65_4, simplifying with
% 48.48/7.06 | | | (1), (10), (22) gives:
% 48.48/7.06 | | | (23) $false
% 48.48/7.06 | | |
% 48.48/7.06 | | | CLOSE: (23) is inconsistent.
% 48.48/7.06 | | |
% 48.48/7.06 | | End of split
% 48.48/7.06 | |
% 48.48/7.06 | Case 2:
% 48.48/7.06 | |
% 48.48/7.06 | | (24) (index(pendack, all_65_1) = all_97_0 & $i(all_97_0) & leq(all_97_0,
% 48.48/7.06 | | all_65_12)) | (queue(all_65_12) = all_97_3 & $i(all_97_3) & ~
% 48.48/7.06 | | elem(all_65_10, all_97_3))
% 48.48/7.06 | |
% 48.48/7.06 | | BETA: splitting (24) gives:
% 48.48/7.06 | |
% 48.48/7.06 | | Case 1:
% 48.48/7.06 | | |
% 48.48/7.06 | | | (25) index(pendack, all_65_1) = all_97_0 & $i(all_97_0) & leq(all_97_0,
% 48.48/7.06 | | | all_65_12)
% 48.48/7.06 | | |
% 48.48/7.06 | | | ALPHA: (25) implies:
% 48.48/7.06 | | | (26) leq(all_97_0, all_65_12)
% 48.48/7.06 | | | (27) $i(all_97_0)
% 48.48/7.06 | | | (28) index(pendack, all_65_1) = all_97_0
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (14) with all_65_0, all_97_0, all_65_1,
% 48.48/7.06 | | | pendack, simplifying with (11), (28) gives:
% 48.48/7.06 | | | (29) all_97_0 = all_65_0
% 48.48/7.06 | | |
% 48.48/7.06 | | | GROUND_INST: instantiating (12) with all_65_4, all_65_0, all_65_12,
% 48.48/7.06 | | | simplifying with (1), (3), (4), (6), (13) gives:
% 48.48/7.07 | | | (30) leq(all_65_4, all_65_12)
% 48.48/7.07 | | |
% 48.48/7.07 | | | GROUND_INST: instantiating (2) with all_65_12, all_65_4, simplifying with
% 48.48/7.07 | | | (1), (10), (30) gives:
% 48.48/7.07 | | | (31) $false
% 48.48/7.07 | | |
% 48.48/7.07 | | | CLOSE: (31) is inconsistent.
% 48.48/7.07 | | |
% 48.48/7.07 | | Case 2:
% 48.48/7.07 | | |
% 48.48/7.07 | | | (32) queue(all_65_12) = all_97_3 & $i(all_97_3) & ~ elem(all_65_10,
% 48.48/7.07 | | | all_97_3)
% 48.48/7.07 | | |
% 48.48/7.07 | | | REF_CLOSE: (5), (8), (9), (32) are inconsistent by sub-proof #2.
% 48.48/7.07 | | |
% 48.48/7.07 | | End of split
% 48.48/7.07 | |
% 48.48/7.07 | End of split
% 48.48/7.07 |
% 48.48/7.07 End of proof
% 48.48/7.07
% 48.48/7.07 Sub-proof #2 shows that the following formulas are inconsistent:
% 48.48/7.07 ----------------------------------------------------------------
% 48.48/7.07 (1) queue(all_65_12) = all_97_3 & $i(all_97_3) & ~ elem(all_65_10, all_97_3)
% 48.48/7.07 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (queue(v2) = v1)
% 48.48/7.07 | ~ (queue(v2) = v0))
% 48.48/7.07 (3) queue(all_65_12) = all_65_11
% 48.48/7.07 (4) elem(all_65_10, all_65_11)
% 48.48/7.07
% 48.48/7.07 Begin of proof
% 48.48/7.07 |
% 48.48/7.07 | ALPHA: (1) implies:
% 48.48/7.07 | (5) ~ elem(all_65_10, all_97_3)
% 48.48/7.07 | (6) queue(all_65_12) = all_97_3
% 48.48/7.07 |
% 48.48/7.07 | GROUND_INST: instantiating (2) with all_65_11, all_97_3, all_65_12,
% 48.48/7.07 | simplifying with (3), (6) gives:
% 48.48/7.07 | (7) all_97_3 = all_65_11
% 48.48/7.07 |
% 48.48/7.07 | REDUCE: (5), (7) imply:
% 48.48/7.07 | (8) ~ elem(all_65_10, all_65_11)
% 48.48/7.07 |
% 48.48/7.07 | PRED_UNIFY: (4), (8) imply:
% 48.48/7.07 | (9) $false
% 48.48/7.07 |
% 48.48/7.07 | CLOSE: (9) is inconsistent.
% 48.48/7.07 |
% 48.48/7.07 End of proof
% 48.48/7.07 % SZS output end Proof for theBenchmark
% 48.48/7.07
% 48.48/7.07 6440ms
%------------------------------------------------------------------------------