TSTP Solution File: SET016+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 15:23:08 EDT 2023
% Result : Theorem 9.78s 1.97s
% Output : Proof 10.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 11:13:58 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.50 ________ _____
% 0.14/0.50 ___ __ \_________(_)________________________________
% 0.14/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.50 (2023-06-19)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2023
% 0.14/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.50 Amanda Stjerna.
% 0.14/0.50 Free software under BSD-3-Clause.
% 0.14/0.50
% 0.14/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.50
% 0.14/0.50 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.14/0.51 Running up to 7 provers in parallel.
% 0.14/0.52 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.52 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.52 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.52 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.52 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.52 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.95/0.88 Prover 4: Preprocessing ...
% 1.95/0.88 Prover 1: Preprocessing ...
% 2.28/0.92 Prover 0: Preprocessing ...
% 2.28/0.92 Prover 5: Preprocessing ...
% 2.28/0.92 Prover 6: Preprocessing ...
% 2.28/0.92 Prover 3: Preprocessing ...
% 2.28/0.93 Prover 2: Preprocessing ...
% 4.76/1.30 Prover 5: Proving ...
% 4.76/1.31 Prover 1: Constructing countermodel ...
% 4.76/1.31 Prover 6: Proving ...
% 4.76/1.33 Prover 3: Constructing countermodel ...
% 4.76/1.33 Prover 2: Proving ...
% 4.76/1.35 Prover 4: Constructing countermodel ...
% 4.76/1.36 Prover 0: Proving ...
% 4.76/1.45 Prover 3: gave up
% 4.76/1.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.76/1.46 Prover 1: gave up
% 5.96/1.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.96/1.49 Prover 7: Preprocessing ...
% 5.96/1.51 Prover 8: Preprocessing ...
% 7.06/1.58 Prover 7: Warning: ignoring some quantifiers
% 7.06/1.61 Prover 4: gave up
% 7.06/1.61 Prover 7: Constructing countermodel ...
% 7.06/1.62 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.61/1.65 Prover 9: Preprocessing ...
% 7.61/1.65 Prover 8: Warning: ignoring some quantifiers
% 7.61/1.66 Prover 8: Constructing countermodel ...
% 8.38/1.79 Prover 8: gave up
% 8.38/1.79 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.38/1.81 Prover 10: Preprocessing ...
% 8.91/1.84 Prover 9: Constructing countermodel ...
% 9.24/1.89 Prover 10: Warning: ignoring some quantifiers
% 9.24/1.92 Prover 10: Constructing countermodel ...
% 9.78/1.96 Prover 7: Found proof (size 32)
% 9.78/1.96 Prover 7: proved (509ms)
% 9.78/1.97 Prover 9: stopped
% 9.78/1.97 Prover 6: stopped
% 9.78/1.97 Prover 5: stopped
% 9.78/1.97 Prover 0: stopped
% 9.78/1.97 Prover 2: stopped
% 9.78/1.97 Prover 10: stopped
% 9.78/1.97
% 9.78/1.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.78/1.97
% 10.00/1.98 % SZS output start Proof for theBenchmark
% 10.00/1.98 Assumptions after simplification:
% 10.00/1.98 ---------------------------------
% 10.00/1.98
% 10.00/1.98 (equal_set)
% 10.00/1.99 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0, v1) |
% 10.00/1.99 subset(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 10.00/1.99 equal_set(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1)
% 10.00/1.99 | ~ $i(v0) | ~ subset(v1, v0) | ~ subset(v0, v1) | equal_set(v0, v1))
% 10.00/1.99
% 10.00/1.99 (singleton)
% 10.00/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1) = v2) |
% 10.00/2.01 ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 10.00/2.01 (singleton(v0) = v1) | ~ $i(v0) | member(v0, v1))
% 10.00/2.01
% 10.00/2.01 (subset)
% 10.00/2.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.00/2.01 ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1)) & ? [v0: $i] : ?
% 10.00/2.01 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | subset(v0, v1) | ? [v2: $i] : ($i(v2) &
% 10.00/2.01 member(v2, v0) & ~ member(v2, v1)))
% 10.00/2.01
% 10.00/2.01 (thI50a)
% 10.00/2.01 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.00/2.01 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ( ~ (v2 = v0)
% 10.00/2.01 & unordered_pair(v7, v8) = v9 & unordered_pair(v4, v5) = v6 &
% 10.00/2.01 unordered_pair(v2, v3) = v8 & unordered_pair(v0, v1) = v5 & singleton(v2) =
% 10.00/2.01 v7 & singleton(v0) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 10.00/2.01 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & equal_set(v6, v9))
% 10.00/2.01
% 10.00/2.01 (unordered_pair)
% 10.00/2.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 = v0 |
% 10.00/2.02 ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 10.00/2.02 member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.00/2.02 (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2)) & !
% 10.00/2.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~
% 10.00/2.02 $i(v1) | ~ $i(v0) | member(v0, v2))
% 10.00/2.02
% 10.00/2.02 Further assumptions not needed in the proof:
% 10.00/2.02 --------------------------------------------
% 10.00/2.02 difference, empty_set, intersection, power_set, product, sum, union
% 10.00/2.02
% 10.00/2.02 Those formulas are unsatisfiable:
% 10.00/2.02 ---------------------------------
% 10.00/2.02
% 10.00/2.02 Begin of proof
% 10.00/2.02 |
% 10.00/2.02 | ALPHA: (subset) implies:
% 10.00/2.02 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 10.00/2.02 | $i(v0) | ~ member(v2, v0) | ~ subset(v0, v1) | member(v2, v1))
% 10.00/2.02 |
% 10.00/2.02 | ALPHA: (equal_set) implies:
% 10.00/2.02 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ equal_set(v0,
% 10.00/2.02 | v1) | subset(v1, v0))
% 10.00/2.02 |
% 10.00/2.02 | ALPHA: (singleton) implies:
% 10.00/2.02 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 10.00/2.02 | member(v0, v1))
% 10.00/2.02 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1)
% 10.00/2.02 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, v2))
% 10.00/2.02 |
% 10.00/2.02 | ALPHA: (unordered_pair) implies:
% 10.00/2.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 10.00/2.02 | v2) | ~ $i(v1) | ~ $i(v0) | member(v0, v2))
% 10.00/2.03 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 10.00/2.03 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 10.00/2.03 | $i(v0) | ~ member(v0, v3))
% 10.00/2.03 |
% 10.00/2.03 | DELTA: instantiating (thI50a) with fresh symbols all_18_0, all_18_1, all_18_2,
% 10.00/2.03 | all_18_3, all_18_4, all_18_5, all_18_6, all_18_7, all_18_8, all_18_9
% 10.00/2.03 | gives:
% 10.00/2.03 | (7) ~ (all_18_7 = all_18_9) & unordered_pair(all_18_2, all_18_1) =
% 10.00/2.03 | all_18_0 & unordered_pair(all_18_5, all_18_4) = all_18_3 &
% 10.00/2.03 | unordered_pair(all_18_7, all_18_6) = all_18_1 &
% 10.00/2.03 | unordered_pair(all_18_9, all_18_8) = all_18_4 & singleton(all_18_7) =
% 10.00/2.03 | all_18_2 & singleton(all_18_9) = all_18_5 & $i(all_18_0) & $i(all_18_1)
% 10.00/2.03 | & $i(all_18_2) & $i(all_18_3) & $i(all_18_4) & $i(all_18_5) &
% 10.00/2.03 | $i(all_18_6) & $i(all_18_7) & $i(all_18_8) & $i(all_18_9) &
% 10.00/2.03 | equal_set(all_18_3, all_18_0)
% 10.00/2.03 |
% 10.00/2.03 | ALPHA: (7) implies:
% 10.00/2.03 | (8) ~ (all_18_7 = all_18_9)
% 10.00/2.03 | (9) equal_set(all_18_3, all_18_0)
% 10.00/2.03 | (10) $i(all_18_9)
% 10.00/2.03 | (11) $i(all_18_8)
% 10.00/2.03 | (12) $i(all_18_7)
% 10.00/2.03 | (13) $i(all_18_5)
% 10.00/2.03 | (14) $i(all_18_4)
% 10.00/2.03 | (15) $i(all_18_3)
% 10.00/2.03 | (16) $i(all_18_2)
% 10.00/2.04 | (17) $i(all_18_1)
% 10.00/2.04 | (18) $i(all_18_0)
% 10.00/2.04 | (19) singleton(all_18_9) = all_18_5
% 10.00/2.04 | (20) singleton(all_18_7) = all_18_2
% 10.00/2.04 | (21) unordered_pair(all_18_9, all_18_8) = all_18_4
% 10.00/2.04 | (22) unordered_pair(all_18_5, all_18_4) = all_18_3
% 10.00/2.04 | (23) unordered_pair(all_18_2, all_18_1) = all_18_0
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (2) with all_18_3, all_18_0, simplifying with (9),
% 10.00/2.04 | (15), (18) gives:
% 10.00/2.04 | (24) subset(all_18_0, all_18_3)
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (3) with all_18_7, all_18_2, simplifying with (12),
% 10.00/2.04 | (20) gives:
% 10.00/2.04 | (25) member(all_18_7, all_18_2)
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (5) with all_18_9, all_18_8, all_18_4, simplifying
% 10.00/2.04 | with (10), (11), (21) gives:
% 10.00/2.04 | (26) member(all_18_9, all_18_4)
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (5) with all_18_2, all_18_1, all_18_0, simplifying
% 10.00/2.04 | with (16), (17), (23) gives:
% 10.00/2.04 | (27) member(all_18_2, all_18_0)
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (4) with all_18_9, all_18_7, all_18_4, simplifying
% 10.00/2.04 | with (10), (12), (26) gives:
% 10.00/2.04 | (28) all_18_7 = all_18_9 | ~ (singleton(all_18_7) = all_18_4)
% 10.00/2.04 |
% 10.00/2.04 | GROUND_INST: instantiating (4) with all_18_7, all_18_9, all_18_5, simplifying
% 10.00/2.04 | with (10), (12), (19) gives:
% 10.00/2.05 | (29) all_18_7 = all_18_9 | ~ member(all_18_7, all_18_5)
% 10.00/2.05 |
% 10.00/2.05 | GROUND_INST: instantiating (6) with all_18_2, all_18_5, all_18_4, all_18_3,
% 10.00/2.05 | simplifying with (13), (14), (16), (22) gives:
% 10.00/2.05 | (30) all_18_2 = all_18_4 | all_18_2 = all_18_5 | ~ member(all_18_2,
% 10.00/2.05 | all_18_3)
% 10.00/2.05 |
% 10.00/2.05 | GROUND_INST: instantiating (1) with all_18_0, all_18_3, all_18_2, simplifying
% 10.00/2.05 | with (15), (16), (18), (24), (27) gives:
% 10.00/2.05 | (31) member(all_18_2, all_18_3)
% 10.00/2.05 |
% 10.00/2.05 | BETA: splitting (29) gives:
% 10.00/2.05 |
% 10.00/2.05 | Case 1:
% 10.00/2.05 | |
% 10.00/2.05 | | (32) ~ member(all_18_7, all_18_5)
% 10.00/2.05 | |
% 10.00/2.05 | | BETA: splitting (28) gives:
% 10.00/2.05 | |
% 10.00/2.05 | | Case 1:
% 10.00/2.05 | | |
% 10.00/2.05 | | | (33) ~ (singleton(all_18_7) = all_18_4)
% 10.00/2.05 | | |
% 10.00/2.05 | | | PRED_UNIFY: (25), (32) imply:
% 10.00/2.05 | | | (34) ~ (all_18_2 = all_18_5)
% 10.00/2.05 | | |
% 10.00/2.05 | | | PRED_UNIFY: (20), (33) imply:
% 10.00/2.05 | | | (35) ~ (all_18_2 = all_18_4)
% 10.00/2.05 | | |
% 10.00/2.05 | | | BETA: splitting (30) gives:
% 10.00/2.05 | | |
% 10.00/2.05 | | | Case 1:
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | (36) ~ member(all_18_2, all_18_3)
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | PRED_UNIFY: (31), (36) imply:
% 10.00/2.05 | | | | (37) $false
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | CLOSE: (37) is inconsistent.
% 10.00/2.05 | | | |
% 10.00/2.05 | | | Case 2:
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | (38) all_18_2 = all_18_4 | all_18_2 = all_18_5
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | BETA: splitting (38) gives:
% 10.00/2.05 | | | |
% 10.00/2.05 | | | | Case 1:
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | | (39) all_18_2 = all_18_4
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | | REDUCE: (35), (39) imply:
% 10.00/2.05 | | | | | (40) $false
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | | CLOSE: (40) is inconsistent.
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | Case 2:
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | | (41) all_18_2 = all_18_5
% 10.00/2.05 | | | | |
% 10.00/2.05 | | | | | REDUCE: (34), (41) imply:
% 10.00/2.05 | | | | | (42) $false
% 10.00/2.06 | | | | |
% 10.00/2.06 | | | | | CLOSE: (42) is inconsistent.
% 10.00/2.06 | | | | |
% 10.00/2.06 | | | | End of split
% 10.00/2.06 | | | |
% 10.00/2.06 | | | End of split
% 10.00/2.06 | | |
% 10.00/2.06 | | Case 2:
% 10.00/2.06 | | |
% 10.00/2.06 | | | (43) all_18_7 = all_18_9
% 10.00/2.06 | | |
% 10.00/2.06 | | | REDUCE: (8), (43) imply:
% 10.00/2.06 | | | (44) $false
% 10.00/2.06 | | |
% 10.00/2.06 | | | CLOSE: (44) is inconsistent.
% 10.00/2.06 | | |
% 10.00/2.06 | | End of split
% 10.00/2.06 | |
% 10.00/2.06 | Case 2:
% 10.00/2.06 | |
% 10.00/2.06 | | (45) all_18_7 = all_18_9
% 10.00/2.06 | |
% 10.00/2.06 | | REDUCE: (8), (45) imply:
% 10.00/2.06 | | (46) $false
% 10.00/2.06 | |
% 10.00/2.06 | | CLOSE: (46) is inconsistent.
% 10.00/2.06 | |
% 10.00/2.06 | End of split
% 10.00/2.06 |
% 10.00/2.06 End of proof
% 10.00/2.06 % SZS output end Proof for theBenchmark
% 10.00/2.06
% 10.00/2.06 1556ms
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