TSTP Solution File: SYN417+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 : 600s
% DateTime : Thu Jul 21 05:02:15 EDT 2022
% Result : Theorem 2.00s 1.20s
% Output : Proof 2.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN417+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 02:44:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.59 (ePrincess v.1.0)
% 0.54/0.59
% 0.54/0.59 (c) Philipp Rümmer, 2009-2015
% 0.54/0.59 (c) Peter Backeman, 2014-2015
% 0.54/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.59 Bug reports to peter@backeman.se
% 0.54/0.59
% 0.54/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.59
% 0.54/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.87 Prover 0: Preprocessing ...
% 1.32/0.96 Prover 0: Warning: ignoring some quantifiers
% 1.39/0.98 Prover 0: Constructing countermodel ...
% 1.69/1.08 Prover 0: gave up
% 1.69/1.08 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.69/1.10 Prover 1: Preprocessing ...
% 1.69/1.14 Prover 1: Constructing countermodel ...
% 2.00/1.19 Prover 1: proved (112ms)
% 2.00/1.20
% 2.00/1.20 No countermodel exists, formula is valid
% 2.00/1.20 % SZS status Theorem for theBenchmark
% 2.00/1.20
% 2.00/1.20 Generating proof ... found it (size 49)
% 2.48/1.41
% 2.48/1.41 % SZS output start Proof for theBenchmark
% 2.48/1.41 Assumed formulas after preprocessing and simplification:
% 2.48/1.41 | (0) ? [v0] : ? [v1] : ? [v2] : ( ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (g(v5) = v4) | ~ (g(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (f(v5) = v4) | ~ (f(v5) = v3)) & ((v2 = v0 & g(v1) = v0 & f(v0) = v1 & ! [v3] : ! [v4] : (v3 = v0 | ~ (f(v3) = v4) | ? [v5] : ( ~ (v5 = v3) & g(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (g(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & ~ (v5 = v3) & g(v5) = v6 & f(v6) = v5) | ( ~ (v5 = v3) & f(v4) = v5)))) | (v2 = v0 & g(v0) = v1 & f(v1) = v0 & ! [v3] : ! [v4] : (v3 = v0 | ~ (g(v3) = v4) | ? [v5] : ( ~ (v5 = v3) & f(v4) = v5)) & ! [v3] : ! [v4] : ( ~ (f(v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = v5 & ~ (v5 = v3) & g(v6) = v5 & f(v5) = v6) | ( ~ (v5 = v3) & g(v4) = v5))))))
% 2.48/1.43 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.48/1.43 | (1) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0)) & ((all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2)))))
% 2.48/1.44 |
% 2.48/1.44 | Applying alpha-rule on (1) yields:
% 2.48/1.44 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (g(v2) = v1) | ~ (g(v2) = v0))
% 2.48/1.44 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (f(v2) = v1) | ~ (f(v2) = v0))
% 2.48/1.44 | (4) (all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))) | (all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2))))
% 2.48/1.44 |
% 2.48/1.44 +-Applying beta-rule and splitting (4), into two cases.
% 2.48/1.44 |-Branch one:
% 2.48/1.44 | (5) all_0_0_0 = all_0_2_2 & g(all_0_1_1) = all_0_2_2 & f(all_0_2_2) = all_0_1_1 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))
% 2.81/1.45 |
% 2.81/1.45 | Applying alpha-rule on (5) yields:
% 2.81/1.45 | (6) f(all_0_2_2) = all_0_1_1
% 2.81/1.45 | (7) ! [v0] : ! [v1] : ( ~ (g(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v2) = v3 & f(v3) = v2) | ( ~ (v2 = v0) & f(v1) = v2)))
% 2.81/1.45 | (8) g(all_0_1_1) = all_0_2_2
% 2.81/1.45 | (9) all_0_0_0 = all_0_2_2
% 2.81/1.45 | (10) ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (f(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & g(v1) = v2))
% 2.81/1.45 |
% 2.81/1.45 | Instantiating formula (7) with all_0_2_2, all_0_1_1 and discharging atoms g(all_0_1_1) = all_0_2_2, yields:
% 2.81/1.45 | (11) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & ~ (v0 = all_0_1_1) & g(v0) = v1 & f(v1) = v0) | ( ~ (v0 = all_0_1_1) & f(all_0_2_2) = v0))
% 2.81/1.45 |
% 2.81/1.45 | Instantiating (11) with all_12_0_3, all_12_1_4, all_12_2_5 yields:
% 2.81/1.45 | (12) (all_12_0_3 = all_12_2_5 & ~ (all_12_2_5 = all_0_1_1) & g(all_12_2_5) = all_12_1_4 & f(all_12_1_4) = all_12_2_5) | ( ~ (all_12_2_5 = all_0_1_1) & f(all_0_2_2) = all_12_2_5)
% 2.81/1.45 |
% 2.81/1.45 +-Applying beta-rule and splitting (12), into two cases.
% 2.81/1.45 |-Branch one:
% 2.81/1.45 | (13) all_12_0_3 = all_12_2_5 & ~ (all_12_2_5 = all_0_1_1) & g(all_12_2_5) = all_12_1_4 & f(all_12_1_4) = all_12_2_5
% 2.81/1.45 |
% 2.81/1.45 | Applying alpha-rule on (13) yields:
% 2.81/1.45 | (14) all_12_0_3 = all_12_2_5
% 2.81/1.45 | (15) ~ (all_12_2_5 = all_0_1_1)
% 2.81/1.45 | (16) g(all_12_2_5) = all_12_1_4
% 2.81/1.45 | (17) f(all_12_1_4) = all_12_2_5
% 2.81/1.45 |
% 2.81/1.45 | Instantiating formula (3) with all_0_2_2, all_12_2_5, all_0_1_1 and discharging atoms f(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.45 | (18) all_12_2_5 = all_0_1_1 | ~ (f(all_0_2_2) = all_12_2_5)
% 2.81/1.45 |
% 2.81/1.45 | Instantiating formula (10) with all_12_2_5, all_12_1_4 and discharging atoms f(all_12_1_4) = all_12_2_5, yields:
% 2.81/1.45 | (19) all_12_1_4 = all_0_2_2 | ? [v0] : ( ~ (v0 = all_12_1_4) & g(all_12_2_5) = v0)
% 2.81/1.45 |
% 2.81/1.45 +-Applying beta-rule and splitting (18), into two cases.
% 2.81/1.45 |-Branch one:
% 2.81/1.45 | (20) ~ (f(all_0_2_2) = all_12_2_5)
% 2.81/1.45 |
% 2.81/1.45 +-Applying beta-rule and splitting (19), into two cases.
% 2.81/1.45 |-Branch one:
% 2.81/1.45 | (21) all_12_1_4 = all_0_2_2
% 2.81/1.45 |
% 2.81/1.45 | From (21) and (17) follows:
% 2.81/1.45 | (22) f(all_0_2_2) = all_12_2_5
% 2.81/1.45 |
% 2.81/1.45 | Using (22) and (20) yields:
% 2.81/1.45 | (23) $false
% 2.81/1.45 |
% 2.81/1.45 |-The branch is then unsatisfiable
% 2.81/1.45 |-Branch two:
% 2.81/1.45 | (24) ~ (all_12_1_4 = all_0_2_2)
% 2.81/1.45 | (25) ? [v0] : ( ~ (v0 = all_12_1_4) & g(all_12_2_5) = v0)
% 2.81/1.46 |
% 2.81/1.46 | Instantiating (25) with all_27_0_9 yields:
% 2.81/1.46 | (26) ~ (all_27_0_9 = all_12_1_4) & g(all_12_2_5) = all_27_0_9
% 2.81/1.46 |
% 2.81/1.46 | Applying alpha-rule on (26) yields:
% 2.81/1.46 | (27) ~ (all_27_0_9 = all_12_1_4)
% 2.81/1.46 | (28) g(all_12_2_5) = all_27_0_9
% 2.81/1.46 |
% 2.81/1.46 | Instantiating formula (2) with all_12_2_5, all_27_0_9, all_12_1_4 and discharging atoms g(all_12_2_5) = all_27_0_9, g(all_12_2_5) = all_12_1_4, yields:
% 2.81/1.46 | (29) all_27_0_9 = all_12_1_4
% 2.81/1.46 |
% 2.81/1.46 | Equations (29) can reduce 27 to:
% 2.81/1.46 | (30) $false
% 2.81/1.46 |
% 2.81/1.46 |-The branch is then unsatisfiable
% 2.81/1.46 |-Branch two:
% 2.81/1.46 | (22) f(all_0_2_2) = all_12_2_5
% 2.81/1.46 | (32) all_12_2_5 = all_0_1_1
% 2.81/1.46 |
% 2.81/1.46 | Equations (32) can reduce 15 to:
% 2.81/1.46 | (30) $false
% 2.81/1.46 |
% 2.81/1.46 |-The branch is then unsatisfiable
% 2.81/1.46 |-Branch two:
% 2.81/1.46 | (34) ~ (all_12_2_5 = all_0_1_1) & f(all_0_2_2) = all_12_2_5
% 2.81/1.46 |
% 2.81/1.46 | Applying alpha-rule on (34) yields:
% 2.81/1.46 | (15) ~ (all_12_2_5 = all_0_1_1)
% 2.81/1.46 | (22) f(all_0_2_2) = all_12_2_5
% 2.81/1.46 |
% 2.81/1.46 | Instantiating formula (3) with all_0_2_2, all_12_2_5, all_0_1_1 and discharging atoms f(all_0_2_2) = all_12_2_5, f(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.46 | (32) all_12_2_5 = all_0_1_1
% 2.81/1.46 |
% 2.81/1.46 | Equations (32) can reduce 15 to:
% 2.81/1.46 | (30) $false
% 2.81/1.46 |
% 2.81/1.46 |-The branch is then unsatisfiable
% 2.81/1.46 |-Branch two:
% 2.81/1.46 | (39) all_0_0_0 = all_0_2_2 & g(all_0_2_2) = all_0_1_1 & f(all_0_1_1) = all_0_2_2 & ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2)))
% 2.81/1.46 |
% 2.81/1.46 | Applying alpha-rule on (39) yields:
% 2.81/1.46 | (40) ! [v0] : ! [v1] : ( ~ (f(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v2 & ~ (v2 = v0) & g(v3) = v2 & f(v2) = v3) | ( ~ (v2 = v0) & g(v1) = v2)))
% 2.81/1.46 | (9) all_0_0_0 = all_0_2_2
% 2.81/1.46 | (42) g(all_0_2_2) = all_0_1_1
% 2.81/1.46 | (43) ! [v0] : ! [v1] : (v0 = all_0_2_2 | ~ (g(v0) = v1) | ? [v2] : ( ~ (v2 = v0) & f(v1) = v2))
% 2.81/1.46 | (44) f(all_0_1_1) = all_0_2_2
% 2.81/1.46 |
% 2.81/1.46 | Instantiating formula (40) with all_0_2_2, all_0_1_1 and discharging atoms f(all_0_1_1) = all_0_2_2, yields:
% 2.81/1.46 | (45) ? [v0] : ? [v1] : ? [v2] : ((v2 = v0 & ~ (v0 = all_0_1_1) & g(v1) = v0 & f(v0) = v1) | ( ~ (v0 = all_0_1_1) & g(all_0_2_2) = v0))
% 2.81/1.46 |
% 2.81/1.46 | Instantiating (45) with all_12_0_10, all_12_1_11, all_12_2_12 yields:
% 2.81/1.46 | (46) (all_12_0_10 = all_12_2_12 & ~ (all_12_2_12 = all_0_1_1) & g(all_12_1_11) = all_12_2_12 & f(all_12_2_12) = all_12_1_11) | ( ~ (all_12_2_12 = all_0_1_1) & g(all_0_2_2) = all_12_2_12)
% 2.81/1.46 |
% 2.81/1.46 +-Applying beta-rule and splitting (46), into two cases.
% 2.81/1.46 |-Branch one:
% 2.81/1.46 | (47) all_12_0_10 = all_12_2_12 & ~ (all_12_2_12 = all_0_1_1) & g(all_12_1_11) = all_12_2_12 & f(all_12_2_12) = all_12_1_11
% 2.81/1.46 |
% 2.81/1.46 | Applying alpha-rule on (47) yields:
% 2.81/1.46 | (48) all_12_0_10 = all_12_2_12
% 2.81/1.46 | (49) ~ (all_12_2_12 = all_0_1_1)
% 2.81/1.46 | (50) g(all_12_1_11) = all_12_2_12
% 2.81/1.46 | (51) f(all_12_2_12) = all_12_1_11
% 2.81/1.46 |
% 2.81/1.46 | Instantiating formula (2) with all_0_2_2, all_12_2_12, all_0_1_1 and discharging atoms g(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.46 | (52) all_12_2_12 = all_0_1_1 | ~ (g(all_0_2_2) = all_12_2_12)
% 2.81/1.46 |
% 2.81/1.46 | Instantiating formula (43) with all_12_2_12, all_12_1_11 and discharging atoms g(all_12_1_11) = all_12_2_12, yields:
% 2.81/1.46 | (53) all_12_1_11 = all_0_2_2 | ? [v0] : ( ~ (v0 = all_12_1_11) & f(all_12_2_12) = v0)
% 2.81/1.46 |
% 2.81/1.46 +-Applying beta-rule and splitting (52), into two cases.
% 2.81/1.46 |-Branch one:
% 2.81/1.46 | (54) ~ (g(all_0_2_2) = all_12_2_12)
% 2.81/1.46 |
% 2.81/1.46 +-Applying beta-rule and splitting (53), into two cases.
% 2.81/1.46 |-Branch one:
% 2.81/1.46 | (55) all_12_1_11 = all_0_2_2
% 2.81/1.47 |
% 2.81/1.47 | From (55) and (50) follows:
% 2.81/1.47 | (56) g(all_0_2_2) = all_12_2_12
% 2.81/1.47 |
% 2.81/1.47 | Using (56) and (54) yields:
% 2.81/1.47 | (23) $false
% 2.81/1.47 |
% 2.81/1.47 |-The branch is then unsatisfiable
% 2.81/1.47 |-Branch two:
% 2.81/1.47 | (58) ~ (all_12_1_11 = all_0_2_2)
% 2.81/1.47 | (59) ? [v0] : ( ~ (v0 = all_12_1_11) & f(all_12_2_12) = v0)
% 2.81/1.47 |
% 2.81/1.47 | Instantiating (59) with all_27_0_16 yields:
% 2.81/1.47 | (60) ~ (all_27_0_16 = all_12_1_11) & f(all_12_2_12) = all_27_0_16
% 2.81/1.47 |
% 2.81/1.47 | Applying alpha-rule on (60) yields:
% 2.81/1.47 | (61) ~ (all_27_0_16 = all_12_1_11)
% 2.81/1.47 | (62) f(all_12_2_12) = all_27_0_16
% 2.81/1.47 |
% 2.81/1.47 | Instantiating formula (3) with all_12_2_12, all_27_0_16, all_12_1_11 and discharging atoms f(all_12_2_12) = all_27_0_16, f(all_12_2_12) = all_12_1_11, yields:
% 2.81/1.47 | (63) all_27_0_16 = all_12_1_11
% 2.81/1.47 |
% 2.81/1.47 | Equations (63) can reduce 61 to:
% 2.81/1.47 | (30) $false
% 2.81/1.47 |
% 2.81/1.47 |-The branch is then unsatisfiable
% 2.81/1.47 |-Branch two:
% 2.81/1.47 | (56) g(all_0_2_2) = all_12_2_12
% 2.81/1.47 | (66) all_12_2_12 = all_0_1_1
% 2.81/1.47 |
% 2.81/1.47 | Equations (66) can reduce 49 to:
% 2.81/1.47 | (30) $false
% 2.81/1.47 |
% 2.81/1.47 |-The branch is then unsatisfiable
% 2.81/1.47 |-Branch two:
% 2.81/1.47 | (68) ~ (all_12_2_12 = all_0_1_1) & g(all_0_2_2) = all_12_2_12
% 2.81/1.47 |
% 2.81/1.47 | Applying alpha-rule on (68) yields:
% 2.81/1.47 | (49) ~ (all_12_2_12 = all_0_1_1)
% 2.81/1.47 | (56) g(all_0_2_2) = all_12_2_12
% 2.81/1.47 |
% 2.81/1.47 | Instantiating formula (2) with all_0_2_2, all_12_2_12, all_0_1_1 and discharging atoms g(all_0_2_2) = all_12_2_12, g(all_0_2_2) = all_0_1_1, yields:
% 2.81/1.47 | (66) all_12_2_12 = all_0_1_1
% 2.81/1.47 |
% 2.81/1.47 | Equations (66) can reduce 49 to:
% 2.81/1.47 | (30) $false
% 2.81/1.47 |
% 2.81/1.47 |-The branch is then unsatisfiable
% 2.81/1.47 % SZS output end Proof for theBenchmark
% 2.81/1.47
% 2.81/1.47 873ms
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