TSTP Solution File: GEG025_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEG025_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%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  : 300s
% DateTime : Wed Aug 30 22:40:40 EDT 2023

% Result   : Theorem 12.24s 2.36s
% Output   : Proof 22.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEG025_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33  % Computer : n024.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Mon Aug 28 00:58:53 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.18/0.60  ________       _____
% 0.18/0.60  ___  __ \_________(_)________________________________
% 0.18/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60  
% 0.18/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60  (2023-06-19)
% 0.18/0.60  
% 0.18/0.60  (c) Philipp Rümmer, 2009-2023
% 0.18/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60                Amanda Stjerna.
% 0.18/0.60  Free software under BSD-3-Clause.
% 0.18/0.60  
% 0.18/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60  
% 0.18/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61  Running up to 7 provers in parallel.
% 0.18/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.02/1.03  Prover 1: Preprocessing ...
% 2.02/1.03  Prover 4: Preprocessing ...
% 2.61/1.08  Prover 3: Preprocessing ...
% 2.61/1.08  Prover 0: Preprocessing ...
% 2.61/1.08  Prover 5: Preprocessing ...
% 2.61/1.08  Prover 6: Preprocessing ...
% 2.61/1.08  Prover 2: Preprocessing ...
% 3.88/1.24  Prover 1: Constructing countermodel ...
% 3.88/1.24  Prover 6: Proving ...
% 3.88/1.24  Prover 3: Constructing countermodel ...
% 4.17/1.25  Prover 4: Constructing countermodel ...
% 4.17/1.27  Prover 0: Proving ...
% 4.17/1.30  Prover 5: Proving ...
% 4.17/1.31  Prover 2: Proving ...
% 12.24/2.36  Prover 3: proved (1738ms)
% 12.24/2.36  
% 12.24/2.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.24/2.36  
% 12.24/2.36  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.24/2.36  Prover 2: stopped
% 12.24/2.36  Prover 5: stopped
% 12.24/2.36  Prover 0: stopped
% 12.45/2.40  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.45/2.40  Prover 6: stopped
% 12.45/2.40  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.45/2.40  Prover 8: Preprocessing ...
% 12.45/2.40  Prover 7: Preprocessing ...
% 12.45/2.40  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.45/2.40  Prover 10: Preprocessing ...
% 12.45/2.40  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.45/2.41  Prover 8: Warning: ignoring some quantifiers
% 12.45/2.41  Prover 8: Constructing countermodel ...
% 12.88/2.42  Prover 13: Preprocessing ...
% 12.88/2.43  Prover 7: Constructing countermodel ...
% 12.88/2.43  Prover 11: Preprocessing ...
% 12.88/2.43  Prover 10: Constructing countermodel ...
% 13.13/2.48  Prover 11: Constructing countermodel ...
% 13.13/2.48  Prover 13: Warning: ignoring some quantifiers
% 13.13/2.49  Prover 13: Constructing countermodel ...
% 21.65/3.61  Prover 1: Found proof (size 209)
% 21.65/3.61  Prover 1: proved (2988ms)
% 21.65/3.61  Prover 10: stopped
% 21.65/3.61  Prover 8: stopped
% 21.65/3.61  Prover 13: stopped
% 21.65/3.61  Prover 11: stopped
% 21.65/3.61  Prover 7: stopped
% 21.65/3.61  Prover 4: stopped
% 21.65/3.61  
% 21.65/3.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.65/3.61  
% 22.20/3.67  % SZS output start Proof for theBenchmark
% 22.20/3.67  Assumptions after simplification:
% 22.20/3.67  ---------------------------------
% 22.20/3.67  
% 22.20/3.67    (exists_big_city_distance_2)
% 22.33/3.69    inh(munich) = 1330440 & inh(saarbruecken) = 175810 & inh(frankfurt) = 671927 &
% 22.33/3.69    inh(cologne) = 998105 & inh(berlin) = 3442675 & inh(hamburg) = 1774224 &
% 22.33/3.69    inh(kiel) = 238281 & d(munich, saarbruecken) = 360 & d(munich, frankfurt) =
% 22.33/3.69    300 & d(saarbruecken, frankfurt) = 160 & d(saarbruecken, cologne) = 190 &
% 22.33/3.69    d(cologne, frankfurt) = 150 & d(berlin, munich) = 510 & d(berlin, frankfurt) =
% 22.33/3.69    420 & d(berlin, cologne) = 480 & d(hamburg, frankfurt) = 390 & d(hamburg,
% 22.33/3.69      cologne) = 360 & d(hamburg, berlin) = 250 & d(hamburg, kiel) = 90 &
% 22.33/3.69    city(munich) & city(saarbruecken) & city(frankfurt) & city(cologne) &
% 22.33/3.69    city(berlin) & city(hamburg) & city(kiel) &  ! [v0: city] :  ! [v1: city] :  !
% 22.33/3.69    [v2: city] :  ! [v3: int] :  ! [v4: int] : ( ~ (d(v0, v2) = v4) |  ~ (d(v0,
% 22.33/3.69          v1) = v3) |  ~ city(v2) |  ~ city(v1) |  ~ city(v0) |  ? [v5: int] :
% 22.33/3.69      ($lesseq(0, $sum($difference(v5, v4), v3)) & d(v1, v2) = v5)) &  ! [v0:
% 22.33/3.69      city] :  ! [v1: city] :  ! [v2: int] : ( ~ (d(v0, v1) = v2) |  ~ city(v1) | 
% 22.33/3.69      ~ city(v0) | d(v1, v0) = v2) &  ! [v0: city] :  ! [v1: int] : (v1 = 0 |  ~
% 22.33/3.69      (d(v0, v0) = v1) |  ~ city(v0)) &  ! [v0: city] :  ! [v1: int] : ( ~
% 22.33/3.69      ($lesseq(v1, 600)) |  ~ (d(saarbruecken, v0) = v1) |  ~ city(v0) |  ? [v2:
% 22.33/3.69        int] : ($lesseq(v2, 2999999) & inh(v0) = v2))
% 22.33/3.69  
% 22.33/3.69    (function-axioms)
% 22.33/3.69     ! [v0: int] :  ! [v1: int] :  ! [v2: city] :  ! [v3: city] : (v1 = v0 |  ~
% 22.33/3.69      (d(v3, v2) = v1) |  ~ (d(v3, v2) = v0)) &  ! [v0: int] :  ! [v1: int] :  !
% 22.33/3.69    [v2: city] : (v1 = v0 |  ~ (inh(v2) = v1) |  ~ (inh(v2) = v0))
% 22.33/3.69  
% 22.33/3.69  Those formulas are unsatisfiable:
% 22.33/3.69  ---------------------------------
% 22.33/3.69  
% 22.33/3.69  Begin of proof
% 22.33/3.69  | 
% 22.33/3.69  | ALPHA: (exists_big_city_distance_2) implies:
% 22.33/3.69  |   (1)  city(kiel)
% 22.33/3.69  |   (2)  city(hamburg)
% 22.33/3.69  |   (3)  city(berlin)
% 22.33/3.69  |   (4)  city(cologne)
% 22.33/3.69  |   (5)  city(frankfurt)
% 22.33/3.70  |   (6)  city(saarbruecken)
% 22.33/3.70  |   (7)  city(munich)
% 22.33/3.70  |   (8)  d(hamburg, kiel) = 90
% 22.33/3.70  |   (9)  d(hamburg, berlin) = 250
% 22.33/3.70  |   (10)  d(hamburg, cologne) = 360
% 22.33/3.70  |   (11)  d(hamburg, frankfurt) = 390
% 22.33/3.70  |   (12)  d(berlin, cologne) = 480
% 22.33/3.70  |   (13)  d(berlin, frankfurt) = 420
% 22.33/3.70  |   (14)  d(berlin, munich) = 510
% 22.33/3.70  |   (15)  d(cologne, frankfurt) = 150
% 22.33/3.70  |   (16)  d(saarbruecken, cologne) = 190
% 22.33/3.70  |   (17)  d(saarbruecken, frankfurt) = 160
% 22.33/3.70  |   (18)  d(munich, frankfurt) = 300
% 22.33/3.70  |   (19)  d(munich, saarbruecken) = 360
% 22.33/3.70  |   (20)  inh(berlin) = 3442675
% 22.33/3.70  |   (21)   ! [v0: city] :  ! [v1: int] : ( ~ ($lesseq(v1, 600)) |  ~
% 22.33/3.70  |           (d(saarbruecken, v0) = v1) |  ~ city(v0) |  ? [v2: int] :
% 22.33/3.70  |           ($lesseq(v2, 2999999) & inh(v0) = v2))
% 22.33/3.70  |   (22)   ! [v0: city] :  ! [v1: city] :  ! [v2: int] : ( ~ (d(v0, v1) = v2) | 
% 22.33/3.70  |           ~ city(v1) |  ~ city(v0) | d(v1, v0) = v2)
% 22.33/3.70  |   (23)   ! [v0: city] :  ! [v1: city] :  ! [v2: city] :  ! [v3: int] :  ! [v4:
% 22.33/3.70  |           int] : ( ~ (d(v0, v2) = v4) |  ~ (d(v0, v1) = v3) |  ~ city(v2) |  ~
% 22.33/3.70  |           city(v1) |  ~ city(v0) |  ? [v5: int] : ($lesseq(0,
% 22.33/3.70  |               $sum($difference(v5, v4), v3)) & d(v1, v2) = v5))
% 22.33/3.70  | 
% 22.33/3.70  | ALPHA: (function-axioms) implies:
% 22.33/3.70  |   (24)   ! [v0: int] :  ! [v1: int] :  ! [v2: city] : (v1 = v0 |  ~ (inh(v2) =
% 22.33/3.70  |             v1) |  ~ (inh(v2) = v0))
% 22.33/3.70  |   (25)   ! [v0: int] :  ! [v1: int] :  ! [v2: city] :  ! [v3: city] : (v1 = v0
% 22.33/3.70  |           |  ~ (d(v3, v2) = v1) |  ~ (d(v3, v2) = v0))
% 22.33/3.70  | 
% 22.33/3.70  | GROUND_INST: instantiating (22) with hamburg, kiel, 90, simplifying with (1),
% 22.33/3.70  |              (2), (8) gives:
% 22.33/3.70  |   (26)  d(kiel, hamburg) = 90
% 22.33/3.70  | 
% 22.33/3.70  | GROUND_INST: instantiating (23) with hamburg, berlin, berlin, 250, 250,
% 22.33/3.71  |              simplifying with (2), (3), (9) gives:
% 22.33/3.71  |   (27)   ? [v0: int] : ($lesseq(0, v0) & d(berlin, berlin) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, kiel, berlin, 90, 250,
% 22.33/3.71  |              simplifying with (1), (2), (3), (8), (9) gives:
% 22.33/3.71  |   (28)   ? [v0: int] : ($lesseq(160, v0) & d(kiel, berlin) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, berlin, kiel, 250, 90,
% 22.33/3.71  |              simplifying with (1), (2), (3), (8), (9) gives:
% 22.33/3.71  |   (29)   ? [v0: int] : ($lesseq(-160, v0) & d(berlin, kiel) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with hamburg, berlin, 250, simplifying with
% 22.33/3.71  |              (2), (3), (9) gives:
% 22.33/3.71  |   (30)  d(berlin, hamburg) = 250
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, cologne, berlin, 360, 250,
% 22.33/3.71  |              simplifying with (2), (3), (4), (9), (10) gives:
% 22.33/3.71  |   (31)   ? [v0: int] : ($lesseq(-110, v0) & d(cologne, berlin) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, cologne, kiel, 360, 90,
% 22.33/3.71  |              simplifying with (1), (2), (4), (8), (10) gives:
% 22.33/3.71  |   (32)   ? [v0: int] : ($lesseq(-270, v0) & d(cologne, kiel) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with hamburg, cologne, 360, simplifying with
% 22.33/3.71  |              (2), (4), (10) gives:
% 22.33/3.71  |   (33)  d(cologne, hamburg) = 360
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, frankfurt, berlin, 390, 250,
% 22.33/3.71  |              simplifying with (2), (3), (5), (9), (11) gives:
% 22.33/3.71  |   (34)   ? [v0: int] : ($lesseq(-140, v0) & d(frankfurt, berlin) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, kiel, frankfurt, 90, 390,
% 22.33/3.71  |              simplifying with (1), (2), (5), (8), (11) gives:
% 22.33/3.71  |   (35)   ? [v0: int] : ($lesseq(300, v0) & d(kiel, frankfurt) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (23) with hamburg, frankfurt, kiel, 390, 90,
% 22.33/3.71  |              simplifying with (1), (2), (5), (8), (11) gives:
% 22.33/3.71  |   (36)   ? [v0: int] : ($lesseq(-300, v0) & d(frankfurt, kiel) = v0)
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with hamburg, frankfurt, 390, simplifying with
% 22.33/3.71  |              (2), (5), (11) gives:
% 22.33/3.71  |   (37)  d(frankfurt, hamburg) = 390
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with berlin, cologne, 480, simplifying with
% 22.33/3.71  |              (3), (4), (12) gives:
% 22.33/3.71  |   (38)  d(cologne, berlin) = 480
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with berlin, frankfurt, 420, simplifying with
% 22.33/3.71  |              (3), (5), (13) gives:
% 22.33/3.71  |   (39)  d(frankfurt, berlin) = 420
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with berlin, munich, 510, simplifying with
% 22.33/3.71  |              (3), (7), (14) gives:
% 22.33/3.71  |   (40)  d(munich, berlin) = 510
% 22.33/3.71  | 
% 22.33/3.71  | GROUND_INST: instantiating (22) with saarbruecken, cologne, 190, simplifying
% 22.33/3.71  |              with (4), (6), (16) gives:
% 22.33/3.71  |   (41)  d(cologne, saarbruecken) = 190
% 22.33/3.71  | 
% 22.33/3.72  | GROUND_INST: instantiating (22) with saarbruecken, frankfurt, 160, simplifying
% 22.33/3.72  |              with (5), (6), (17) gives:
% 22.33/3.72  |   (42)  d(frankfurt, saarbruecken) = 160
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (23) with munich, frankfurt, frankfurt, 300, 300,
% 22.33/3.72  |              simplifying with (5), (7), (18) gives:
% 22.33/3.72  |   (43)   ? [v0: int] : ($lesseq(0, v0) & d(frankfurt, frankfurt) = v0)
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (23) with munich, saarbruecken, saarbruecken, 360,
% 22.33/3.72  |              360, simplifying with (6), (7), (19) gives:
% 22.33/3.72  |   (44)   ? [v0: int] : ($lesseq(0, v0) & d(saarbruecken, saarbruecken) = v0)
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (23) with munich, frankfurt, saarbruecken, 300,
% 22.33/3.72  |              360, simplifying with (5), (6), (7), (18), (19) gives:
% 22.33/3.72  |   (45)   ? [v0: int] : ($lesseq(60, v0) & d(frankfurt, saarbruecken) = v0)
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (32) with fresh symbol all_13_0 gives:
% 22.33/3.72  |   (46)  $lesseq(-270, all_13_0) & d(cologne, kiel) = all_13_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (46) implies:
% 22.33/3.72  |   (47)  d(cologne, kiel) = all_13_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (29) with fresh symbol all_19_0 gives:
% 22.33/3.72  |   (48)  $lesseq(-160, all_19_0) & d(berlin, kiel) = all_19_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (48) implies:
% 22.33/3.72  |   (49)  d(berlin, kiel) = all_19_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (31) with fresh symbol all_22_0 gives:
% 22.33/3.72  |   (50)  $lesseq(-110, all_22_0) & d(cologne, berlin) = all_22_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (50) implies:
% 22.33/3.72  |   (51)  d(cologne, berlin) = all_22_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (45) with fresh symbol all_31_0 gives:
% 22.33/3.72  |   (52)  $lesseq(60, all_31_0) & d(frankfurt, saarbruecken) = all_31_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (52) implies:
% 22.33/3.72  |   (53)  d(frankfurt, saarbruecken) = all_31_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (36) with fresh symbol all_34_0 gives:
% 22.33/3.72  |   (54)  $lesseq(-300, all_34_0) & d(frankfurt, kiel) = all_34_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (54) implies:
% 22.33/3.72  |   (55)  d(frankfurt, kiel) = all_34_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (35) with fresh symbol all_37_0 gives:
% 22.33/3.72  |   (56)  $lesseq(300, all_37_0) & d(kiel, frankfurt) = all_37_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (56) implies:
% 22.33/3.72  |   (57)  d(kiel, frankfurt) = all_37_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (43) with fresh symbol all_40_0 gives:
% 22.33/3.72  |   (58)  $lesseq(0, all_40_0) & d(frankfurt, frankfurt) = all_40_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (58) implies:
% 22.33/3.72  |   (59)  d(frankfurt, frankfurt) = all_40_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (34) with fresh symbol all_43_0 gives:
% 22.33/3.72  |   (60)  $lesseq(-140, all_43_0) & d(frankfurt, berlin) = all_43_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (60) implies:
% 22.33/3.72  |   (61)  d(frankfurt, berlin) = all_43_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (44) with fresh symbol all_49_0 gives:
% 22.33/3.72  |   (62)  $lesseq(0, all_49_0) & d(saarbruecken, saarbruecken) = all_49_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (62) implies:
% 22.33/3.72  |   (63)  d(saarbruecken, saarbruecken) = all_49_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (28) with fresh symbol all_55_0 gives:
% 22.33/3.72  |   (64)  $lesseq(160, all_55_0) & d(kiel, berlin) = all_55_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (64) implies:
% 22.33/3.72  |   (65)  d(kiel, berlin) = all_55_0
% 22.33/3.72  | 
% 22.33/3.72  | DELTA: instantiating (27) with fresh symbol all_58_0 gives:
% 22.33/3.72  |   (66)  $lesseq(0, all_58_0) & d(berlin, berlin) = all_58_0
% 22.33/3.72  | 
% 22.33/3.72  | ALPHA: (66) implies:
% 22.33/3.72  |   (67)  d(berlin, berlin) = all_58_0
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (25) with 480, all_22_0, berlin, cologne,
% 22.33/3.72  |              simplifying with (38), (51) gives:
% 22.33/3.72  |   (68)  all_22_0 = 480
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (25) with 420, all_43_0, berlin, frankfurt,
% 22.33/3.72  |              simplifying with (39), (61) gives:
% 22.33/3.72  |   (69)  all_43_0 = 420
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (25) with 160, all_31_0, saarbruecken, frankfurt,
% 22.33/3.72  |              simplifying with (42), (53) gives:
% 22.33/3.72  |   (70)  all_31_0 = 160
% 22.33/3.72  | 
% 22.33/3.72  | GROUND_INST: instantiating (23) with kiel, hamburg, berlin, 90, all_55_0,
% 22.33/3.72  |              simplifying with (1), (2), (3), (26), (65) gives:
% 22.33/3.72  |   (71)   ? [v0: int] : ($lesseq(-90, $difference(v0, all_55_0)) & d(hamburg,
% 22.33/3.72  |             berlin) = v0)
% 22.33/3.72  | 
% 22.33/3.73  | GROUND_INST: instantiating (23) with kiel, berlin, frankfurt, all_55_0,
% 22.33/3.73  |              all_37_0, simplifying with (1), (3), (5), (57), (65) gives:
% 22.33/3.73  |   (72)   ? [v0: int] : ($lesseq(all_37_0, $sum(v0, all_55_0)) & d(berlin,
% 22.33/3.73  |             frankfurt) = v0)
% 22.33/3.73  | 
% 22.33/3.73  | GROUND_INST: instantiating (23) with kiel, hamburg, frankfurt, 90, all_37_0,
% 22.33/3.73  |              simplifying with (1), (2), (5), (26), (57) gives:
% 22.53/3.73  |   (73)   ? [v0: int] : ($lesseq(-90, $difference(v0, all_37_0)) & d(hamburg,
% 22.53/3.73  |             frankfurt) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with berlin, kiel, frankfurt, all_19_0, 420,
% 22.53/3.73  |              simplifying with (1), (3), (5), (13), (49) gives:
% 22.53/3.73  |   (74)   ? [v0: int] : ($lesseq(420, $sum(v0, all_19_0)) & d(kiel, frankfurt)
% 22.53/3.73  |           = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (22) with berlin, kiel, all_19_0, simplifying with
% 22.53/3.73  |              (1), (3), (49) gives:
% 22.53/3.73  |   (75)  d(kiel, berlin) = all_19_0
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with berlin, hamburg, berlin, 250, all_58_0,
% 22.53/3.73  |              simplifying with (2), (3), (30), (67) gives:
% 22.53/3.73  |   (76)   ? [v0: int] : ($lesseq(-250, $difference(v0, all_58_0)) & d(hamburg,
% 22.53/3.73  |             berlin) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with berlin, kiel, berlin, all_19_0, all_58_0,
% 22.53/3.73  |              simplifying with (1), (3), (49), (67) gives:
% 22.53/3.73  |   (77)   ? [v0: int] : ($lesseq(0, $sum($difference(v0, all_58_0), all_19_0))
% 22.53/3.73  |           & d(kiel, berlin) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, kiel, frankfurt, all_13_0, 150,
% 22.53/3.73  |              simplifying with (1), (4), (5), (15), (47) gives:
% 22.53/3.73  |   (78)   ? [v0: int] : ($lesseq(150, $sum(v0, all_13_0)) & d(kiel, frankfurt)
% 22.53/3.73  |           = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, kiel, berlin, all_13_0, 480,
% 22.53/3.73  |              simplifying with (1), (3), (4), (38), (47) gives:
% 22.53/3.73  |   (79)   ? [v0: int] : ($lesseq(480, $sum(v0, all_13_0)) & d(kiel, berlin) =
% 22.53/3.73  |           v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, berlin, saarbruecken, 480, 190,
% 22.53/3.73  |              simplifying with (3), (4), (6), (38), (41) gives:
% 22.53/3.73  |   (80)   ? [v0: int] : ($lesseq(-290, v0) & d(berlin, saarbruecken) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, saarbruecken, berlin, 190, 480,
% 22.53/3.73  |              simplifying with (3), (4), (6), (38), (41) gives:
% 22.53/3.73  |   (81)   ? [v0: int] : ($lesseq(290, v0) & d(saarbruecken, berlin) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, hamburg, saarbruecken, 360, 190,
% 22.53/3.73  |              simplifying with (2), (4), (6), (33), (41) gives:
% 22.53/3.73  |   (82)   ? [v0: int] : ($lesseq(-170, v0) & d(hamburg, saarbruecken) = v0)
% 22.53/3.73  | 
% 22.53/3.73  | GROUND_INST: instantiating (23) with cologne, kiel, saarbruecken, all_13_0,
% 22.53/3.73  |              190, simplifying with (1), (4), (6), (41), (47) gives:
% 22.53/3.73  |   (83)   ? [v0: int] : ($lesseq(190, $sum(v0, all_13_0)) & d(kiel,
% 22.53/3.73  |             saarbruecken) = v0)
% 22.53/3.73  | 
% 22.53/3.74  | GROUND_INST: instantiating (22) with frankfurt, kiel, all_34_0, simplifying
% 22.53/3.74  |              with (1), (5), (55) gives:
% 22.53/3.74  |   (84)  d(kiel, frankfurt) = all_34_0
% 22.53/3.74  | 
% 22.53/3.74  | GROUND_INST: instantiating (23) with frankfurt, kiel, berlin, all_34_0, 420,
% 22.53/3.74  |              simplifying with (1), (3), (5), (39), (55) gives:
% 22.53/3.74  |   (85)   ? [v0: int] : ($lesseq(420, $sum(v0, all_34_0)) & d(kiel, berlin) =
% 22.53/3.74  |           v0)
% 22.53/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, berlin, frankfurt, 420,
% 22.58/3.74  |              all_40_0, simplifying with (3), (5), (39), (59) gives:
% 22.58/3.74  |   (86)   ? [v0: int] : ($lesseq(-420, $difference(v0, all_40_0)) & d(berlin,
% 22.58/3.74  |             frankfurt) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, hamburg, frankfurt, 390,
% 22.58/3.74  |              all_40_0, simplifying with (2), (5), (37), (59) gives:
% 22.58/3.74  |   (87)   ? [v0: int] : ($lesseq(-390, $difference(v0, all_40_0)) & d(hamburg,
% 22.58/3.74  |             frankfurt) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, kiel, frankfurt, all_34_0,
% 22.58/3.74  |              all_40_0, simplifying with (1), (5), (55), (59) gives:
% 22.58/3.74  |   (88)   ? [v0: int] : ($lesseq(0, $sum($difference(v0, all_40_0), all_34_0))
% 22.58/3.74  |           & d(kiel, frankfurt) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, berlin, saarbruecken, 420,
% 22.58/3.74  |              160, simplifying with (3), (5), (6), (39), (42) gives:
% 22.58/3.74  |   (89)   ? [v0: int] : ($lesseq(-260, v0) & d(berlin, saarbruecken) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, saarbruecken, berlin, 160,
% 22.58/3.74  |              420, simplifying with (3), (5), (6), (39), (42) gives:
% 22.58/3.74  |   (90)   ? [v0: int] : ($lesseq(260, v0) & d(saarbruecken, berlin) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, hamburg, saarbruecken, 390,
% 22.58/3.74  |              160, simplifying with (2), (5), (6), (37), (42) gives:
% 22.58/3.74  |   (91)   ? [v0: int] : ($lesseq(-230, v0) & d(hamburg, saarbruecken) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with frankfurt, kiel, saarbruecken, all_34_0,
% 22.58/3.74  |              160, simplifying with (1), (5), (6), (42), (55) gives:
% 22.58/3.74  |   (92)   ? [v0: int] : ($lesseq(160, $sum(v0, all_34_0)) & d(kiel,
% 22.58/3.74  |             saarbruecken) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with saarbruecken, frankfurt, saarbruecken,
% 22.58/3.74  |              160, all_49_0, simplifying with (5), (6), (17), (63) gives:
% 22.58/3.74  |   (93)   ? [v0: int] : ($lesseq(-160, $difference(v0, all_49_0)) &
% 22.58/3.74  |           d(frankfurt, saarbruecken) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with munich, saarbruecken, berlin, 360, 510,
% 22.58/3.74  |              simplifying with (3), (6), (7), (19), (40) gives:
% 22.58/3.74  |   (94)   ? [v0: int] : ($lesseq(150, v0) & d(saarbruecken, berlin) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | GROUND_INST: instantiating (23) with munich, berlin, saarbruecken, 510, 360,
% 22.58/3.74  |              simplifying with (3), (6), (7), (19), (40) gives:
% 22.58/3.74  |   (95)   ? [v0: int] : ($lesseq(-150, v0) & d(berlin, saarbruecken) = v0)
% 22.58/3.74  | 
% 22.58/3.74  | DELTA: instantiating (73) with fresh symbol all_106_0 gives:
% 22.58/3.75  |   (96)  $lesseq(-90, $difference(all_106_0, all_37_0)) & d(hamburg, frankfurt)
% 22.58/3.75  |         = all_106_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (96) implies:
% 22.58/3.75  |   (97)  d(hamburg, frankfurt) = all_106_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (72) with fresh symbol all_109_0 gives:
% 22.58/3.75  |   (98)  $lesseq(all_37_0, $sum(all_109_0, all_55_0)) & d(berlin, frankfurt) =
% 22.58/3.75  |         all_109_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (98) implies:
% 22.58/3.75  |   (99)  d(berlin, frankfurt) = all_109_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (77) with fresh symbol all_124_0 gives:
% 22.58/3.75  |   (100)  $lesseq(0, $sum($difference(all_124_0, all_58_0), all_19_0)) &
% 22.58/3.75  |          d(kiel, berlin) = all_124_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (100) implies:
% 22.58/3.75  |   (101)  d(kiel, berlin) = all_124_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (76) with fresh symbol all_127_0 gives:
% 22.58/3.75  |   (102)  $lesseq(-250, $difference(all_127_0, all_58_0)) & d(hamburg, berlin)
% 22.58/3.75  |          = all_127_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (102) implies:
% 22.58/3.75  |   (103)  d(hamburg, berlin) = all_127_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (78) with fresh symbol all_154_0 gives:
% 22.58/3.75  |   (104)  $lesseq(150, $sum(all_154_0, all_13_0)) & d(kiel, frankfurt) =
% 22.58/3.75  |          all_154_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (104) implies:
% 22.58/3.75  |   (105)  d(kiel, frankfurt) = all_154_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (94) with fresh symbol all_163_0 gives:
% 22.58/3.75  |   (106)  $lesseq(150, all_163_0) & d(saarbruecken, berlin) = all_163_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (106) implies:
% 22.58/3.75  |   (107)  d(saarbruecken, berlin) = all_163_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (90) with fresh symbol all_193_0 gives:
% 22.58/3.75  |   (108)  $lesseq(260, all_193_0) & d(saarbruecken, berlin) = all_193_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (108) implies:
% 22.58/3.75  |   (109)  d(saarbruecken, berlin) = all_193_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (89) with fresh symbol all_196_0 gives:
% 22.58/3.75  |   (110)  $lesseq(-260, all_196_0) & d(berlin, saarbruecken) = all_196_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (110) implies:
% 22.58/3.75  |   (111)  d(berlin, saarbruecken) = all_196_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (79) with fresh symbol all_199_0 gives:
% 22.58/3.75  |   (112)  $lesseq(480, $sum(all_199_0, all_13_0)) & d(kiel, berlin) = all_199_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (112) implies:
% 22.58/3.75  |   (113)  d(kiel, berlin) = all_199_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (91) with fresh symbol all_202_0 gives:
% 22.58/3.75  |   (114)  $lesseq(-230, all_202_0) & d(hamburg, saarbruecken) = all_202_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (114) implies:
% 22.58/3.75  |   (115)  d(hamburg, saarbruecken) = all_202_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (74) with fresh symbol all_208_0 gives:
% 22.58/3.75  |   (116)  $lesseq(420, $sum(all_208_0, all_19_0)) & d(kiel, frankfurt) =
% 22.58/3.75  |          all_208_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (116) implies:
% 22.58/3.75  |   (117)  d(kiel, frankfurt) = all_208_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (95) with fresh symbol all_223_0 gives:
% 22.58/3.75  |   (118)  $lesseq(-150, all_223_0) & d(berlin, saarbruecken) = all_223_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (118) implies:
% 22.58/3.75  |   (119)  d(berlin, saarbruecken) = all_223_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (71) with fresh symbol all_232_0 gives:
% 22.58/3.75  |   (120)  $lesseq(-90, $difference(all_232_0, all_55_0)) & d(hamburg, berlin) =
% 22.58/3.75  |          all_232_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (120) implies:
% 22.58/3.75  |   (121)  d(hamburg, berlin) = all_232_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (88) with fresh symbol all_262_0 gives:
% 22.58/3.75  |   (122)  $lesseq(0, $sum($difference(all_262_0, all_40_0), all_34_0)) &
% 22.58/3.75  |          d(kiel, frankfurt) = all_262_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (122) implies:
% 22.58/3.75  |   (123)  d(kiel, frankfurt) = all_262_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (86) with fresh symbol all_265_0 gives:
% 22.58/3.75  |   (124)  $lesseq(-420, $difference(all_265_0, all_40_0)) & d(berlin,
% 22.58/3.75  |            frankfurt) = all_265_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (124) implies:
% 22.58/3.75  |   (125)  d(berlin, frankfurt) = all_265_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (87) with fresh symbol all_277_0 gives:
% 22.58/3.75  |   (126)  $lesseq(-390, $difference(all_277_0, all_40_0)) & d(hamburg,
% 22.58/3.75  |            frankfurt) = all_277_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (126) implies:
% 22.58/3.75  |   (127)  d(hamburg, frankfurt) = all_277_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (85) with fresh symbol all_283_0 gives:
% 22.58/3.75  |   (128)  $lesseq(420, $sum(all_283_0, all_34_0)) & d(kiel, berlin) = all_283_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (128) implies:
% 22.58/3.75  |   (129)  d(kiel, berlin) = all_283_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (83) with fresh symbol all_292_0 gives:
% 22.58/3.75  |   (130)  $lesseq(190, $sum(all_292_0, all_13_0)) & d(kiel, saarbruecken) =
% 22.58/3.75  |          all_292_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (130) implies:
% 22.58/3.75  |   (131)  d(kiel, saarbruecken) = all_292_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (93) with fresh symbol all_325_0 gives:
% 22.58/3.75  |   (132)  $lesseq(-160, $difference(all_325_0, all_49_0)) & d(frankfurt,
% 22.58/3.75  |            saarbruecken) = all_325_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (132) implies:
% 22.58/3.75  |   (133)  d(frankfurt, saarbruecken) = all_325_0
% 22.58/3.75  | 
% 22.58/3.75  | DELTA: instantiating (92) with fresh symbol all_328_0 gives:
% 22.58/3.75  |   (134)  $lesseq(160, $sum(all_328_0, all_34_0)) & d(kiel, saarbruecken) =
% 22.58/3.75  |          all_328_0
% 22.58/3.75  | 
% 22.58/3.75  | ALPHA: (134) implies:
% 22.58/3.76  |   (135)  d(kiel, saarbruecken) = all_328_0
% 22.58/3.76  | 
% 22.58/3.76  | DELTA: instantiating (81) with fresh symbol all_343_0 gives:
% 22.58/3.76  |   (136)  $lesseq(290, all_343_0) & d(saarbruecken, berlin) = all_343_0
% 22.58/3.76  | 
% 22.58/3.76  | ALPHA: (136) implies:
% 22.58/3.76  |   (137)  d(saarbruecken, berlin) = all_343_0
% 22.58/3.76  | 
% 22.58/3.76  | DELTA: instantiating (80) with fresh symbol all_355_0 gives:
% 22.58/3.76  |   (138)  $lesseq(-290, all_355_0) & d(berlin, saarbruecken) = all_355_0
% 22.58/3.76  | 
% 22.58/3.76  | ALPHA: (138) implies:
% 22.58/3.76  |   (139)  d(berlin, saarbruecken) = all_355_0
% 22.58/3.76  | 
% 22.58/3.76  | DELTA: instantiating (82) with fresh symbol all_361_0 gives:
% 22.58/3.76  |   (140)  $lesseq(-170, all_361_0) & d(hamburg, saarbruecken) = all_361_0
% 22.58/3.76  | 
% 22.58/3.76  | ALPHA: (140) implies:
% 22.58/3.76  |   (141)  d(hamburg, saarbruecken) = all_361_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_55_0, all_199_0, berlin, kiel,
% 22.58/3.76  |              simplifying with (65), (113) gives:
% 22.58/3.76  |   (142)  all_199_0 = all_55_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_19_0, all_199_0, berlin, kiel,
% 22.58/3.76  |              simplifying with (75), (113) gives:
% 22.58/3.76  |   (143)  all_199_0 = all_19_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_199_0, all_283_0, berlin, kiel,
% 22.58/3.76  |              simplifying with (113), (129) gives:
% 22.58/3.76  |   (144)  all_283_0 = all_199_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_124_0, all_283_0, berlin, kiel,
% 22.58/3.76  |              simplifying with (101), (129) gives:
% 22.58/3.76  |   (145)  all_283_0 = all_124_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_37_0, all_154_0, frankfurt, kiel,
% 22.58/3.76  |              simplifying with (57), (105) gives:
% 22.58/3.76  |   (146)  all_154_0 = all_37_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_154_0, all_208_0, frankfurt, kiel,
% 22.58/3.76  |              simplifying with (105), (117) gives:
% 22.58/3.76  |   (147)  all_208_0 = all_154_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_208_0, all_262_0, frankfurt, kiel,
% 22.58/3.76  |              simplifying with (117), (123) gives:
% 22.58/3.76  |   (148)  all_262_0 = all_208_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_34_0, all_262_0, frankfurt, kiel,
% 22.58/3.76  |              simplifying with (84), (123) gives:
% 22.58/3.76  |   (149)  all_262_0 = all_34_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_292_0, all_328_0, saarbruecken, kiel,
% 22.58/3.76  |              simplifying with (131), (135) gives:
% 22.58/3.76  |   (150)  all_328_0 = all_292_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with 250, all_232_0, berlin, hamburg,
% 22.58/3.76  |              simplifying with (9), (121) gives:
% 22.58/3.76  |   (151)  all_232_0 = 250
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_127_0, all_232_0, berlin, hamburg,
% 22.58/3.76  |              simplifying with (103), (121) gives:
% 22.58/3.76  |   (152)  all_232_0 = all_127_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with 390, all_277_0, frankfurt, hamburg,
% 22.58/3.76  |              simplifying with (11), (127) gives:
% 22.58/3.76  |   (153)  all_277_0 = 390
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_106_0, all_277_0, frankfurt, hamburg,
% 22.58/3.76  |              simplifying with (97), (127) gives:
% 22.58/3.76  |   (154)  all_277_0 = all_106_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_202_0, all_361_0, saarbruecken,
% 22.58/3.76  |              hamburg, simplifying with (115), (141) gives:
% 22.58/3.76  |   (155)  all_361_0 = all_202_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with 420, all_265_0, frankfurt, berlin,
% 22.58/3.76  |              simplifying with (13), (125) gives:
% 22.58/3.76  |   (156)  all_265_0 = 420
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_109_0, all_265_0, frankfurt, berlin,
% 22.58/3.76  |              simplifying with (99), (125) gives:
% 22.58/3.76  |   (157)  all_265_0 = all_109_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_223_0, all_355_0, saarbruecken,
% 22.58/3.76  |              berlin, simplifying with (119), (139) gives:
% 22.58/3.76  |   (158)  all_355_0 = all_223_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_196_0, all_355_0, saarbruecken,
% 22.58/3.76  |              berlin, simplifying with (111), (139) gives:
% 22.58/3.76  |   (159)  all_355_0 = all_196_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with 160, all_325_0, saarbruecken, frankfurt,
% 22.58/3.76  |              simplifying with (42), (133) gives:
% 22.58/3.76  |   (160)  all_325_0 = 160
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_193_0, all_343_0, berlin,
% 22.58/3.76  |              saarbruecken, simplifying with (109), (137) gives:
% 22.58/3.76  |   (161)  all_343_0 = all_193_0
% 22.58/3.76  | 
% 22.58/3.76  | GROUND_INST: instantiating (25) with all_163_0, all_343_0, berlin,
% 22.58/3.76  |              saarbruecken, simplifying with (107), (137) gives:
% 22.58/3.77  |   (162)  all_343_0 = all_163_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (158), (159) imply:
% 22.58/3.77  |   (163)  all_223_0 = all_196_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (161), (162) imply:
% 22.58/3.77  |   (164)  all_193_0 = all_163_0
% 22.58/3.77  | 
% 22.58/3.77  | SIMP: (164) implies:
% 22.58/3.77  |   (165)  all_193_0 = all_163_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (144), (145) imply:
% 22.58/3.77  |   (166)  all_199_0 = all_124_0
% 22.58/3.77  | 
% 22.58/3.77  | SIMP: (166) implies:
% 22.58/3.77  |   (167)  all_199_0 = all_124_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (153), (154) imply:
% 22.58/3.77  |   (168)  all_106_0 = 390
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (156), (157) imply:
% 22.58/3.77  |   (169)  all_109_0 = 420
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (148), (149) imply:
% 22.58/3.77  |   (170)  all_208_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | SIMP: (170) implies:
% 22.58/3.77  |   (171)  all_208_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (151), (152) imply:
% 22.58/3.77  |   (172)  all_127_0 = 250
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (147), (171) imply:
% 22.58/3.77  |   (173)  all_154_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | SIMP: (173) implies:
% 22.58/3.77  |   (174)  all_154_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (142), (167) imply:
% 22.58/3.77  |   (175)  all_124_0 = all_55_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (143), (167) imply:
% 22.58/3.77  |   (176)  all_124_0 = all_19_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (146), (174) imply:
% 22.58/3.77  |   (177)  all_37_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | SIMP: (177) implies:
% 22.58/3.77  |   (178)  all_37_0 = all_34_0
% 22.58/3.77  | 
% 22.58/3.77  | COMBINE_EQS: (175), (176) imply:
% 22.58/3.77  |   (179)  all_55_0 = all_19_0
% 22.58/3.77  | 
% 22.58/3.77  | GROUND_INST: instantiating (23) with kiel, frankfurt, saarbruecken, all_34_0,
% 22.58/3.77  |              all_292_0, simplifying with (1), (5), (6), (84), (131) gives:
% 22.58/3.77  |   (180)   ? [v0: int] : ($lesseq(0, $sum($difference(v0, all_292_0),
% 22.58/3.77  |                all_34_0)) & d(frankfurt, saarbruecken) = v0)
% 22.58/3.77  | 
% 22.58/3.77  | GROUND_INST: instantiating (23) with kiel, saarbruecken, berlin, all_292_0,
% 22.58/3.77  |              all_19_0, simplifying with (1), (3), (6), (75), (131) gives:
% 22.58/3.77  |   (181)   ? [v0: int] : ($lesseq(all_19_0, $sum(v0, all_292_0)) &
% 22.58/3.77  |            d(saarbruecken, berlin) = v0)
% 22.58/3.77  | 
% 22.58/3.77  | GROUND_INST: instantiating (23) with hamburg, frankfurt, saarbruecken, 390,
% 22.58/3.77  |              all_202_0, simplifying with (2), (5), (6), (11), (115) gives:
% 22.58/3.77  |   (182)   ? [v0: int] : ($lesseq(-390, $difference(v0, all_202_0)) &
% 22.58/3.77  |            d(frankfurt, saarbruecken) = v0)
% 22.58/3.77  | 
% 22.58/3.77  | GROUND_INST: instantiating (23) with hamburg, saarbruecken, berlin, all_202_0,
% 22.58/3.77  |              250, simplifying with (2), (3), (6), (9), (115) gives:
% 22.58/3.77  |   (183)   ? [v0: int] : ($lesseq(250, $sum(v0, all_202_0)) & d(saarbruecken,
% 22.58/3.77  |              berlin) = v0)
% 22.58/3.77  | 
% 22.58/3.78  | GROUND_INST: instantiating (23) with berlin, frankfurt, saarbruecken, 420,
% 22.58/3.78  |              all_196_0, simplifying with (3), (5), (6), (13), (111) gives:
% 22.58/3.78  |   (184)   ? [v0: int] : ($lesseq(-420, $difference(v0, all_196_0)) &
% 22.58/3.78  |            d(frankfurt, saarbruecken) = v0)
% 22.58/3.78  | 
% 22.58/3.78  | GROUND_INST: instantiating (22) with berlin, saarbruecken, all_196_0,
% 22.58/3.78  |              simplifying with (3), (6), (111) gives:
% 22.58/3.78  |   (185)  d(saarbruecken, berlin) = all_196_0
% 22.58/3.78  | 
% 22.58/3.78  | GROUND_INST: instantiating (21) with berlin, all_163_0, simplifying with (3),
% 22.58/3.78  |              (107) gives:
% 22.58/3.78  |   (186)   ~ ($lesseq(all_163_0, 600)) |  ? [v0: int] : ($lesseq(v0, 2999999) &
% 22.58/3.78  |            inh(berlin) = v0)
% 22.58/3.78  | 
% 22.58/3.78  | DELTA: instantiating (184) with fresh symbol all_403_0 gives:
% 22.58/3.78  |   (187)  $lesseq(-420, $difference(all_403_0, all_196_0)) & d(frankfurt,
% 22.58/3.78  |            saarbruecken) = all_403_0
% 22.58/3.78  | 
% 22.58/3.78  | ALPHA: (187) implies:
% 22.58/3.78  |   (188)  $lesseq(-420, $difference(all_403_0, all_196_0))
% 22.58/3.78  |   (189)  d(frankfurt, saarbruecken) = all_403_0
% 22.58/3.78  | 
% 22.58/3.78  | DELTA: instantiating (182) with fresh symbol all_412_0 gives:
% 22.58/3.78  |   (190)  $lesseq(-390, $difference(all_412_0, all_202_0)) & d(frankfurt,
% 22.58/3.78  |            saarbruecken) = all_412_0
% 22.58/3.78  | 
% 22.58/3.78  | ALPHA: (190) implies:
% 22.58/3.78  |   (191)  d(frankfurt, saarbruecken) = all_412_0
% 22.58/3.78  | 
% 22.58/3.78  | DELTA: instantiating (183) with fresh symbol all_421_0 gives:
% 22.58/3.78  |   (192)  $lesseq(250, $sum(all_421_0, all_202_0)) & d(saarbruecken, berlin) =
% 22.58/3.78  |          all_421_0
% 22.58/3.78  | 
% 22.58/3.78  | ALPHA: (192) implies:
% 22.58/3.78  |   (193)  d(saarbruecken, berlin) = all_421_0
% 22.58/3.78  | 
% 22.58/3.78  | DELTA: instantiating (181) with fresh symbol all_562_0 gives:
% 22.58/3.78  |   (194)  $lesseq(all_19_0, $sum(all_562_0, all_292_0)) & d(saarbruecken,
% 22.58/3.78  |            berlin) = all_562_0
% 22.58/3.78  | 
% 22.58/3.78  | ALPHA: (194) implies:
% 22.58/3.78  |   (195)  d(saarbruecken, berlin) = all_562_0
% 22.58/3.78  | 
% 22.58/3.78  | DELTA: instantiating (180) with fresh symbol all_607_0 gives:
% 22.58/3.78  |   (196)  $lesseq(0, $sum($difference(all_607_0, all_292_0), all_34_0)) &
% 22.58/3.78  |          d(frankfurt, saarbruecken) = all_607_0
% 22.58/3.78  | 
% 22.58/3.78  | ALPHA: (196) implies:
% 22.58/3.78  |   (197)  d(frankfurt, saarbruecken) = all_607_0
% 22.58/3.78  | 
% 22.58/3.78  | BETA: splitting (186) gives:
% 22.58/3.78  | 
% 22.58/3.78  | Case 1:
% 22.58/3.78  | | 
% 22.58/3.78  | |   (198)  $lesseq(601, all_163_0)
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with 160, all_412_0, saarbruecken,
% 22.58/3.78  | |              frankfurt, simplifying with (42), (191) gives:
% 22.58/3.78  | |   (199)  all_412_0 = 160
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with all_412_0, all_607_0, saarbruecken,
% 22.58/3.78  | |              frankfurt, simplifying with (191), (197) gives:
% 22.58/3.78  | |   (200)  all_607_0 = all_412_0
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with all_403_0, all_607_0, saarbruecken,
% 22.58/3.78  | |              frankfurt, simplifying with (189), (197) gives:
% 22.58/3.78  | |   (201)  all_607_0 = all_403_0
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with all_163_0, all_421_0, berlin,
% 22.58/3.78  | |              saarbruecken, simplifying with (107), (193) gives:
% 22.58/3.78  | |   (202)  all_421_0 = all_163_0
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with all_421_0, all_562_0, berlin,
% 22.58/3.78  | |              saarbruecken, simplifying with (193), (195) gives:
% 22.58/3.78  | |   (203)  all_562_0 = all_421_0
% 22.58/3.78  | | 
% 22.58/3.78  | | GROUND_INST: instantiating (25) with all_196_0, all_562_0, berlin,
% 22.58/3.78  | |              saarbruecken, simplifying with (185), (195) gives:
% 22.58/3.78  | |   (204)  all_562_0 = all_196_0
% 22.58/3.78  | | 
% 22.58/3.78  | | COMBINE_EQS: (200), (201) imply:
% 22.58/3.78  | |   (205)  all_412_0 = all_403_0
% 22.58/3.78  | | 
% 22.58/3.78  | | SIMP: (205) implies:
% 22.58/3.78  | |   (206)  all_412_0 = all_403_0
% 22.58/3.78  | | 
% 22.58/3.78  | | COMBINE_EQS: (203), (204) imply:
% 22.58/3.78  | |   (207)  all_421_0 = all_196_0
% 22.58/3.78  | | 
% 22.58/3.78  | | SIMP: (207) implies:
% 22.58/3.78  | |   (208)  all_421_0 = all_196_0
% 22.58/3.78  | | 
% 22.58/3.78  | | COMBINE_EQS: (202), (208) imply:
% 22.58/3.78  | |   (209)  all_196_0 = all_163_0
% 22.58/3.78  | | 
% 22.58/3.78  | | SIMP: (209) implies:
% 22.58/3.78  | |   (210)  all_196_0 = all_163_0
% 22.58/3.78  | | 
% 22.58/3.78  | | COMBINE_EQS: (199), (206) imply:
% 22.58/3.78  | |   (211)  all_403_0 = 160
% 22.58/3.78  | | 
% 22.58/3.78  | | SIMP: (211) implies:
% 22.58/3.78  | |   (212)  all_403_0 = 160
% 22.58/3.78  | | 
% 22.58/3.78  | | REDUCE: (188), (210), (212) imply:
% 22.58/3.78  | |   (213)  $lesseq(all_163_0, 580)
% 22.58/3.78  | | 
% 22.58/3.78  | | COMBINE_INEQS: (198), (213) imply:
% 22.58/3.79  | |   (214)  $false
% 22.58/3.79  | | 
% 22.58/3.79  | | CLOSE: (214) is inconsistent.
% 22.58/3.79  | | 
% 22.58/3.79  | Case 2:
% 22.58/3.79  | | 
% 22.58/3.79  | |   (215)   ? [v0: int] : ($lesseq(v0, 2999999) & inh(berlin) = v0)
% 22.58/3.79  | | 
% 22.58/3.79  | | DELTA: instantiating (215) with fresh symbol all_614_0 gives:
% 22.58/3.79  | |   (216)  $lesseq(all_614_0, 2999999) & inh(berlin) = all_614_0
% 22.58/3.79  | | 
% 22.58/3.79  | | ALPHA: (216) implies:
% 22.58/3.79  | |   (217)  $lesseq(all_614_0, 2999999)
% 22.58/3.79  | |   (218)  inh(berlin) = all_614_0
% 22.58/3.79  | | 
% 22.58/3.79  | | GROUND_INST: instantiating (24) with 3442675, all_614_0, berlin, simplifying
% 22.58/3.79  | |              with (20), (218) gives:
% 22.58/3.79  | |   (219)  all_614_0 = 3442675
% 22.58/3.79  | | 
% 22.58/3.79  | | REDUCE: (217), (219) imply:
% 22.58/3.79  | |   (220)  $false
% 22.58/3.79  | | 
% 22.58/3.79  | | CLOSE: (220) is inconsistent.
% 22.58/3.79  | | 
% 22.58/3.79  | End of split
% 22.58/3.79  | 
% 22.58/3.79  End of proof
% 22.58/3.79  % SZS output end Proof for theBenchmark
% 22.58/3.79  
% 22.58/3.79  3187ms
%------------------------------------------------------------------------------