TSTP Solution File: GEG023_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : GEG023_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 : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 22:40:40 EDT 2023

% Result   : Theorem 8.91s 2.00s
% Output   : Proof 16.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEG023_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Aug 28 01:10:39 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/0.99  Prover 4: Preprocessing ...
% 1.94/1.00  Prover 1: Preprocessing ...
% 2.41/1.03  Prover 6: Preprocessing ...
% 2.41/1.03  Prover 2: Preprocessing ...
% 2.41/1.03  Prover 0: Preprocessing ...
% 2.41/1.04  Prover 3: Preprocessing ...
% 2.41/1.04  Prover 5: Preprocessing ...
% 3.46/1.17  Prover 1: Constructing countermodel ...
% 3.46/1.17  Prover 3: Constructing countermodel ...
% 3.46/1.18  Prover 4: Constructing countermodel ...
% 3.46/1.18  Prover 6: Proving ...
% 3.46/1.19  Prover 0: Proving ...
% 3.66/1.19  Prover 2: Proving ...
% 3.66/1.21  Prover 5: Proving ...
% 8.91/2.00  Prover 3: proved (1365ms)
% 8.91/2.00  
% 8.91/2.00  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.91/2.00  
% 8.91/2.01  Prover 2: stopped
% 8.91/2.01  Prover 5: stopped
% 8.91/2.02  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.91/2.02  Prover 6: stopped
% 8.91/2.02  Prover 0: stopped
% 8.91/2.03  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.91/2.03  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.91/2.03  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.91/2.03  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.91/2.03  Prover 7: Preprocessing ...
% 9.15/2.06  Prover 10: Preprocessing ...
% 9.15/2.06  Prover 8: Preprocessing ...
% 9.15/2.06  Prover 11: Preprocessing ...
% 9.15/2.06  Prover 13: Preprocessing ...
% 9.15/2.09  Prover 10: Constructing countermodel ...
% 9.15/2.09  Prover 8: Warning: ignoring some quantifiers
% 9.15/2.09  Prover 8: Constructing countermodel ...
% 9.15/2.10  Prover 11: Constructing countermodel ...
% 9.15/2.11  Prover 7: Constructing countermodel ...
% 9.15/2.11  Prover 13: Warning: ignoring some quantifiers
% 9.15/2.11  Prover 13: Constructing countermodel ...
% 16.32/2.95  Prover 1: Found proof (size 71)
% 16.32/2.95  Prover 1: proved (2318ms)
% 16.32/2.95  Prover 11: stopped
% 16.32/2.95  Prover 13: stopped
% 16.32/2.95  Prover 10: stopped
% 16.32/2.95  Prover 8: stopped
% 16.32/2.95  Prover 7: stopped
% 16.32/2.95  Prover 4: stopped
% 16.32/2.95  
% 16.32/2.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.32/2.95  
% 16.48/2.97  % SZS output start Proof for theBenchmark
% 16.48/2.97  Assumptions after simplification:
% 16.48/2.97  ---------------------------------
% 16.48/2.97  
% 16.48/2.97    (city_distance_3)
% 16.48/2.99    city(munich) & city(saarbruecken) & city(frankfurt) & city(cologne) &
% 16.48/2.99    city(berlin) & city(hamburg) & city(kiel) &  ? [v0: int] : ($lesseq(641, v0) &
% 16.48/2.99      d(munich, saarbruecken) = 360 & d(munich, frankfurt) = 300 & d(saarbruecken,
% 16.48/2.99        frankfurt) = 160 & d(saarbruecken, cologne) = 190 & d(cologne, frankfurt)
% 16.48/2.99      = 150 & d(berlin, munich) = 510 & d(berlin, frankfurt) = 420 & d(berlin,
% 16.48/2.99        cologne) = 480 & d(hamburg, frankfurt) = 390 & d(hamburg, cologne) = 360 &
% 16.48/2.99      d(hamburg, berlin) = 250 & d(hamburg, kiel) = 90 & d(kiel, saarbruecken) =
% 16.48/2.99      v0 &  ! [v1: city] :  ! [v2: city] :  ! [v3: city] :  ! [v4: int] :  ! [v5:
% 16.48/2.99        int] : ( ~ (d(v1, v3) = v5) |  ~ (d(v1, v2) = v4) |  ~ city(v3) |  ~
% 16.48/2.99        city(v2) |  ~ city(v1) |  ? [v6: int] : ($lesseq(0, $sum($difference(v6,
% 16.48/2.99                v5), v4)) & d(v2, v3) = v6)) &  ! [v1: city] :  ! [v2: city] :  !
% 16.48/2.99      [v3: int] : ( ~ (d(v1, v2) = v3) |  ~ city(v2) |  ~ city(v1) | d(v2, v1) =
% 16.48/2.99        v3) &  ! [v1: city] :  ! [v2: int] : (v2 = 0 |  ~ (d(v1, v1) = v2) |  ~
% 16.48/2.99        city(v1)))
% 16.48/2.99  
% 16.48/2.99    (function-axioms)
% 16.48/2.99     ! [v0: int] :  ! [v1: int] :  ! [v2: city] :  ! [v3: city] : (v1 = v0 |  ~
% 16.48/2.99      (d(v3, v2) = v1) |  ~ (d(v3, v2) = v0))
% 16.48/2.99  
% 16.48/2.99  Those formulas are unsatisfiable:
% 16.48/2.99  ---------------------------------
% 16.48/2.99  
% 16.48/2.99  Begin of proof
% 16.48/2.99  | 
% 16.48/2.99  | ALPHA: (city_distance_3) implies:
% 16.48/3.00  |   (1)  city(kiel)
% 16.48/3.00  |   (2)  city(hamburg)
% 16.48/3.00  |   (3)  city(berlin)
% 16.48/3.00  |   (4)  city(cologne)
% 16.48/3.00  |   (5)  city(frankfurt)
% 16.48/3.00  |   (6)  city(saarbruecken)
% 16.48/3.00  |   (7)  city(munich)
% 16.48/3.00  |   (8)   ? [v0: int] : ($lesseq(641, v0) & d(munich, saarbruecken) = 360 &
% 16.48/3.00  |          d(munich, frankfurt) = 300 & d(saarbruecken, frankfurt) = 160 &
% 16.48/3.00  |          d(saarbruecken, cologne) = 190 & d(cologne, frankfurt) = 150 &
% 16.48/3.00  |          d(berlin, munich) = 510 & d(berlin, frankfurt) = 420 & d(berlin,
% 16.48/3.00  |            cologne) = 480 & d(hamburg, frankfurt) = 390 & d(hamburg, cologne)
% 16.48/3.00  |          = 360 & d(hamburg, berlin) = 250 & d(hamburg, kiel) = 90 & d(kiel,
% 16.48/3.00  |            saarbruecken) = v0 &  ! [v1: city] :  ! [v2: city] :  ! [v3: city]
% 16.48/3.00  |          :  ! [v4: int] :  ! [v5: int] : ( ~ (d(v1, v3) = v5) |  ~ (d(v1, v2)
% 16.48/3.00  |              = v4) |  ~ city(v3) |  ~ city(v2) |  ~ city(v1) |  ? [v6: int] :
% 16.48/3.00  |            ($lesseq(0, $sum($difference(v6, v5), v4)) & d(v2, v3) = v6)) &  !
% 16.48/3.00  |          [v1: city] :  ! [v2: city] :  ! [v3: int] : ( ~ (d(v1, v2) = v3) |  ~
% 16.48/3.00  |            city(v2) |  ~ city(v1) | d(v2, v1) = v3) &  ! [v1: city] :  ! [v2:
% 16.48/3.00  |            int] : (v2 = 0 |  ~ (d(v1, v1) = v2) |  ~ city(v1)))
% 16.48/3.00  | 
% 16.48/3.00  | DELTA: instantiating (8) with fresh symbol all_6_0 gives:
% 16.48/3.01  |   (9)  $lesseq(641, all_6_0) & d(munich, saarbruecken) = 360 & d(munich,
% 16.48/3.01  |          frankfurt) = 300 & d(saarbruecken, frankfurt) = 160 & d(saarbruecken,
% 16.48/3.01  |          cologne) = 190 & d(cologne, frankfurt) = 150 & d(berlin, munich) =
% 16.48/3.01  |        510 & d(berlin, frankfurt) = 420 & d(berlin, cologne) = 480 &
% 16.48/3.01  |        d(hamburg, frankfurt) = 390 & d(hamburg, cologne) = 360 & d(hamburg,
% 16.48/3.01  |          berlin) = 250 & d(hamburg, kiel) = 90 & d(kiel, saarbruecken) =
% 16.48/3.01  |        all_6_0 &  ! [v0: city] :  ! [v1: city] :  ! [v2: city] :  ! [v3: int]
% 16.48/3.01  |        :  ! [v4: int] : ( ~ (d(v0, v2) = v4) |  ~ (d(v0, v1) = v3) |  ~
% 16.48/3.01  |          city(v2) |  ~ city(v1) |  ~ city(v0) |  ? [v5: int] : ($lesseq(0,
% 16.48/3.01  |              $sum($difference(v5, v4), v3)) & d(v1, v2) = v5)) &  ! [v0: city]
% 16.48/3.01  |        :  ! [v1: city] :  ! [v2: int] : ( ~ (d(v0, v1) = v2) |  ~ city(v1) | 
% 16.48/3.01  |          ~ city(v0) | d(v1, v0) = v2) &  ! [v0: city] :  ! [v1: int] : (v1 = 0
% 16.48/3.01  |          |  ~ (d(v0, v0) = v1) |  ~ city(v0))
% 16.48/3.01  | 
% 16.48/3.01  | ALPHA: (9) implies:
% 16.48/3.01  |   (10)  $lesseq(641, all_6_0)
% 16.48/3.01  |   (11)  d(kiel, saarbruecken) = all_6_0
% 16.48/3.01  |   (12)  d(hamburg, kiel) = 90
% 16.48/3.01  |   (13)  d(hamburg, berlin) = 250
% 16.48/3.01  |   (14)  d(hamburg, cologne) = 360
% 16.48/3.01  |   (15)  d(hamburg, frankfurt) = 390
% 16.48/3.01  |   (16)  d(berlin, frankfurt) = 420
% 16.48/3.01  |   (17)  d(cologne, frankfurt) = 150
% 16.48/3.01  |   (18)  d(saarbruecken, frankfurt) = 160
% 16.48/3.01  |   (19)  d(munich, frankfurt) = 300
% 16.48/3.01  |   (20)  d(munich, saarbruecken) = 360
% 16.48/3.01  |   (21)   ! [v0: city] :  ! [v1: city] :  ! [v2: int] : ( ~ (d(v0, v1) = v2) | 
% 16.48/3.01  |           ~ city(v1) |  ~ city(v0) | d(v1, v0) = v2)
% 16.48/3.01  |   (22)   ! [v0: city] :  ! [v1: city] :  ! [v2: city] :  ! [v3: int] :  ! [v4:
% 16.48/3.01  |           int] : ( ~ (d(v0, v2) = v4) |  ~ (d(v0, v1) = v3) |  ~ city(v2) |  ~
% 16.48/3.01  |           city(v1) |  ~ city(v0) |  ? [v5: int] : ($lesseq(0,
% 16.48/3.01  |               $sum($difference(v5, v4), v3)) & d(v1, v2) = v5))
% 16.48/3.01  | 
% 16.48/3.01  | GROUND_INST: instantiating (21) with hamburg, kiel, 90, simplifying with (1),
% 16.48/3.01  |              (2), (12) gives:
% 16.48/3.01  |   (23)  d(kiel, hamburg) = 90
% 16.48/3.01  | 
% 16.48/3.01  | GROUND_INST: instantiating (22) with hamburg, berlin, kiel, 250, 90,
% 16.48/3.01  |              simplifying with (1), (2), (3), (12), (13) gives:
% 16.48/3.01  |   (24)   ? [v0: int] : ($lesseq(-160, v0) & d(berlin, kiel) = v0)
% 16.48/3.01  | 
% 16.48/3.01  | GROUND_INST: instantiating (22) with hamburg, cologne, kiel, 360, 90,
% 16.48/3.01  |              simplifying with (1), (2), (4), (12), (14) gives:
% 16.48/3.01  |   (25)   ? [v0: int] : ($lesseq(-270, v0) & d(cologne, kiel) = v0)
% 16.48/3.01  | 
% 16.48/3.02  | GROUND_INST: instantiating (22) with hamburg, kiel, frankfurt, 90, 390,
% 16.48/3.02  |              simplifying with (1), (2), (5), (12), (15) gives:
% 16.48/3.02  |   (26)   ? [v0: int] : ($lesseq(300, v0) & d(kiel, frankfurt) = v0)
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (22) with hamburg, frankfurt, kiel, 390, 90,
% 16.48/3.02  |              simplifying with (1), (2), (5), (12), (15) gives:
% 16.48/3.02  |   (27)   ? [v0: int] : ($lesseq(-300, v0) & d(frankfurt, kiel) = v0)
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (21) with hamburg, frankfurt, 390, simplifying with
% 16.48/3.02  |              (2), (5), (15) gives:
% 16.48/3.02  |   (28)  d(frankfurt, hamburg) = 390
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (21) with saarbruecken, frankfurt, 160, simplifying
% 16.48/3.02  |              with (5), (6), (18) gives:
% 16.48/3.02  |   (29)  d(frankfurt, saarbruecken) = 160
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (22) with munich, frankfurt, frankfurt, 300, 300,
% 16.48/3.02  |              simplifying with (5), (7), (19) gives:
% 16.48/3.02  |   (30)   ? [v0: int] : ($lesseq(0, v0) & d(frankfurt, frankfurt) = v0)
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (22) with munich, saarbruecken, saarbruecken, 360,
% 16.48/3.02  |              360, simplifying with (6), (7), (20) gives:
% 16.48/3.02  |   (31)   ? [v0: int] : ($lesseq(0, v0) & d(saarbruecken, saarbruecken) = v0)
% 16.48/3.02  | 
% 16.48/3.02  | GROUND_INST: instantiating (22) with munich, frankfurt, saarbruecken, 300,
% 16.48/3.02  |              360, simplifying with (5), (6), (7), (19), (20) gives:
% 16.48/3.02  |   (32)   ? [v0: int] : ($lesseq(60, v0) & d(frankfurt, saarbruecken) = v0)
% 16.48/3.02  | 
% 16.48/3.02  | DELTA: instantiating (31) with fresh symbol all_16_0 gives:
% 16.48/3.02  |   (33)  $lesseq(0, all_16_0) & d(saarbruecken, saarbruecken) = all_16_0
% 16.48/3.02  | 
% 16.48/3.02  | ALPHA: (33) implies:
% 16.48/3.02  |   (34)  d(saarbruecken, saarbruecken) = all_16_0
% 16.48/3.02  | 
% 16.48/3.02  | DELTA: instantiating (24) with fresh symbol all_19_0 gives:
% 16.48/3.02  |   (35)  $lesseq(-160, all_19_0) & d(berlin, kiel) = all_19_0
% 16.48/3.02  | 
% 16.48/3.02  | ALPHA: (35) implies:
% 16.75/3.02  |   (36)  d(berlin, kiel) = all_19_0
% 16.75/3.02  | 
% 16.75/3.02  | DELTA: instantiating (27) with fresh symbol all_25_0 gives:
% 16.75/3.02  |   (37)  $lesseq(-300, all_25_0) & d(frankfurt, kiel) = all_25_0
% 16.75/3.02  | 
% 16.75/3.02  | ALPHA: (37) implies:
% 16.75/3.02  |   (38)  d(frankfurt, kiel) = all_25_0
% 16.75/3.02  | 
% 16.75/3.02  | DELTA: instantiating (26) with fresh symbol all_28_0 gives:
% 16.75/3.02  |   (39)  $lesseq(300, all_28_0) & d(kiel, frankfurt) = all_28_0
% 16.75/3.02  | 
% 16.75/3.02  | ALPHA: (39) implies:
% 16.75/3.02  |   (40)  d(kiel, frankfurt) = all_28_0
% 16.75/3.02  | 
% 16.75/3.02  | DELTA: instantiating (30) with fresh symbol all_40_0 gives:
% 16.75/3.02  |   (41)  $lesseq(0, all_40_0) & d(frankfurt, frankfurt) = all_40_0
% 16.75/3.02  | 
% 16.75/3.02  | ALPHA: (41) implies:
% 16.75/3.02  |   (42)  d(frankfurt, frankfurt) = all_40_0
% 16.75/3.02  | 
% 16.75/3.02  | DELTA: instantiating (25) with fresh symbol all_43_0 gives:
% 16.75/3.02  |   (43)  $lesseq(-270, all_43_0) & d(cologne, kiel) = all_43_0
% 16.75/3.02  | 
% 16.75/3.02  | ALPHA: (43) implies:
% 16.75/3.02  |   (44)  d(cologne, kiel) = all_43_0
% 16.75/3.02  | 
% 16.75/3.02  | DELTA: instantiating (32) with fresh symbol all_55_0 gives:
% 16.75/3.02  |   (45)  $lesseq(60, all_55_0) & d(frankfurt, saarbruecken) = all_55_0
% 16.75/3.02  | 
% 16.75/3.02  | ALPHA: (45) implies:
% 16.75/3.02  |   (46)  d(frankfurt, saarbruecken) = all_55_0
% 16.75/3.02  | 
% 16.75/3.02  | GROUND_INST: instantiating (function-axioms) with 160, all_55_0, saarbruecken,
% 16.75/3.02  |              frankfurt, simplifying with (29), (46) gives:
% 16.75/3.02  |   (47)  all_55_0 = 160
% 16.75/3.02  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with kiel, frankfurt, saarbruecken, all_28_0,
% 16.75/3.03  |              all_6_0, simplifying with (1), (5), (6), (11), (40) gives:
% 16.75/3.03  |   (48)   ? [v0: int] : ($lesseq(all_6_0, $sum(v0, all_28_0)) & d(frankfurt,
% 16.75/3.03  |             saarbruecken) = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with kiel, hamburg, frankfurt, 90, all_28_0,
% 16.75/3.03  |              simplifying with (1), (2), (5), (23), (40) gives:
% 16.75/3.03  |   (49)   ? [v0: int] : ($lesseq(-90, $difference(v0, all_28_0)) & d(hamburg,
% 16.75/3.03  |             frankfurt) = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with berlin, kiel, frankfurt, all_19_0, 420,
% 16.75/3.03  |              simplifying with (1), (3), (5), (16), (36) gives:
% 16.75/3.03  |   (50)   ? [v0: int] : ($lesseq(420, $sum(v0, all_19_0)) & d(kiel, frankfurt)
% 16.75/3.03  |           = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with cologne, kiel, frankfurt, all_43_0, 150,
% 16.75/3.03  |              simplifying with (1), (4), (5), (17), (44) gives:
% 16.75/3.03  |   (51)   ? [v0: int] : ($lesseq(150, $sum(v0, all_43_0)) & d(kiel, frankfurt)
% 16.75/3.03  |           = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (21) with frankfurt, kiel, all_25_0, simplifying
% 16.75/3.03  |              with (1), (5), (38) gives:
% 16.75/3.03  |   (52)  d(kiel, frankfurt) = all_25_0
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with frankfurt, hamburg, frankfurt, 390,
% 16.75/3.03  |              all_40_0, simplifying with (2), (5), (28), (42) gives:
% 16.75/3.03  |   (53)   ? [v0: int] : ($lesseq(-390, $difference(v0, all_40_0)) & d(hamburg,
% 16.75/3.03  |             frankfurt) = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with frankfurt, kiel, frankfurt, all_25_0,
% 16.75/3.03  |              all_40_0, simplifying with (1), (5), (38), (42) gives:
% 16.75/3.03  |   (54)   ? [v0: int] : ($lesseq(0, $sum($difference(v0, all_40_0), all_25_0))
% 16.75/3.03  |           & d(kiel, frankfurt) = v0)
% 16.75/3.03  | 
% 16.75/3.03  | GROUND_INST: instantiating (22) with saarbruecken, frankfurt, saarbruecken,
% 16.75/3.03  |              160, all_16_0, simplifying with (5), (6), (18), (34) gives:
% 16.75/3.03  |   (55)   ? [v0: int] : ($lesseq(-160, $difference(v0, all_16_0)) &
% 16.75/3.03  |           d(frankfurt, saarbruecken) = v0)
% 16.75/3.03  | 
% 16.75/3.03  | DELTA: instantiating (51) with fresh symbol all_104_0 gives:
% 16.75/3.03  |   (56)  $lesseq(150, $sum(all_104_0, all_43_0)) & d(kiel, frankfurt) =
% 16.75/3.03  |         all_104_0
% 16.75/3.03  | 
% 16.75/3.03  | ALPHA: (56) implies:
% 16.75/3.03  |   (57)  d(kiel, frankfurt) = all_104_0
% 16.75/3.03  | 
% 16.75/3.03  | DELTA: instantiating (48) with fresh symbol all_119_0 gives:
% 16.75/3.03  |   (58)  $lesseq(all_6_0, $sum(all_119_0, all_28_0)) & d(frankfurt,
% 16.75/3.03  |           saarbruecken) = all_119_0
% 16.75/3.03  | 
% 16.75/3.03  | ALPHA: (58) implies:
% 16.75/3.03  |   (59)  $lesseq(all_6_0, $sum(all_119_0, all_28_0))
% 16.75/3.03  |   (60)  d(frankfurt, saarbruecken) = all_119_0
% 16.75/3.03  | 
% 16.75/3.03  | DELTA: instantiating (49) with fresh symbol all_227_0 gives:
% 16.75/3.03  |   (61)  $lesseq(-90, $difference(all_227_0, all_28_0)) & d(hamburg, frankfurt)
% 16.75/3.03  |         = all_227_0
% 16.75/3.03  | 
% 16.75/3.03  | ALPHA: (61) implies:
% 16.75/3.03  |   (62)  $lesseq(-90, $difference(all_227_0, all_28_0))
% 16.75/3.03  |   (63)  d(hamburg, frankfurt) = all_227_0
% 16.75/3.03  | 
% 16.75/3.03  | DELTA: instantiating (55) with fresh symbol all_257_0 gives:
% 16.75/3.03  |   (64)  $lesseq(-160, $difference(all_257_0, all_16_0)) & d(frankfurt,
% 16.75/3.03  |           saarbruecken) = all_257_0
% 16.75/3.03  | 
% 16.75/3.03  | ALPHA: (64) implies:
% 16.75/3.03  |   (65)  d(frankfurt, saarbruecken) = all_257_0
% 16.75/3.03  | 
% 16.75/3.03  | DELTA: instantiating (50) with fresh symbol all_287_0 gives:
% 16.75/3.03  |   (66)  $lesseq(420, $sum(all_287_0, all_19_0)) & d(kiel, frankfurt) =
% 16.75/3.03  |         all_287_0
% 16.75/3.04  | 
% 16.75/3.04  | ALPHA: (66) implies:
% 16.75/3.04  |   (67)  d(kiel, frankfurt) = all_287_0
% 16.75/3.04  | 
% 16.75/3.04  | DELTA: instantiating (54) with fresh symbol all_365_0 gives:
% 16.75/3.04  |   (68)  $lesseq(0, $sum($difference(all_365_0, all_40_0), all_25_0)) & d(kiel,
% 16.75/3.04  |           frankfurt) = all_365_0
% 16.75/3.04  | 
% 16.75/3.04  | ALPHA: (68) implies:
% 16.75/3.04  |   (69)  d(kiel, frankfurt) = all_365_0
% 16.75/3.04  | 
% 16.75/3.04  | DELTA: instantiating (53) with fresh symbol all_368_0 gives:
% 16.75/3.04  |   (70)  $lesseq(-390, $difference(all_368_0, all_40_0)) & d(hamburg,
% 16.75/3.04  |           frankfurt) = all_368_0
% 16.75/3.04  | 
% 16.75/3.04  | ALPHA: (70) implies:
% 16.75/3.04  |   (71)  d(hamburg, frankfurt) = all_368_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_28_0, all_287_0,
% 16.75/3.04  |              frankfurt, kiel, simplifying with (40), (67) gives:
% 16.75/3.04  |   (72)  all_287_0 = all_28_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_25_0, all_287_0,
% 16.75/3.04  |              frankfurt, kiel, simplifying with (52), (67) gives:
% 16.75/3.04  |   (73)  all_287_0 = all_25_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_287_0, all_365_0,
% 16.75/3.04  |              frankfurt, kiel, simplifying with (67), (69) gives:
% 16.75/3.04  |   (74)  all_365_0 = all_287_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_104_0, all_365_0,
% 16.75/3.04  |              frankfurt, kiel, simplifying with (57), (69) gives:
% 16.75/3.04  |   (75)  all_365_0 = all_104_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with 390, all_368_0, frankfurt,
% 16.75/3.04  |              hamburg, simplifying with (15), (71) gives:
% 16.75/3.04  |   (76)  all_368_0 = 390
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_227_0, all_368_0,
% 16.75/3.04  |              frankfurt, hamburg, simplifying with (63), (71) gives:
% 16.75/3.04  |   (77)  all_368_0 = all_227_0
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with 160, all_257_0,
% 16.75/3.04  |              saarbruecken, frankfurt, simplifying with (29), (65) gives:
% 16.75/3.04  |   (78)  all_257_0 = 160
% 16.75/3.04  | 
% 16.75/3.04  | GROUND_INST: instantiating (function-axioms) with all_119_0, all_257_0,
% 16.75/3.04  |              saarbruecken, frankfurt, simplifying with (60), (65) gives:
% 16.75/3.04  |   (79)  all_257_0 = all_119_0
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (76), (77) imply:
% 16.75/3.04  |   (80)  all_227_0 = 390
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (74), (75) imply:
% 16.75/3.04  |   (81)  all_287_0 = all_104_0
% 16.75/3.04  | 
% 16.75/3.04  | SIMP: (81) implies:
% 16.75/3.04  |   (82)  all_287_0 = all_104_0
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (73), (82) imply:
% 16.75/3.04  |   (83)  all_104_0 = all_25_0
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (72), (82) imply:
% 16.75/3.04  |   (84)  all_104_0 = all_28_0
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (78), (79) imply:
% 16.75/3.04  |   (85)  all_119_0 = 160
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_EQS: (83), (84) imply:
% 16.75/3.04  |   (86)  all_28_0 = all_25_0
% 16.75/3.04  | 
% 16.75/3.04  | REDUCE: (62), (80), (86) imply:
% 16.75/3.04  |   (87)  $lesseq(all_25_0, 480)
% 16.75/3.04  | 
% 16.75/3.04  | REDUCE: (59), (85), (86) imply:
% 16.75/3.04  |   (88)  $lesseq(-160, $difference(all_25_0, all_6_0))
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_INEQS: (87), (88) imply:
% 16.75/3.04  |   (89)  $lesseq(all_6_0, 640)
% 16.75/3.04  | 
% 16.75/3.04  | COMBINE_INEQS: (10), (89) imply:
% 16.75/3.04  |   (90)  $false
% 16.75/3.04  | 
% 16.75/3.04  | CLOSE: (90) is inconsistent.
% 16.75/3.04  | 
% 16.75/3.04  End of proof
% 16.75/3.04  % SZS output end Proof for theBenchmark
% 16.75/3.04  
% 16.75/3.04  2430ms
%------------------------------------------------------------------------------