TSTP Solution File: GEG021_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GEG021_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 : n008.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 22:40:39 EDT 2023
% Result : Theorem 5.24s 1.49s
% Output : Proof 7.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEG021_1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 01:04:47 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.22/1.01 Prover 4: Preprocessing ...
% 2.22/1.02 Prover 1: Preprocessing ...
% 2.70/1.06 Prover 3: Preprocessing ...
% 2.70/1.06 Prover 6: Preprocessing ...
% 2.70/1.06 Prover 0: Preprocessing ...
% 2.70/1.06 Prover 2: Preprocessing ...
% 2.70/1.06 Prover 5: Preprocessing ...
% 3.37/1.19 Prover 1: Constructing countermodel ...
% 3.37/1.20 Prover 3: Constructing countermodel ...
% 3.37/1.20 Prover 6: Proving ...
% 3.37/1.20 Prover 4: Constructing countermodel ...
% 3.37/1.21 Prover 0: Proving ...
% 3.37/1.22 Prover 2: Proving ...
% 3.90/1.25 Prover 5: Proving ...
% 5.24/1.49 Prover 3: proved (839ms)
% 5.24/1.49
% 5.24/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.24/1.49
% 5.24/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.24/1.50 Prover 5: stopped
% 5.24/1.50 Prover 6: stopped
% 5.24/1.51 Prover 0: stopped
% 5.24/1.51 Prover 2: stopped
% 5.24/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.24/1.52 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.24/1.52 Prover 7: Preprocessing ...
% 5.24/1.52 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.24/1.53 Prover 11: Preprocessing ...
% 5.24/1.53 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.04/1.53 Prover 8: Preprocessing ...
% 6.04/1.53 Prover 10: Preprocessing ...
% 6.04/1.56 Prover 13: Preprocessing ...
% 6.25/1.58 Prover 11: Constructing countermodel ...
% 6.25/1.58 Prover 8: Warning: ignoring some quantifiers
% 6.25/1.59 Prover 10: Constructing countermodel ...
% 6.25/1.60 Prover 8: Constructing countermodel ...
% 6.25/1.60 Prover 13: Warning: ignoring some quantifiers
% 6.25/1.60 Prover 13: Constructing countermodel ...
% 6.25/1.60 Prover 7: Constructing countermodel ...
% 6.95/1.70 Prover 1: Found proof (size 7)
% 6.95/1.70 Prover 1: proved (1051ms)
% 6.95/1.70 Prover 4: stopped
% 6.95/1.70 Prover 8: stopped
% 6.95/1.70 Prover 10: stopped
% 6.95/1.70 Prover 11: stopped
% 6.95/1.70 Prover 13: stopped
% 6.95/1.70 Prover 7: stopped
% 6.95/1.70
% 6.95/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.95/1.71
% 6.95/1.71 % SZS output start Proof for theBenchmark
% 6.95/1.71 Assumptions after simplification:
% 6.95/1.71 ---------------------------------
% 6.95/1.71
% 6.95/1.71 (city_distance_1)
% 7.40/1.74 city(munich) & city(saarbruecken) & city(frankfurt) & city(cologne) &
% 7.40/1.74 city(berlin) & city(hamburg) & city(kiel) & ? [v0: int] : ($lesseq(501, v0) &
% 7.40/1.74 d(munich, saarbruecken) = 360 & d(munich, frankfurt) = 300 & d(saarbruecken,
% 7.40/1.74 frankfurt) = 160 & d(saarbruecken, cologne) = 190 & d(cologne, frankfurt)
% 7.40/1.74 = 150 & d(cologne, berlin) = v0 & d(berlin, munich) = 510 & d(berlin,
% 7.40/1.74 frankfurt) = 420 & d(berlin, cologne) = 480 & d(hamburg, frankfurt) = 390
% 7.40/1.74 & d(hamburg, cologne) = 360 & d(hamburg, berlin) = 250 & d(hamburg, kiel) =
% 7.40/1.74 90 & ! [v1: city] : ! [v2: city] : ! [v3: city] : ! [v4: int] : ! [v5:
% 7.40/1.74 int] : ( ~ (d(v1, v3) = v5) | ~ (d(v1, v2) = v4) | ~ city(v3) | ~
% 7.40/1.74 city(v2) | ~ city(v1) | ? [v6: int] : ($lesseq(0, $sum($difference(v6,
% 7.40/1.74 v5), v4)) & d(v2, v3) = v6)) & ! [v1: city] : ! [v2: city] : !
% 7.40/1.74 [v3: int] : ( ~ (d(v1, v2) = v3) | ~ city(v2) | ~ city(v1) | d(v2, v1) =
% 7.40/1.74 v3) & ! [v1: city] : ! [v2: int] : (v2 = 0 | ~ (d(v1, v1) = v2) | ~
% 7.40/1.74 city(v1)))
% 7.40/1.74
% 7.40/1.74 (function-axioms)
% 7.40/1.74 ! [v0: int] : ! [v1: int] : ! [v2: city] : ! [v3: city] : (v1 = v0 | ~
% 7.40/1.74 (d(v3, v2) = v1) | ~ (d(v3, v2) = v0))
% 7.40/1.74
% 7.40/1.74 Those formulas are unsatisfiable:
% 7.40/1.74 ---------------------------------
% 7.40/1.74
% 7.40/1.74 Begin of proof
% 7.40/1.74 |
% 7.40/1.74 | ALPHA: (city_distance_1) implies:
% 7.40/1.74 | (1) city(berlin)
% 7.40/1.74 | (2) city(cologne)
% 7.40/1.75 | (3) ? [v0: int] : ($lesseq(501, v0) & d(munich, saarbruecken) = 360 &
% 7.40/1.75 | d(munich, frankfurt) = 300 & d(saarbruecken, frankfurt) = 160 &
% 7.40/1.75 | d(saarbruecken, cologne) = 190 & d(cologne, frankfurt) = 150 &
% 7.40/1.75 | d(cologne, berlin) = v0 & d(berlin, munich) = 510 & d(berlin,
% 7.40/1.75 | frankfurt) = 420 & d(berlin, cologne) = 480 & d(hamburg, frankfurt)
% 7.40/1.75 | = 390 & d(hamburg, cologne) = 360 & d(hamburg, berlin) = 250 &
% 7.40/1.75 | d(hamburg, kiel) = 90 & ! [v1: city] : ! [v2: city] : ! [v3: city]
% 7.40/1.75 | : ! [v4: int] : ! [v5: int] : ( ~ (d(v1, v3) = v5) | ~ (d(v1, v2)
% 7.40/1.75 | = v4) | ~ city(v3) | ~ city(v2) | ~ city(v1) | ? [v6: int] :
% 7.40/1.75 | ($lesseq(0, $sum($difference(v6, v5), v4)) & d(v2, v3) = v6)) & !
% 7.40/1.75 | [v1: city] : ! [v2: city] : ! [v3: int] : ( ~ (d(v1, v2) = v3) | ~
% 7.40/1.75 | city(v2) | ~ city(v1) | d(v2, v1) = v3) & ! [v1: city] : ! [v2:
% 7.40/1.75 | int] : (v2 = 0 | ~ (d(v1, v1) = v2) | ~ city(v1)))
% 7.40/1.75 |
% 7.40/1.75 | DELTA: instantiating (3) with fresh symbol all_6_0 gives:
% 7.40/1.76 | (4) $lesseq(501, all_6_0) & d(munich, saarbruecken) = 360 & d(munich,
% 7.40/1.76 | frankfurt) = 300 & d(saarbruecken, frankfurt) = 160 & d(saarbruecken,
% 7.40/1.76 | cologne) = 190 & d(cologne, frankfurt) = 150 & d(cologne, berlin) =
% 7.40/1.76 | all_6_0 & d(berlin, munich) = 510 & d(berlin, frankfurt) = 420 &
% 7.40/1.76 | d(berlin, cologne) = 480 & d(hamburg, frankfurt) = 390 & d(hamburg,
% 7.40/1.76 | cologne) = 360 & d(hamburg, berlin) = 250 & d(hamburg, kiel) = 90 &
% 7.40/1.76 | ! [v0: city] : ! [v1: city] : ! [v2: city] : ! [v3: int] : ! [v4:
% 7.40/1.76 | int] : ( ~ (d(v0, v2) = v4) | ~ (d(v0, v1) = v3) | ~ city(v2) | ~
% 7.40/1.76 | city(v1) | ~ city(v0) | ? [v5: int] : ($lesseq(0,
% 7.40/1.76 | $sum($difference(v5, v4), v3)) & d(v1, v2) = v5)) & ! [v0: city]
% 7.40/1.76 | : ! [v1: city] : ! [v2: int] : ( ~ (d(v0, v1) = v2) | ~ city(v1) |
% 7.40/1.76 | ~ city(v0) | d(v1, v0) = v2) & ! [v0: city] : ! [v1: int] : (v1 = 0
% 7.40/1.76 | | ~ (d(v0, v0) = v1) | ~ city(v0))
% 7.40/1.76 |
% 7.40/1.76 | ALPHA: (4) implies:
% 7.40/1.76 | (5) $lesseq(501, all_6_0)
% 7.40/1.76 | (6) d(berlin, cologne) = 480
% 7.40/1.76 | (7) d(cologne, berlin) = all_6_0
% 7.40/1.76 | (8) ! [v0: city] : ! [v1: city] : ! [v2: int] : ( ~ (d(v0, v1) = v2) |
% 7.40/1.76 | ~ city(v1) | ~ city(v0) | d(v1, v0) = v2)
% 7.40/1.76 |
% 7.40/1.76 | GROUND_INST: instantiating (8) with berlin, cologne, 480, simplifying with
% 7.40/1.76 | (1), (2), (6) gives:
% 7.40/1.76 | (9) d(cologne, berlin) = 480
% 7.40/1.76 |
% 7.40/1.76 | GROUND_INST: instantiating (function-axioms) with all_6_0, 480, berlin,
% 7.40/1.76 | cologne, simplifying with (7), (9) gives:
% 7.40/1.76 | (10) all_6_0 = 480
% 7.40/1.76 |
% 7.40/1.76 | REDUCE: (5), (10) imply:
% 7.40/1.76 | (11) $false
% 7.40/1.76 |
% 7.40/1.76 | CLOSE: (11) is inconsistent.
% 7.40/1.76 |
% 7.40/1.76 End of proof
% 7.40/1.76 % SZS output end Proof for theBenchmark
% 7.40/1.76
% 7.40/1.76 1137ms
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