TSTP Solution File: ARI616_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n015.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 17:48:35 EDT 2023

% Result   : Theorem 3.48s 1.20s
% Output   : Proof 3.69s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34  % Computer : n015.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Aug 29 18:30:41 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.20/0.62  ________       _____
% 0.20/0.62  ___  __ \_________(_)________________________________
% 0.20/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62  
% 0.20/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62  (2023-06-19)
% 0.20/0.62  
% 0.20/0.62  (c) Philipp Rümmer, 2009-2023
% 0.20/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62                Amanda Stjerna.
% 0.20/0.62  Free software under BSD-3-Clause.
% 0.20/0.62  
% 0.20/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62  
% 0.20/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63  Running up to 7 provers in parallel.
% 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 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 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
% 2.22/1.01  Prover 1: Preprocessing ...
% 2.22/1.01  Prover 4: Preprocessing ...
% 2.22/1.05  Prover 0: Preprocessing ...
% 2.22/1.05  Prover 5: Preprocessing ...
% 2.22/1.05  Prover 2: Preprocessing ...
% 2.22/1.05  Prover 6: Preprocessing ...
% 2.22/1.05  Prover 3: Preprocessing ...
% 2.70/1.12  Prover 1: Constructing countermodel ...
% 2.70/1.12  Prover 4: Constructing countermodel ...
% 2.70/1.12  Prover 5: Proving ...
% 2.70/1.12  Prover 2: Proving ...
% 2.70/1.12  Prover 6: Proving ...
% 2.70/1.12  Prover 3: Constructing countermodel ...
% 2.70/1.12  Prover 0: Proving ...
% 3.48/1.20  Prover 3: proved (556ms)
% 3.48/1.20  
% 3.48/1.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.20  
% 3.48/1.20  Prover 2: stopped
% 3.48/1.20  Prover 6: stopped
% 3.48/1.21  Prover 0: stopped
% 3.48/1.21  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.48/1.21  Prover 5: proved (563ms)
% 3.48/1.21  
% 3.48/1.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.21  
% 3.48/1.21  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.48/1.21  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.48/1.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.48/1.22  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.65/1.22  Prover 7: Preprocessing ...
% 3.65/1.22  Prover 4: Found proof (size 7)
% 3.65/1.22  Prover 4: proved (581ms)
% 3.69/1.22  Prover 1: Found proof (size 12)
% 3.69/1.22  Prover 1: proved (585ms)
% 3.69/1.22  Prover 8: Preprocessing ...
% 3.69/1.23  Prover 10: Preprocessing ...
% 3.69/1.23  Prover 13: Preprocessing ...
% 3.69/1.24  Prover 11: Preprocessing ...
% 3.69/1.24  Prover 7: Warning: ignoring some quantifiers
% 3.69/1.24  Prover 7: Constructing countermodel ...
% 3.69/1.24  Prover 7: stopped
% 3.69/1.25  Prover 13: Warning: ignoring some quantifiers
% 3.69/1.25  Prover 13: Constructing countermodel ...
% 3.69/1.25  Prover 13: stopped
% 3.69/1.25  Prover 8: Warning: ignoring some quantifiers
% 3.69/1.25  Prover 10: Warning: ignoring some quantifiers
% 3.69/1.25  Prover 10: Constructing countermodel ...
% 3.69/1.26  Prover 10: stopped
% 3.69/1.26  Prover 8: Constructing countermodel ...
% 3.69/1.26  Prover 8: stopped
% 3.69/1.27  Prover 11: Constructing countermodel ...
% 3.69/1.27  Prover 11: stopped
% 3.69/1.27  
% 3.69/1.27  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.69/1.27  
% 3.69/1.28  % SZS output start Proof for theBenchmark
% 3.69/1.28  Assumptions after simplification:
% 3.69/1.28  ---------------------------------
% 3.69/1.28  
% 3.69/1.28    (sum_of_radii_gt_distance_of_centers)
% 3.69/1.30     ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :  ? [v4: int] :
% 3.69/1.30    ($lesseq(1, $sum($difference($difference($product(-1, v3), v2), v1), v0)) &
% 3.69/1.30      p(v4, v2, v3) = 0 & p(v4, v0, v1) = 0 &  ! [v5: int] :  ! [v6: int] :  !
% 3.69/1.30      [v7: int] :  ! [v8: int] : (v8 = 0 |  ~ ($lesseq(0, $sum($difference(v7,
% 3.69/1.30                v6), v5))) |  ~ ($lesseq(v5, $sum(v7, v6))) |  ~ (p(v5, v6, v7) =
% 3.69/1.30          v8)) &  ! [v5: int] :  ! [v6: int] :  ! [v7: int] : ( ~ ($lesseq(1,
% 3.69/1.30            $sum($difference($product(-1, v7), v6), v5))) |  ~ (p(v5, v6, v7) =
% 3.69/1.30          0)) &  ! [v5: int] :  ! [v6: int] :  ! [v7: int] : ( ~ ($lesseq(1,
% 3.69/1.30            $difference($difference(v6, v7), v5))) |  ~ (p(v5, v6, v7) = 0)))
% 3.69/1.30  
% 3.69/1.30  Those formulas are unsatisfiable:
% 3.69/1.30  ---------------------------------
% 3.69/1.30  
% 3.69/1.30  Begin of proof
% 3.69/1.30  | 
% 3.69/1.31  | DELTA: instantiating (sum_of_radii_gt_distance_of_centers) with fresh symbols
% 3.69/1.31  |        all_3_0, all_3_1, all_3_2, all_3_3, all_3_4 gives:
% 3.69/1.31  |   (1)  $lesseq(1, $sum($difference($difference($product(-1, all_3_1),
% 3.69/1.31  |                all_3_2), all_3_3), all_3_4)) & p(all_3_0, all_3_2, all_3_1) =
% 3.69/1.31  |        0 & p(all_3_0, all_3_4, all_3_3) = 0 &  ! [v0: int] :  ! [v1: int] :  !
% 3.69/1.31  |        [v2: int] :  ! [v3: int] : (v3 = 0 |  ~ ($lesseq(0,
% 3.69/1.31  |              $sum($difference(v2, v1), v0))) |  ~ ($lesseq(v0, $sum(v2, v1)))
% 3.69/1.31  |          |  ~ (p(v0, v1, v2) = v3)) &  ! [v0: int] :  ! [v1: int] :  ! [v2:
% 3.69/1.31  |          int] : ( ~ ($lesseq(1, $sum($difference($product(-1, v2), v1), v0)))
% 3.69/1.31  |          |  ~ (p(v0, v1, v2) = 0)) &  ! [v0: int] :  ! [v1: int] :  ! [v2:
% 3.69/1.31  |          int] : ( ~ ($lesseq(1, $difference($difference(v1, v2), v0))) |  ~
% 3.69/1.31  |          (p(v0, v1, v2) = 0))
% 3.69/1.31  | 
% 3.69/1.31  | ALPHA: (1) implies:
% 3.69/1.31  |   (2)  $lesseq(1, $sum($difference($difference($product(-1, all_3_1),
% 3.69/1.31  |                all_3_2), all_3_3), all_3_4))
% 3.69/1.32  |   (3)  p(all_3_0, all_3_4, all_3_3) = 0
% 3.69/1.32  |   (4)  p(all_3_0, all_3_2, all_3_1) = 0
% 3.69/1.32  |   (5)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : ( ~ ($lesseq(1,
% 3.69/1.32  |              $difference($difference(v1, v2), v0))) |  ~ (p(v0, v1, v2) = 0))
% 3.69/1.32  |   (6)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : ( ~ ($lesseq(1,
% 3.69/1.32  |              $sum($difference($product(-1, v2), v1), v0))) |  ~ (p(v0, v1, v2)
% 3.69/1.32  |            = 0))
% 3.69/1.32  | 
% 3.69/1.32  | GROUND_INST: instantiating (5) with all_3_0, all_3_4, all_3_3, simplifying
% 3.69/1.32  |              with (3) gives:
% 3.69/1.32  |   (7)  $lesseq(all_3_4, $sum(all_3_0, all_3_3))
% 3.69/1.32  | 
% 3.69/1.32  | GROUND_INST: instantiating (6) with all_3_0, all_3_2, all_3_1, simplifying
% 3.69/1.32  |              with (4) gives:
% 3.69/1.32  |   (8)  $lesseq(0, $sum($difference(all_3_1, all_3_0), all_3_2))
% 3.69/1.32  | 
% 3.69/1.32  | COMBINE_INEQS: (7), (8) imply:
% 3.69/1.32  |   (9)  $lesseq(all_3_4, $sum($sum(all_3_1, all_3_2), all_3_3))
% 3.69/1.32  | 
% 3.69/1.32  | COMBINE_INEQS: (2), (9) imply:
% 3.69/1.32  |   (10)  $false
% 3.69/1.32  | 
% 3.69/1.32  | CLOSE: (10) is inconsistent.
% 3.69/1.32  | 
% 3.69/1.32  End of proof
% 3.69/1.32  % SZS output end Proof for theBenchmark
% 3.69/1.32  
% 3.69/1.32  703ms
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