TSTP Solution File: ARI679_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI679_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n018.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 17:48:47 EDT 2023

% Result   : Theorem 3.84s 1.43s
% Output   : Proof 4.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : ARI679_1 : TPTP v8.1.2. Released v6.3.0.
% 0.10/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n018.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 : Tue Aug 29 18:08:03 EDT 2023
% 0.13/0.35  % 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  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 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 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 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
% 2.40/1.15  Prover 0: Preprocessing ...
% 2.40/1.15  Prover 3: Preprocessing ...
% 2.40/1.15  Prover 4: Preprocessing ...
% 2.40/1.15  Prover 2: Preprocessing ...
% 2.40/1.15  Prover 5: Preprocessing ...
% 2.40/1.15  Prover 6: Preprocessing ...
% 2.40/1.15  Prover 1: Preprocessing ...
% 2.48/1.22  Prover 5: Constructing countermodel ...
% 2.48/1.23  Prover 0: Constructing countermodel ...
% 2.48/1.23  Prover 3: Constructing countermodel ...
% 2.48/1.23  Prover 4: Constructing countermodel ...
% 2.48/1.23  Prover 6: Constructing countermodel ...
% 2.48/1.23  Prover 1: Constructing countermodel ...
% 2.48/1.23  Prover 2: Constructing countermodel ...
% 3.84/1.43  Prover 5: proved (787ms)
% 3.84/1.43  Prover 6: proved (786ms)
% 3.84/1.43  Prover 0: proved (791ms)
% 3.84/1.43  
% 3.84/1.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.43  
% 3.84/1.43  Prover 3: proved (790ms)
% 3.84/1.43  
% 3.84/1.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.43  
% 3.84/1.43  Prover 2: proved (790ms)
% 3.84/1.44  
% 3.84/1.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.44  
% 3.84/1.44  
% 3.84/1.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.44  
% 3.84/1.44  
% 3.84/1.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.84/1.44  
% 3.84/1.44  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.84/1.44  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.84/1.44  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.84/1.44  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.84/1.45  Prover 10: Preprocessing ...
% 3.84/1.45  Prover 7: Preprocessing ...
% 3.84/1.45  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.84/1.45  Prover 11: Preprocessing ...
% 3.84/1.45  Prover 8: Preprocessing ...
% 3.84/1.46  Prover 10: Constructing countermodel ...
% 3.84/1.46  Prover 11: Constructing countermodel ...
% 3.84/1.46  Prover 8: Constructing countermodel ...
% 3.84/1.46  Prover 7: Constructing countermodel ...
% 3.84/1.47  Prover 13: Preprocessing ...
% 3.84/1.47  Prover 4: Found proof (size 22)
% 3.84/1.47  Prover 4: proved (829ms)
% 3.84/1.47  Prover 1: Found proof (size 22)
% 3.84/1.47  Prover 1: proved (833ms)
% 3.84/1.47  Prover 7: stopped
% 3.84/1.47  Prover 11: stopped
% 3.84/1.47  Prover 10: stopped
% 3.84/1.47  Prover 8: stopped
% 4.39/1.48  Prover 13: Constructing countermodel ...
% 4.39/1.48  Prover 13: stopped
% 4.39/1.48  
% 4.39/1.48  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.39/1.48  
% 4.39/1.49  % SZS output start Proof for theBenchmark
% 4.39/1.49  Assumptions after simplification:
% 4.39/1.49  ---------------------------------
% 4.39/1.49  
% 4.39/1.49    (conj)
% 4.39/1.49    $lesseq(3, d)
% 4.39/1.49  
% 4.39/1.49    (conj_001)
% 4.39/1.49    $lesseq(2, c)
% 4.39/1.49  
% 4.39/1.49    (conj_002)
% 4.47/1.50     ? [v0: int] :  ? [v1: int] : ($product(c, $sum(d, -3)) = v1 & $product(c, d)
% 4.47/1.50      = v0 & (($lesseq(7, $difference($product(2, d), v1)) & $lesseq(6, v0)) |
% 4.47/1.50        ($lesseq(-6, $difference(v1, $product(2, d))) & $lesseq(v0, 5))))
% 4.47/1.50  
% 4.47/1.50  Those formulas are unsatisfiable:
% 4.47/1.50  ---------------------------------
% 4.47/1.50  
% 4.47/1.50  Begin of proof
% 4.47/1.50  | 
% 4.47/1.50  | DELTA: instantiating (conj_002) with fresh symbols all_3_0, all_3_1 gives:
% 4.47/1.50  |   (1)  $product(c, $sum(d, -3)) = all_3_0 & $product(c, d) = all_3_1 &
% 4.47/1.50  |        (($lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6,
% 4.47/1.50  |              all_3_1)) | ($lesseq(-6, $difference(all_3_0, $product(2, d))) &
% 4.47/1.50  |            $lesseq(all_3_1, 5)))
% 4.47/1.50  | 
% 4.47/1.50  | ALPHA: (1) implies:
% 4.47/1.50  |   (2)  $product(c, d) = all_3_1
% 4.47/1.50  |   (3)  $product(c, $sum(d, -3)) = all_3_0
% 4.47/1.51  |   (4)  ($lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6,
% 4.47/1.51  |            all_3_1)) | ($lesseq(-6, $difference(all_3_0, $product(2, d))) &
% 4.47/1.51  |          $lesseq(all_3_1, 5))
% 4.47/1.51  | 
% 4.47/1.51  | THEORY_AXIOM GroebnerMultiplication: 
% 4.47/1.51  |   (5)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :
% 4.47/1.51  |        ($sum($difference(v3, v2), $product(3, v1)) = 0 |  ~ ($product(v1,
% 4.47/1.51  |              $sum(v0, -3)) = v3) |  ~ ($product(v1, v0) = v2))
% 4.47/1.51  | 
% 4.47/1.51  | GROUND_INST: instantiating (5) with d, c, all_3_1, all_3_0, simplifying with
% 4.47/1.51  |              (2), (3) gives:
% 4.47/1.51  |   (6)  $sum($difference(all_3_0, all_3_1), $product(3, c)) = 0
% 4.47/1.51  | 
% 4.47/1.51  | THEORY_AXIOM GroebnerMultiplication: 
% 4.47/1.51  |   (7)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : ( ~ ($lesseq(7,
% 4.47/1.51  |              $sum($difference($product(3, v1), v2), $product(2, v0)))) |  ~
% 4.47/1.51  |          ($lesseq(2, v1)) |  ~ ($lesseq(3, v0)) |  ~ ($product(v1, v0) = v2))
% 4.47/1.51  | 
% 4.47/1.51  | GROUND_INST: instantiating (7) with d, c, all_3_1, simplifying with (2) gives:
% 4.47/1.51  |   (8)   ~ ($lesseq(7, $sum($difference($product(3, c), all_3_1), $product(2,
% 4.47/1.51  |                d)))) |  ~ ($lesseq(2, c)) |  ~ ($lesseq(3, d))
% 4.47/1.51  | 
% 4.47/1.51  | BETA: splitting (8) gives:
% 4.47/1.51  | 
% 4.47/1.51  | Case 1:
% 4.47/1.51  | | 
% 4.47/1.51  | |   (9)  $lesseq(c, 1)
% 4.47/1.51  | | 
% 4.47/1.51  | | COMBINE_INEQS: (9), (conj_001) imply:
% 4.47/1.51  | |   (10)  $false
% 4.47/1.51  | | 
% 4.47/1.51  | | CLOSE: (10) is inconsistent.
% 4.47/1.51  | | 
% 4.47/1.51  | Case 2:
% 4.47/1.51  | | 
% 4.47/1.51  | |   (11)   ~ ($lesseq(7, $sum($difference($product(3, c), all_3_1),
% 4.47/1.51  | |               $product(2, d)))) |  ~ ($lesseq(3, d))
% 4.47/1.51  | | 
% 4.47/1.51  | | BETA: splitting (11) gives:
% 4.47/1.51  | | 
% 4.47/1.51  | | Case 1:
% 4.47/1.51  | | | 
% 4.47/1.51  | | |   (12)  $lesseq(d, 2)
% 4.47/1.51  | | | 
% 4.47/1.51  | | | COMBINE_INEQS: (12), (conj) imply:
% 4.47/1.51  | | |   (13)  $false
% 4.47/1.51  | | | 
% 4.54/1.51  | | | CLOSE: (13) is inconsistent.
% 4.54/1.51  | | | 
% 4.54/1.51  | | Case 2:
% 4.54/1.51  | | | 
% 4.54/1.51  | | |   (14)  $lesseq(-6, $difference($difference(all_3_1, $product(3, c)),
% 4.54/1.51  | | |             $product(2, d)))
% 4.54/1.51  | | | 
% 4.54/1.51  | | | COMBINE_INEQS: (14), (conj_001) imply:
% 4.54/1.51  | | |   (15)  $lesseq(0, $difference(all_3_1, $product(2, d)))
% 4.54/1.51  | | | 
% 4.54/1.52  | | | COMBINE_INEQS: (15), (conj) imply:
% 4.54/1.52  | | |   (16)  $lesseq(6, all_3_1)
% 4.54/1.52  | | | 
% 4.54/1.52  | | | BETA: splitting (4) gives:
% 4.54/1.52  | | | 
% 4.54/1.52  | | | Case 1:
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | |   (17)  $lesseq(7, $difference($product(2, d), all_3_0)) & $lesseq(6,
% 4.54/1.52  | | | |           all_3_1)
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | ALPHA: (17) implies:
% 4.54/1.52  | | | |   (18)  $lesseq(7, $difference($product(2, d), all_3_0))
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | REDUCE: (6), (18) imply:
% 4.54/1.52  | | | |   (19)  $lesseq(7, $sum($difference($product(3, c), all_3_1),
% 4.54/1.52  | | | |             $product(2, d)))
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | COMBINE_INEQS: (14), (19) imply:
% 4.54/1.52  | | | |   (20)  $false
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | CLOSE: (20) is inconsistent.
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | Case 2:
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | |   (21)  $lesseq(-6, $difference(all_3_0, $product(2, d))) &
% 4.54/1.52  | | | |         $lesseq(all_3_1, 5)
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | ALPHA: (21) implies:
% 4.54/1.52  | | | |   (22)  $lesseq(all_3_1, 5)
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | COMBINE_INEQS: (16), (22) imply:
% 4.54/1.52  | | | |   (23)  $false
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | | CLOSE: (23) is inconsistent.
% 4.54/1.52  | | | | 
% 4.54/1.52  | | | End of split
% 4.54/1.52  | | | 
% 4.54/1.52  | | End of split
% 4.54/1.52  | | 
% 4.54/1.52  | End of split
% 4.54/1.52  | 
% 4.54/1.52  End of proof
% 4.54/1.52  % SZS output end Proof for theBenchmark
% 4.54/1.52  
% 4.54/1.52  897ms
%------------------------------------------------------------------------------