TSTP Solution File: ARI712_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI712_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 : n002.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 17:48:54 EDT 2023

% Result   : Theorem 5.67s 1.55s
% Output   : Proof 6.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : ARI712_1 : TPTP v8.1.2. Released v6.3.0.
% 0.08/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 18:55:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.47/1.07  Prover 0: Preprocessing ...
% 2.47/1.07  Prover 5: Preprocessing ...
% 2.47/1.08  Prover 3: Preprocessing ...
% 2.47/1.08  Prover 2: Preprocessing ...
% 2.47/1.08  Prover 4: Preprocessing ...
% 2.47/1.08  Prover 1: Preprocessing ...
% 2.47/1.08  Prover 6: Preprocessing ...
% 2.84/1.17  Prover 5: Constructing countermodel ...
% 2.84/1.17  Prover 0: Constructing countermodel ...
% 2.84/1.17  Prover 3: Constructing countermodel ...
% 2.84/1.17  Prover 4: Constructing countermodel ...
% 2.84/1.17  Prover 2: Constructing countermodel ...
% 2.84/1.17  Prover 6: Constructing countermodel ...
% 2.84/1.17  Prover 1: Constructing countermodel ...
% 5.67/1.55  Prover 2: proved (923ms)
% 5.67/1.55  Prover 0: proved (926ms)
% 5.67/1.55  Prover 6: proved (921ms)
% 5.67/1.55  
% 5.67/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55  
% 5.67/1.55  Prover 3: proved (925ms)
% 5.67/1.55  
% 5.67/1.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.55  
% 5.67/1.56  
% 5.67/1.56  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.56  
% 5.85/1.57  
% 5.85/1.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.85/1.57  
% 5.85/1.57  Prover 5: proved (923ms)
% 5.85/1.57  
% 5.85/1.57  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.85/1.57  
% 5.85/1.59  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.85/1.59  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.85/1.59  Prover 7: Preprocessing ...
% 5.85/1.59  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.85/1.59  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.85/1.59  Prover 1: Found proof (size 20)
% 5.85/1.59  Prover 4: Found proof (size 20)
% 5.85/1.59  Prover 4: proved (960ms)
% 5.85/1.59  Prover 1: proved (960ms)
% 5.85/1.59  Prover 8: Preprocessing ...
% 5.85/1.59  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.85/1.59  Prover 7: Constructing countermodel ...
% 5.85/1.59  Prover 7: stopped
% 5.85/1.60  Prover 10: Preprocessing ...
% 5.85/1.60  Prover 8: Constructing countermodel ...
% 5.85/1.60  Prover 8: stopped
% 5.85/1.60  Prover 11: Preprocessing ...
% 5.85/1.61  Prover 13: Preprocessing ...
% 5.85/1.61  Prover 10: Constructing countermodel ...
% 5.85/1.61  Prover 10: stopped
% 5.85/1.62  Prover 11: Constructing countermodel ...
% 5.85/1.62  Prover 11: stopped
% 5.85/1.62  Prover 13: Constructing countermodel ...
% 5.85/1.62  Prover 13: stopped
% 5.85/1.62  
% 5.85/1.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.85/1.62  
% 6.27/1.63  % SZS output start Proof for theBenchmark
% 6.27/1.63  Assumptions after simplification:
% 6.27/1.63  ---------------------------------
% 6.27/1.63  
% 6.27/1.63    (conj)
% 6.27/1.64     ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :  ? [v4: int] :  ?
% 6.27/1.64    [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] :  ?
% 6.27/1.64    [v10: int] :  ? [v11: int] :  ? [v12: int] :  ? [v13: int] :  ? [v14: int] : 
% 6.27/1.64    ? [v15: int] :  ? [v16: int] :  ? [v17: int] :  ? [v18: int] :  ? [v19: int] :
% 6.27/1.64     ? [v20: int] :  ? [v21: int] :  ? [v22: int] :  ? [v23: int] :  ? [v24: int]
% 6.27/1.64    : ( ~
% 6.27/1.64      ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(v24,
% 6.27/1.64                                  v20), v18), v17), v13), v12), v11), v10), v9),
% 6.27/1.64                  v5), v4), $product(2, d)), $product(2, c)), b) = $product(2, a))
% 6.27/1.64      & $product(v23, a) = v24 & $product(v22, a) = v23 & $product(v21, b) = v22 &
% 6.27/1.64      $product(v19, a) = v20 & $product(v18, c) = v21 & $product(v16, a) = v17 &
% 6.27/1.64      $product(v15, a) = v16 & $product(v14, b) = v15 & $product(v13, c) = v14 &
% 6.27/1.64      $product(v11, a) = v12 & $product(v8, a) = v9 & $product(v7, b) = v8 &
% 6.27/1.64      $product(v6, b) = v7 & $product(v3, a) = v4 & $product(v2, b) = v3 &
% 6.27/1.64      $product(v1, b) = v2 & $product(v0, d) = v1 & $product(v0, c) = v6 &
% 6.27/1.64      $product(d, d) = v0 & $product(d, c) = v18 & $product(d, b) = v19 &
% 6.27/1.64      $product(c, c) = v13 & $product(c, b) = v11 & $product(c, a) = v10 &
% 6.27/1.64      $product(a, a) = v5)
% 6.27/1.64  
% 6.27/1.64    (eq)
% 6.27/1.64     ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :  ? [v4: int] :  ?
% 6.27/1.64    [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] :
% 6.27/1.64    ($product(v7, b) = v8 & $product(v5, a) = v6 & $product($sum(v4, v2),
% 6.27/1.64        $sum($sum(v8, v6), 1)) = v9 & $product(v3, a) = v4 & $product(v1, c) = v2
% 6.27/1.64      & $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(v9, v0), b)
% 6.27/1.64      & $product(d, d) = v7 & $product(c, c) = v5 & $product(b, d) = v3 &
% 6.27/1.64      $product(a, b) = v1 & $product(a, a) = v0)
% 6.27/1.64  
% 6.27/1.64  Those formulas are unsatisfiable:
% 6.27/1.64  ---------------------------------
% 6.27/1.64  
% 6.27/1.64  Begin of proof
% 6.27/1.65  | 
% 6.27/1.65  | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1, all_2_2,
% 6.27/1.65  |        all_2_3, all_2_4, all_2_5, all_2_6, all_2_7, all_2_8, all_2_9 gives:
% 6.27/1.65  |   (1)  $product(all_2_2, b) = all_2_1 & $product(all_2_4, a) = all_2_3 &
% 6.27/1.65  |        $product($sum(all_2_5, all_2_7), $sum($sum(all_2_1, all_2_3), 1)) =
% 6.27/1.65  |        all_2_0 & $product(all_2_6, a) = all_2_5 & $product(all_2_8, c) =
% 6.27/1.65  |        all_2_7 & $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) =
% 6.27/1.65  |        $sum($sum(all_2_0, all_2_9), b) & $product(d, d) = all_2_2 &
% 6.27/1.65  |        $product(c, c) = all_2_4 & $product(b, d) = all_2_6 & $product(a, b) =
% 6.27/1.65  |        all_2_8 & $product(a, a) = all_2_9
% 6.27/1.65  | 
% 6.27/1.65  | ALPHA: (1) implies:
% 6.27/1.65  |   (2)  $product(a, a) = all_2_9
% 6.27/1.65  |   (3)  $product(a, b) = all_2_8
% 6.27/1.65  |   (4)  $product(b, d) = all_2_6
% 6.27/1.65  |   (5)  $product(c, c) = all_2_4
% 6.27/1.65  |   (6)  $product(d, d) = all_2_2
% 6.27/1.65  |   (7)  $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(all_2_0,
% 6.27/1.65  |            all_2_9), b)
% 6.27/1.65  |   (8)  $product(all_2_8, c) = all_2_7
% 6.27/1.65  |   (9)  $product(all_2_6, a) = all_2_5
% 6.27/1.65  |   (10)  $product($sum(all_2_5, all_2_7), $sum($sum(all_2_1, all_2_3), 1)) =
% 6.27/1.65  |         all_2_0
% 6.27/1.65  |   (11)  $product(all_2_4, a) = all_2_3
% 6.27/1.65  |   (12)  $product(all_2_2, b) = all_2_1
% 6.27/1.65  | 
% 6.43/1.65  | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2,
% 6.43/1.65  |        all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 6.43/1.65  |        all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16,
% 6.43/1.65  |        all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23,
% 6.43/1.65  |        all_4_24 gives:
% 6.43/1.66  |   (13)   ~
% 6.43/1.66  |         ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(all_4_0,
% 6.43/1.66  |                                     all_4_4), all_4_6), all_4_7), all_4_11),
% 6.43/1.66  |                             all_4_12), all_4_13), all_4_14), all_4_15),
% 6.43/1.66  |                     all_4_19), all_4_20), $product(2, d)), $product(2, c)), b)
% 6.43/1.66  |           = $product(2, a)) & $product(all_4_1, a) = all_4_0 &
% 6.43/1.66  |         $product(all_4_2, a) = all_4_1 & $product(all_4_3, b) = all_4_2 &
% 6.43/1.66  |         $product(all_4_5, a) = all_4_4 & $product(all_4_6, c) = all_4_3 &
% 6.43/1.66  |         $product(all_4_8, a) = all_4_7 & $product(all_4_9, a) = all_4_8 &
% 6.43/1.66  |         $product(all_4_10, b) = all_4_9 & $product(all_4_11, c) = all_4_10 &
% 6.43/1.66  |         $product(all_4_13, a) = all_4_12 & $product(all_4_16, a) = all_4_15 &
% 6.43/1.66  |         $product(all_4_17, b) = all_4_16 & $product(all_4_18, b) = all_4_17 &
% 6.43/1.66  |         $product(all_4_21, a) = all_4_20 & $product(all_4_22, b) = all_4_21 &
% 6.43/1.66  |         $product(all_4_23, b) = all_4_22 & $product(all_4_24, d) = all_4_23 &
% 6.43/1.66  |         $product(all_4_24, c) = all_4_18 & $product(d, d) = all_4_24 &
% 6.43/1.66  |         $product(d, c) = all_4_6 & $product(d, b) = all_4_5 & $product(c, c) =
% 6.43/1.66  |         all_4_11 & $product(c, b) = all_4_13 & $product(c, a) = all_4_14 &
% 6.43/1.66  |         $product(a, a) = all_4_19
% 6.43/1.66  | 
% 6.43/1.66  | ALPHA: (13) implies:
% 6.43/1.66  |   (14)   ~
% 6.43/1.66  |         ($difference($difference($difference($sum($sum($sum($difference($difference($sum($difference($sum($difference($sum(all_4_0,
% 6.43/1.66  |                                     all_4_4), all_4_6), all_4_7), all_4_11),
% 6.43/1.66  |                             all_4_12), all_4_13), all_4_14), all_4_15),
% 6.43/1.66  |                     all_4_19), all_4_20), $product(2, d)), $product(2, c)), b)
% 6.43/1.66  |           = $product(2, a))
% 6.43/1.66  |   (15)  $product(a, a) = all_4_19
% 6.43/1.66  |   (16)  $product(c, a) = all_4_14
% 6.43/1.66  |   (17)  $product(c, b) = all_4_13
% 6.43/1.66  |   (18)  $product(c, c) = all_4_11
% 6.43/1.66  |   (19)  $product(d, b) = all_4_5
% 6.43/1.66  |   (20)  $product(d, c) = all_4_6
% 6.43/1.66  |   (21)  $product(d, d) = all_4_24
% 6.43/1.66  |   (22)  $product(all_4_24, c) = all_4_18
% 6.43/1.66  |   (23)  $product(all_4_24, d) = all_4_23
% 6.43/1.66  |   (24)  $product(all_4_23, b) = all_4_22
% 6.43/1.66  |   (25)  $product(all_4_22, b) = all_4_21
% 6.43/1.66  |   (26)  $product(all_4_21, a) = all_4_20
% 6.43/1.66  |   (27)  $product(all_4_18, b) = all_4_17
% 6.43/1.66  |   (28)  $product(all_4_17, b) = all_4_16
% 6.43/1.66  |   (29)  $product(all_4_16, a) = all_4_15
% 6.43/1.66  |   (30)  $product(all_4_13, a) = all_4_12
% 6.43/1.66  |   (31)  $product(all_4_11, c) = all_4_10
% 6.43/1.66  |   (32)  $product(all_4_10, b) = all_4_9
% 6.43/1.66  |   (33)  $product(all_4_9, a) = all_4_8
% 6.43/1.66  |   (34)  $product(all_4_8, a) = all_4_7
% 6.43/1.66  |   (35)  $product(all_4_6, c) = all_4_3
% 6.43/1.66  |   (36)  $product(all_4_5, a) = all_4_4
% 6.43/1.67  |   (37)  $product(all_4_3, b) = all_4_2
% 6.43/1.67  |   (38)  $product(all_4_2, a) = all_4_1
% 6.43/1.67  |   (39)  $product(all_4_1, a) = all_4_0
% 6.43/1.67  | 
% 6.43/1.67  | THEORY_AXIOM GroebnerMultiplication: 
% 6.43/1.67  |   (40)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 6.43/1.67  |           int] :  ! [v5: int] :  ! [v6: int] :  ! [v7: int] :  ! [v8: int] : 
% 6.43/1.67  |         ! [v9: int] :  ! [v10: int] :  ! [v11: int] :  ! [v12: int] :  ! [v13:
% 6.43/1.67  |           int] :  ! [v14: int] :  ! [v15: int] :  ! [v16: int] :  ! [v17: int]
% 6.43/1.67  |         :  ! [v18: int] :  ! [v19: int] :  ! [v20: int] :  ! [v21: int] :  !
% 6.43/1.67  |         [v22: int] :  ! [v23: int] :  ! [v24: int] :  ! [v25: int] :  ! [v26:
% 6.43/1.67  |           int] :  ! [v27: int] :  ! [v28: int] :  ! [v29: int] :  ! [v30: int]
% 6.43/1.67  |         :  ! [v31: int] :  ! [v32: int] :  ! [v33: int] :  ! [v34: int] :
% 6.43/1.67  |         ($difference($difference($difference($sum($sum($sum($difference($sum($sum($difference($difference($sum($difference(v34,
% 6.43/1.67  |                                     v30), v29), v24), v23), v22), v18), v9),
% 6.43/1.67  |                       v8), v6), v4), $product(2, v3)), $product(2, v2)), v1) =
% 6.43/1.67  |           $product(2, v0) |  ~ ($product(v33, v0) = v34) |  ~ ($product(v32,
% 6.43/1.67  |               v0) = v33) |  ~ ($product(v31, v1) = v32) |  ~ ($product(v30,
% 6.43/1.67  |               v2) = v31) |  ~ ($product(v28, v0) = v29) |  ~ ($product(v27,
% 6.43/1.67  |               v0) = v28) |  ~ ($product(v26, v1) = v27) |  ~ ($product(v25,
% 6.43/1.67  |               v2) = v26) |  ~ ($product(v21, v0) = v22) |  ~ ($product(v20,
% 6.43/1.67  |               v1) = v21) |  ~ ($product(v19, v1) = v20) |  ~ ($product(v17,
% 6.43/1.67  |               v0) = v18) |  ~ ($product(v16, v1) = v17) |  ~ ($product(v15,
% 6.43/1.67  |               v1) = v16) |  ~ ($product(v14, v3) = v15) |  ~ ($product(v14,
% 6.43/1.67  |               v2) = v19) |  ~ ($product(v11, v1) = v12) |  ~ ($product(v9, v0)
% 6.43/1.67  |             = v10) |  ~ ($product($sum(v8, v6), $sum($sum(v12, v10), 1)) =
% 6.43/1.67  |             v13) |  ~ ($product(v7, v0) = v8) |  ~ ($product(v5, v2) = v6) | 
% 6.43/1.67  |           ~ ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) =
% 6.43/1.67  |             $sum($sum(v13, v4), v1)) |  ~ ($product(v3, v3) = v14) |  ~
% 6.43/1.67  |           ($product(v3, v3) = v11) |  ~ ($product(v3, v2) = v30) |  ~
% 6.43/1.67  |           ($product(v2, v2) = v25) |  ~ ($product(v2, v2) = v9) |  ~
% 6.43/1.67  |           ($product(v2, v1) = v24) |  ~ ($product(v2, v0) = v23) |  ~
% 6.43/1.67  |           ($product(v1, v3) = v7) |  ~ ($product(v0, v1) = v5) |  ~
% 6.43/1.67  |           ($product(v0, v0) = v4))
% 6.43/1.67  | 
% 6.43/1.68  | GROUND_INST: instantiating (40) with a, b, c, d, all_2_9, all_2_8, all_2_7,
% 6.43/1.68  |              all_2_6, all_2_5, all_2_4, all_2_3, all_2_2, all_2_1, all_2_0,
% 6.43/1.68  |              all_4_24, all_4_23, all_4_22, all_4_21, all_4_20, all_4_18,
% 6.43/1.68  |              all_4_17, all_4_16, all_4_15, all_4_14, all_4_13, all_4_11,
% 6.43/1.68  |              all_4_10, all_4_9, all_4_8, all_4_7, all_4_6, all_4_3, all_4_2,
% 6.43/1.68  |              all_4_1, all_4_0, simplifying with (2), (3), (4), (5), (6), (7),
% 6.43/1.68  |              (8), (9), (10), (11), (12), (16), (17), (18), (20), (21), (22),
% 6.43/1.68  |              (23), (24), (25), (26), (27), (28), (29), (31), (32), (33), (34),
% 6.43/1.68  |              (35), (37), (38), (39) gives:
% 6.43/1.68  |   (41)  $difference($difference($difference($sum($sum($sum($difference($sum($sum($difference($difference($sum($difference(all_4_0,
% 6.43/1.68  |                                   all_4_6), all_4_7), all_4_13), all_4_14),
% 6.43/1.68  |                           all_4_15), all_4_20), all_2_4), all_2_5), all_2_7),
% 6.43/1.68  |                 all_2_9), $product(2, d)), $product(2, c)), b) = $product(2,
% 6.43/1.68  |           a)
% 6.43/1.68  | 
% 6.43/1.68  | THEORY_AXIOM GroebnerMultiplication: 
% 6.43/1.68  |   (42)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 6.43/1.68  |           int] :  ! [v5: int] :  ! [v6: int] :  ! [v7: int] :  ! [v8: int] : 
% 6.43/1.68  |         ! [v9: int] :  ! [v10: int] :  ! [v11: int] :  ! [v12: int] :  ! [v13:
% 6.43/1.68  |           int] :  ! [v14: int] :  ! [v15: int] :  ! [v16: int] :  ! [v17: int]
% 6.43/1.68  |         :  ! [v18: int] :  ! [v19: int] :  ! [v20: int] :  ! [v21: int] :  !
% 6.43/1.68  |         [v22: int] :  ! [v23: int] :  ! [v24: int] :  ! [v25: int] :  ! [v26:
% 6.43/1.68  |           int] :  ! [v27: int] :  ! [v28: int] :  ! [v29: int] :  ! [v30: int]
% 6.43/1.68  |         :  ! [v31: int] :  ! [v32: int] :
% 6.43/1.68  |         ($sum($sum($difference($sum($sum($sum(v32, v27), v22), v18), v13),
% 6.43/1.68  |               v8), v6) = 0 |  ~ ($product(v31, v0) = v32) |  ~ ($product(v30,
% 6.43/1.68  |               v0) = v31) |  ~ ($product(v29, v1) = v30) |  ~ ($product(v28,
% 6.43/1.68  |               v2) = v29) |  ~ ($product(v26, v0) = v27) |  ~ ($product(v25,
% 6.43/1.68  |               v0) = v26) |  ~ ($product(v24, v1) = v25) |  ~ ($product(v23,
% 6.43/1.68  |               v2) = v24) |  ~ ($product(v21, v0) = v22) |  ~ ($product(v20,
% 6.43/1.68  |               v1) = v21) |  ~ ($product(v19, v1) = v20) |  ~ ($product(v17,
% 6.43/1.68  |               v0) = v18) |  ~ ($product(v16, v1) = v17) |  ~ ($product(v15,
% 6.43/1.68  |               v1) = v16) |  ~ ($product(v14, v3) = v15) |  ~ ($product(v14,
% 6.43/1.68  |               v2) = v19) |  ~ ($product(v11, v1) = v12) |  ~ ($product(v9, v0)
% 6.43/1.68  |             = v10) |  ~ ($product($sum(v8, v6), $sum($sum(v12, v10), 1)) =
% 6.43/1.68  |             v13) |  ~ ($product(v7, v0) = v8) |  ~ ($product(v5, v2) = v6) | 
% 6.43/1.68  |           ~ ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) =
% 6.43/1.68  |             $sum($sum(v13, v4), v1)) |  ~ ($product(v3, v3) = v14) |  ~
% 6.43/1.68  |           ($product(v3, v3) = v11) |  ~ ($product(v3, v2) = v28) |  ~
% 6.43/1.68  |           ($product(v2, v2) = v23) |  ~ ($product(v2, v2) = v9) |  ~
% 6.43/1.68  |           ($product(v1, v3) = v7) |  ~ ($product(v0, v1) = v5) |  ~
% 6.43/1.68  |           ($product(v0, v0) = v4))
% 6.43/1.68  | 
% 6.43/1.68  | GROUND_INST: instantiating (42) with a, b, c, d, all_2_9, all_2_8, all_2_7,
% 6.43/1.68  |              all_2_6, all_2_5, all_2_4, all_2_3, all_2_2, all_2_1, all_2_0,
% 6.43/1.68  |              all_4_24, all_4_23, all_4_22, all_4_21, all_4_20, all_4_18,
% 6.43/1.68  |              all_4_17, all_4_16, all_4_15, all_4_11, all_4_10, all_4_9,
% 6.43/1.68  |              all_4_8, all_4_7, all_4_6, all_4_3, all_4_2, all_4_1, all_4_0,
% 6.43/1.68  |              simplifying with (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 6.43/1.68  |              (11), (12), (18), (20), (21), (22), (23), (24), (25), (26), (27),
% 6.43/1.68  |              (28), (29), (31), (32), (33), (34), (35), (37), (38), (39) gives:
% 6.43/1.69  |   (43)  $sum($sum($difference($sum($sum($sum(all_4_0, all_4_7), all_4_15),
% 6.43/1.69  |                 all_4_20), all_2_0), all_2_5), all_2_7) = 0
% 6.43/1.69  | 
% 6.43/1.69  | THEORY_AXIOM GroebnerMultiplication: 
% 6.43/1.69  |   (44)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 6.43/1.69  |           int] :  ! [v5: int] :  ! [v6: int] : (v6 = v4 |  ~ ($product(v5, v0)
% 6.43/1.69  |             = v6) |  ~ ($product(v3, v0) = v4) |  ~ ($product(v2, v1) = v5) | 
% 6.43/1.69  |           ~ ($product(v1, v2) = v3))
% 6.43/1.69  | 
% 6.43/1.69  | GROUND_INST: instantiating (44) with a, b, d, all_2_6, all_2_5, all_4_5,
% 6.43/1.69  |              all_4_4, simplifying with (4), (9), (19), (36) gives:
% 6.43/1.69  |   (45)  all_4_4 = all_2_5
% 6.43/1.69  | 
% 6.43/1.69  | THEORY_AXIOM GroebnerMultiplication: 
% 6.43/1.69  |   (46)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : (v2 = v1 |  ~
% 6.43/1.69  |           ($product(v0, v0) = v2) |  ~ ($product(v0, v0) = v1))
% 6.43/1.69  | 
% 6.43/1.69  | GROUND_INST: instantiating (46) with c, all_2_4, all_4_11, simplifying with
% 6.43/1.69  |              (5), (18) gives:
% 6.43/1.69  |   (47)  all_4_11 = all_2_4
% 6.43/1.69  | 
% 6.43/1.69  | THEORY_AXIOM GroebnerMultiplication: 
% 6.43/1.69  |   (48)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 6.43/1.69  |           int] :  ! [v5: int] :  ! [v6: int] : (v6 = v4 |  ~ ($product(v5, v0)
% 6.43/1.69  |             = v6) |  ~ ($product(v3, v2) = v4) |  ~ ($product(v2, v1) = v5) | 
% 6.43/1.69  |           ~ ($product(v0, v1) = v3))
% 6.43/1.69  | 
% 6.43/1.69  | GROUND_INST: instantiating (48) with a, b, c, all_2_8, all_2_7, all_4_13,
% 6.43/1.69  |              all_4_12, simplifying with (3), (8), (17), (30) gives:
% 6.43/1.69  |   (49)  all_4_12 = all_2_7
% 6.43/1.69  | 
% 6.43/1.69  | GROUND_INST: instantiating (46) with a, all_2_9, all_4_19, simplifying with
% 6.43/1.69  |              (2), (15) gives:
% 6.43/1.69  |   (50)  all_4_19 = all_2_9
% 6.43/1.69  | 
% 6.43/1.69  | COMBINE_EQS: (41), (43) imply:
% 6.43/1.69  |   (51)  $sum($sum($sum($sum($difference($sum($difference($sum($sum(all_4_6,
% 6.43/1.69  |                           all_4_13), all_4_14), all_2_0), all_2_4), all_2_9),
% 6.43/1.69  |                 $product(2, d)), $product(2, c)), b), $product(2, a)) = 0
% 6.43/1.69  | 
% 6.43/1.69  | REDUCE: (14), (43), (45), (47), (49), (50), (51) imply:
% 6.43/1.69  |   (52)  $false
% 6.43/1.69  | 
% 6.43/1.69  | CLOSE: (52) is inconsistent.
% 6.43/1.69  | 
% 6.43/1.69  End of proof
% 6.43/1.69  % SZS output end Proof for theBenchmark
% 6.43/1.69  
% 6.43/1.69  1089ms
%------------------------------------------------------------------------------