TSTP Solution File: ARI685_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ARI685_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 : n011.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 17:48:48 EDT 2023

% Result   : Theorem 4.66s 1.37s
% Output   : Proof 5.42s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ARI685_1 : TPTP v8.1.2. Released v6.3.0.
% 0.12/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n011.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 18:36:56 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/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.03  Prover 3: Preprocessing ...
% 2.08/1.03  Prover 2: Preprocessing ...
% 2.08/1.03  Prover 0: Preprocessing ...
% 2.08/1.03  Prover 1: Preprocessing ...
% 2.08/1.03  Prover 4: Preprocessing ...
% 2.08/1.03  Prover 5: Preprocessing ...
% 2.08/1.03  Prover 6: Preprocessing ...
% 2.94/1.11  Prover 0: Constructing countermodel ...
% 2.94/1.11  Prover 2: Constructing countermodel ...
% 2.94/1.11  Prover 3: Constructing countermodel ...
% 2.94/1.11  Prover 6: Constructing countermodel ...
% 2.94/1.11  Prover 5: Constructing countermodel ...
% 2.94/1.11  Prover 4: Constructing countermodel ...
% 2.94/1.11  Prover 1: Constructing countermodel ...
% 4.66/1.36  Prover 2: proved (725ms)
% 4.66/1.36  Prover 5: proved (722ms)
% 4.66/1.37  
% 4.66/1.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.66/1.37  
% 4.66/1.37  
% 4.66/1.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.66/1.37  
% 4.66/1.37  Prover 0: proved (727ms)
% 4.66/1.37  
% 4.66/1.37  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.66/1.37  
% 4.66/1.37  Prover 3: stopped
% 4.66/1.38  Prover 6: stopped
% 4.66/1.38  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.66/1.38  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.66/1.38  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.66/1.38  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.66/1.38  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.66/1.39  Prover 7: Preprocessing ...
% 4.66/1.39  Prover 8: Preprocessing ...
% 4.66/1.40  Prover 4: Found proof (size 17)
% 4.66/1.40  Prover 4: proved (760ms)
% 4.66/1.40  Prover 1: stopped
% 4.66/1.40  Prover 11: Preprocessing ...
% 4.66/1.40  Prover 7: Constructing countermodel ...
% 4.66/1.41  Prover 7: stopped
% 4.66/1.41  Prover 8: Constructing countermodel ...
% 4.66/1.41  Prover 8: stopped
% 4.66/1.41  Prover 13: Preprocessing ...
% 4.66/1.41  Prover 10: Preprocessing ...
% 4.66/1.42  Prover 11: Constructing countermodel ...
% 4.66/1.42  Prover 11: stopped
% 4.66/1.42  Prover 13: Constructing countermodel ...
% 4.66/1.42  Prover 13: stopped
% 4.66/1.43  Prover 10: Constructing countermodel ...
% 4.66/1.43  Prover 10: stopped
% 4.66/1.43  
% 4.66/1.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.66/1.43  
% 4.66/1.43  % SZS output start Proof for theBenchmark
% 4.66/1.43  Assumptions after simplification:
% 4.66/1.43  ---------------------------------
% 4.66/1.43  
% 4.66/1.43    (conj)
% 4.66/1.44     ? [v0: int] :  ? [v1: int] :  ? [v2: int] :  ? [v3: int] :  ? [v4: int] :  ?
% 4.66/1.44    [v5: int] :  ? [v6: int] :  ? [v7: int] :  ? [v8: int] :  ? [v9: int] :  ?
% 4.66/1.44    [v10: int] :  ? [v11: int] : ( ~
% 4.66/1.44      ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(v11,
% 4.66/1.44                                    v10), v9), $product(2, v8)), v7), v6), v5),
% 4.66/1.44                        v4), v3), $product(2, v2)), v1), $product(2, v0)),
% 4.66/1.44              $product(2, d)), $product(2, c)), b) = 0) & $product(v8, a) = v11 &
% 4.66/1.44      $product(v5, a) = v9 & $product(v3, a) = v7 & $product(v0, a) = v1 &
% 4.66/1.44      $product(d, c) = v10 & $product(d, b) = v0 & $product(d, a) = v8 &
% 4.66/1.44      $product(c, c) = v6 & $product(c, b) = v5 & $product(c, a) = v3 &
% 4.66/1.44      $product(b, a) = v4 & $product(a, a) = v2)
% 4.66/1.44  
% 4.66/1.44    (eq)
% 4.66/1.45     ? [v0: int] :  ? [v1: int] :  ? [v2: int] : ($product(v1, $sum(a, 2)) = v2 &
% 4.66/1.45      $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(v2, v0), b) &
% 4.66/1.45      $product($sum(b, a), $sum($sum(d, c), 1)) = v1 & $product(a, a) = v0)
% 4.66/1.45  
% 4.66/1.45  Those formulas are unsatisfiable:
% 4.66/1.45  ---------------------------------
% 4.66/1.45  
% 4.66/1.45  Begin of proof
% 4.66/1.45  | 
% 4.66/1.45  | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1, all_2_2 gives:
% 5.31/1.45  |   (1)  $product(all_2_1, $sum(a, 2)) = all_2_0 & $product($sum($sum($sum(d,
% 5.31/1.45  |                c), b), a), $sum(c, 2)) = $sum($sum(all_2_0, all_2_2), b) &
% 5.31/1.45  |        $product($sum(b, a), $sum($sum(d, c), 1)) = all_2_1 & $product(a, a) =
% 5.31/1.45  |        all_2_2
% 5.31/1.45  | 
% 5.31/1.45  | ALPHA: (1) implies:
% 5.31/1.45  |   (2)  $product(a, a) = all_2_2
% 5.31/1.45  |   (3)  $product($sum(b, a), $sum($sum(d, c), 1)) = all_2_1
% 5.31/1.45  |   (4)  $product($sum($sum($sum(d, c), b), a), $sum(c, 2)) = $sum($sum(all_2_0,
% 5.31/1.45  |            all_2_2), b)
% 5.31/1.45  |   (5)  $product(all_2_1, $sum(a, 2)) = all_2_0
% 5.31/1.45  | 
% 5.31/1.45  | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2,
% 5.31/1.45  |        all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 5.31/1.45  |        all_4_10, all_4_11 gives:
% 5.31/1.46  |   (6)   ~
% 5.31/1.46  |        ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_4_0,
% 5.31/1.46  |                                      all_4_1), all_4_2), $product(2,
% 5.31/1.46  |                                    all_4_3)), all_4_4), all_4_5), all_4_6),
% 5.31/1.46  |                          all_4_7), all_4_8), $product(2, all_4_9)), all_4_10),
% 5.31/1.46  |                  $product(2, all_4_11)), $product(2, d)), $product(2, c)), b)
% 5.31/1.46  |          = 0) & $product(all_4_3, a) = all_4_0 & $product(all_4_6, a) =
% 5.31/1.46  |        all_4_2 & $product(all_4_8, a) = all_4_4 & $product(all_4_11, a) =
% 5.31/1.46  |        all_4_10 & $product(d, c) = all_4_1 & $product(d, b) = all_4_11 &
% 5.31/1.46  |        $product(d, a) = all_4_3 & $product(c, c) = all_4_5 & $product(c, b) =
% 5.31/1.46  |        all_4_6 & $product(c, a) = all_4_8 & $product(b, a) = all_4_7 &
% 5.31/1.46  |        $product(a, a) = all_4_9
% 5.31/1.46  | 
% 5.31/1.46  | ALPHA: (6) implies:
% 5.31/1.46  |   (7)   ~
% 5.31/1.46  |        ($sum($difference($difference($sum($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_4_0,
% 5.31/1.46  |                                      all_4_1), all_4_2), $product(2,
% 5.31/1.46  |                                    all_4_3)), all_4_4), all_4_5), all_4_6),
% 5.31/1.46  |                          all_4_7), all_4_8), $product(2, all_4_9)), all_4_10),
% 5.31/1.46  |                  $product(2, all_4_11)), $product(2, d)), $product(2, c)), b)
% 5.31/1.46  |          = 0)
% 5.31/1.46  |   (8)  $product(a, a) = all_4_9
% 5.31/1.46  |   (9)  $product(b, a) = all_4_7
% 5.31/1.46  |   (10)  $product(c, a) = all_4_8
% 5.31/1.46  |   (11)  $product(c, b) = all_4_6
% 5.31/1.46  |   (12)  $product(c, c) = all_4_5
% 5.31/1.46  |   (13)  $product(d, a) = all_4_3
% 5.31/1.46  |   (14)  $product(d, b) = all_4_11
% 5.31/1.46  |   (15)  $product(d, c) = all_4_1
% 5.31/1.46  |   (16)  $product(all_4_11, a) = all_4_10
% 5.31/1.46  |   (17)  $product(all_4_8, a) = all_4_4
% 5.31/1.46  |   (18)  $product(all_4_6, a) = all_4_2
% 5.31/1.46  |   (19)  $product(all_4_3, a) = all_4_0
% 5.31/1.46  | 
% 5.31/1.46  | THEORY_AXIOM GroebnerMultiplication: 
% 5.31/1.47  |   (20)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 5.31/1.47  |           int] :  ! [v5: int] :  ! [v6: int] :  ! [v7: int] :  ! [v8: int] : 
% 5.31/1.47  |         ! [v9: int] :  ! [v10: int] :  ! [v11: int] :  ! [v12: int] :  ! [v13:
% 5.31/1.47  |           int] :  ! [v14: int] :  ! [v15: int] :  ! [v16: int] :  ! [v17: int]
% 5.31/1.47  |         :
% 5.31/1.47  |         ($difference($difference($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(v17,
% 5.31/1.47  |                                   v16), v15), v14), v13), v12), v10), v8),
% 5.31/1.47  |                     v7), v5), $product(2, v4)), $product(2, v3)), $product(2,
% 5.31/1.47  |               v2)) = v0 |  ~ ($product(v14, v0) = v17) |  ~ ($product(v11, v0)
% 5.31/1.47  |             = v15) |  ~ ($product(v9, v0) = v13) |  ~ ($product(v7, v0) = v8)
% 5.31/1.47  |           |  ~ ($product(v5, $sum(v0, 2)) = v6) |  ~
% 5.31/1.47  |           ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) =
% 5.31/1.47  |             $sum($sum(v6, v4), v1)) |  ~ ($product(v3, v2) = v16) |  ~
% 5.31/1.47  |           ($product(v3, v1) = v7) |  ~ ($product(v3, v0) = v14) |  ~
% 5.31/1.47  |           ($product(v2, v2) = v12) |  ~ ($product(v2, v1) = v11) |  ~
% 5.31/1.47  |           ($product(v2, v0) = v9) |  ~ ($product($sum(v1, v0), $sum($sum(v3,
% 5.31/1.47  |                   v2), 1)) = v5) |  ~ ($product(v1, v0) = v10) |  ~
% 5.31/1.47  |           ($product(v0, v0) = v4))
% 5.31/1.47  | 
% 5.31/1.47  | GROUND_INST: instantiating (20) with a, b, c, d, all_2_2, all_2_1, all_2_0,
% 5.31/1.47  |              all_4_11, all_4_10, all_4_8, all_4_7, all_4_6, all_4_5, all_4_4,
% 5.31/1.47  |              all_4_3, all_4_2, all_4_1, all_4_0, simplifying with (2), (3),
% 5.31/1.47  |              (4), (5), (9), (10), (11), (12), (13), (14), (15), (16), (17),
% 5.31/1.47  |              (18), (19) gives:
% 5.31/1.47  |   (21)  $difference($difference($sum($sum($sum($sum($sum($difference($sum($sum($sum($difference(all_4_0,
% 5.31/1.47  |                                 all_4_1), all_4_2), all_4_3), all_4_4),
% 5.31/1.47  |                         all_4_5), all_4_7), all_4_10), all_4_11), all_2_1),
% 5.31/1.47  |               $product(2, all_2_2)), $product(2, d)), $product(2, c)) = a
% 5.31/1.47  | 
% 5.31/1.47  | THEORY_AXIOM GroebnerMultiplication: 
% 5.31/1.47  |   (22)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 5.31/1.47  |           int] :  ! [v5: int] :  ! [v6: int] :  ! [v7: int] :  ! [v8: int] :
% 5.31/1.47  |         ($sum($sum($difference($sum($sum($sum(v8, v7), v6), v5), v4), v1), v0)
% 5.31/1.47  |           = 0 |  ~ ($product(v3, v1) = v5) |  ~ ($product(v3, v0) = v8) |  ~
% 5.31/1.47  |           ($product(v2, v1) = v7) |  ~ ($product(v2, v0) = v6) |  ~
% 5.31/1.47  |           ($product($sum(v1, v0), $sum($sum(v3, v2), 1)) = v4))
% 5.31/1.47  | 
% 5.31/1.47  | GROUND_INST: instantiating (22) with a, b, c, d, all_2_1, all_4_11, all_4_8,
% 5.31/1.47  |              all_4_6, all_4_3, simplifying with (3), (10), (11), (13), (14)
% 5.31/1.47  |              gives:
% 5.31/1.47  |   (23)  $sum($sum($difference($sum($sum($sum(all_4_3, all_4_6), all_4_8),
% 5.31/1.47  |                 all_4_11), all_2_1), b), a) = 0
% 5.31/1.47  | 
% 5.31/1.47  | THEORY_AXIOM GroebnerMultiplication: 
% 5.42/1.48  |   (24)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] :  ! [v3: int] :  ! [v4:
% 5.42/1.48  |           int] :  ! [v5: int] :  ! [v6: int] :  ! [v7: int] :  ! [v8: int] : 
% 5.42/1.48  |         ! [v9: int] :  ! [v10: int] :  ! [v11: int] :  ! [v12: int] :  ! [v13:
% 5.42/1.48  |           int] :  ! [v14: int] :  ! [v15: int] :
% 5.42/1.48  |         ($sum($sum($difference($sum($sum($sum($sum(v15, v14), v12), v10), v8),
% 5.42/1.48  |                 v6), $product(2, v5)), v4) = 0 |  ~ ($product(v13, v0) = v15)
% 5.42/1.48  |           |  ~ ($product(v11, v0) = v14) |  ~ ($product(v9, v0) = v12) |  ~
% 5.42/1.48  |           ($product(v7, v0) = v8) |  ~ ($product(v5, $sum(v0, 2)) = v6) |  ~
% 5.42/1.48  |           ($product($sum($sum($sum(v3, v2), v1), v0), $sum(v2, 2)) =
% 5.42/1.48  |             $sum($sum(v6, v4), v1)) |  ~ ($product(v3, v1) = v7) |  ~
% 5.42/1.48  |           ($product(v3, v0) = v13) |  ~ ($product(v2, v1) = v11) |  ~
% 5.42/1.48  |           ($product(v2, v0) = v9) |  ~ ($product($sum(v1, v0), $sum($sum(v3,
% 5.42/1.48  |                   v2), 1)) = v5) |  ~ ($product(v1, v0) = v10) |  ~
% 5.42/1.48  |           ($product(v0, v0) = v4))
% 5.42/1.48  | 
% 5.42/1.48  | GROUND_INST: instantiating (24) with a, b, c, d, all_2_2, all_2_1, all_2_0,
% 5.42/1.48  |              all_4_11, all_4_10, all_4_8, all_4_7, all_4_6, all_4_4, all_4_3,
% 5.42/1.48  |              all_4_2, all_4_0, simplifying with (2), (3), (4), (5), (9), (10),
% 5.42/1.48  |              (11), (13), (14), (16), (17), (18), (19) gives:
% 5.42/1.48  |   (25)  $sum($sum($difference($sum($sum($sum($sum(all_4_0, all_4_2), all_4_4),
% 5.42/1.48  |                   all_4_7), all_4_10), all_2_0), $product(2, all_2_1)),
% 5.42/1.48  |           all_2_2) = 0
% 5.42/1.48  | 
% 5.42/1.48  | THEORY_AXIOM GroebnerMultiplication: 
% 5.42/1.48  |   (26)   ! [v0: int] :  ! [v1: int] :  ! [v2: int] : (v2 = v1 |  ~
% 5.42/1.48  |           ($product(v0, v0) = v2) |  ~ ($product(v0, v0) = v1))
% 5.42/1.48  | 
% 5.42/1.48  | GROUND_INST: instantiating (26) with a, all_2_2, all_4_9, simplifying with
% 5.42/1.48  |              (2), (8) gives:
% 5.42/1.48  |   (27)  all_4_9 = all_2_2
% 5.42/1.48  | 
% 5.42/1.48  | COMBINE_EQS: (21), (25) imply:
% 5.42/1.48  |   (28)  $sum($sum($sum($difference($sum($difference($difference($sum($difference(all_4_1,
% 5.42/1.48  |                           all_4_3), all_4_5), all_4_11), all_2_0), all_2_1),
% 5.42/1.48  |                 all_2_2), $product(2, d)), $product(2, c)), a) = 0
% 5.42/1.48  | 
% 5.42/1.48  | COMBINE_EQS: (23), (28) imply:
% 5.42/1.48  |   (29)  $sum($sum($sum($sum($difference($difference($sum($sum($sum(all_4_1,
% 5.42/1.48  |                           all_4_5), all_4_6), all_4_8), all_2_0), all_2_2),
% 5.42/1.48  |                 $product(2, d)), $product(2, c)), b), $product(2, a)) = 0
% 5.42/1.48  | 
% 5.42/1.48  | REDUCE: (7), (23), (25), (27), (29) imply:
% 5.42/1.48  |   (30)  $false
% 5.42/1.48  | 
% 5.42/1.48  | CLOSE: (30) is inconsistent.
% 5.42/1.48  | 
% 5.42/1.48  End of proof
% 5.42/1.48  % SZS output end Proof for theBenchmark
% 5.42/1.48  
% 5.42/1.48  864ms
%------------------------------------------------------------------------------