TSTP Solution File: ARI711_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI711_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 : n029.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 6.13s 1.60s
% Output : Proof 7.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI711_1 : TPTP v8.1.2. Released v6.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 18:11:42 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 ________ _____
% 0.19/0.56 ___ __ \_________(_)________________________________
% 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.56
% 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.56 (2023-06-19)
% 0.19/0.56
% 0.19/0.56 (c) Philipp Rümmer, 2009-2023
% 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.56 Amanda Stjerna.
% 0.19/0.56 Free software under BSD-3-Clause.
% 0.19/0.56
% 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.56
% 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.58 Running up to 7 provers in parallel.
% 0.19/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.43/1.06 Prover 1: Preprocessing ...
% 2.43/1.06 Prover 5: Preprocessing ...
% 2.43/1.06 Prover 4: Preprocessing ...
% 2.43/1.06 Prover 2: Preprocessing ...
% 2.43/1.07 Prover 0: Preprocessing ...
% 2.43/1.08 Prover 3: Preprocessing ...
% 2.43/1.08 Prover 6: Preprocessing ...
% 3.50/1.18 Prover 6: Constructing countermodel ...
% 3.50/1.18 Prover 1: Constructing countermodel ...
% 3.50/1.18 Prover 3: Constructing countermodel ...
% 3.50/1.18 Prover 4: Constructing countermodel ...
% 3.50/1.18 Prover 0: Constructing countermodel ...
% 3.50/1.18 Prover 5: Constructing countermodel ...
% 3.50/1.18 Prover 2: Constructing countermodel ...
% 6.13/1.59 Prover 5: proved (1005ms)
% 6.13/1.59 Prover 2: proved (1002ms)
% 6.13/1.60
% 6.13/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.13/1.60
% 6.13/1.60 Prover 6: proved (1000ms)
% 6.13/1.60
% 6.13/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.13/1.60
% 6.62/1.61
% 6.62/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.62/1.61
% 6.62/1.61 Prover 0: proved (1009ms)
% 6.62/1.61
% 6.62/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.62/1.61
% 6.62/1.61 Prover 3: proved (1004ms)
% 6.62/1.61
% 6.62/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.62/1.61
% 6.62/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.62/1.61 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.62/1.61 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.62/1.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.62/1.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.62/1.65 Prover 7: Preprocessing ...
% 6.62/1.65 Prover 4: Found proof (size 28)
% 6.62/1.65 Prover 1: Found proof (size 28)
% 6.62/1.65 Prover 8: Preprocessing ...
% 6.62/1.65 Prover 4: proved (1068ms)
% 6.62/1.65 Prover 1: proved (1072ms)
% 6.62/1.66 Prover 11: Preprocessing ...
% 6.62/1.67 Prover 7: Constructing countermodel ...
% 6.62/1.67 Prover 10: Preprocessing ...
% 6.62/1.67 Prover 7: stopped
% 6.62/1.67 Prover 13: Preprocessing ...
% 6.62/1.67 Prover 8: Constructing countermodel ...
% 6.62/1.67 Prover 8: stopped
% 7.12/1.68 Prover 11: Constructing countermodel ...
% 7.12/1.68 Prover 11: stopped
% 7.12/1.69 Prover 10: Constructing countermodel ...
% 7.12/1.69 Prover 10: stopped
% 7.12/1.69 Prover 13: Constructing countermodel ...
% 7.12/1.69 Prover 13: stopped
% 7.12/1.69
% 7.12/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.12/1.69
% 7.12/1.70 % SZS output start Proof for theBenchmark
% 7.12/1.70 Assumptions after simplification:
% 7.12/1.70 ---------------------------------
% 7.12/1.70
% 7.12/1.70 (conj)
% 7.12/1.72 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ?
% 7.12/1.72 [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ?
% 7.12/1.72 [v10: int] : ? [v11: int] : ? [v12: int] : ? [v13: int] : ? [v14: int] :
% 7.12/1.72 ? [v15: int] : ? [v16: int] : ? [v17: int] : ? [v18: int] : ? [v19: int] :
% 7.12/1.72 ? [v20: int] : ? [v21: int] : ? [v22: int] : ? [v23: int] : ? [v24: int]
% 7.12/1.72 : ? [v25: int] : ? [v26: int] : ? [v27: int] : ? [v28: int] : ? [v29:
% 7.12/1.72 int] : ? [v30: int] : ( ~
% 7.12/1.72 ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.12/1.72 v30),
% 7.12/1.72 $product(4,
% 7.12/1.72 v29)),
% 7.12/1.72 $product(6,
% 7.12/1.72 v28)),
% 7.12/1.72 $product(12,
% 7.12/1.72 v27)),
% 7.12/1.72 $product(6,
% 7.12/1.72 v26)),
% 7.12/1.72 $product(4,
% 7.12/1.72 v25)),
% 7.12/1.72 $product(12,
% 7.12/1.72 v24)),
% 7.12/1.72 $product(12, v23)),
% 7.12/1.72 $product(4, v22)),
% 7.12/1.72 $product(12, v21)),
% 7.12/1.72 $product(12, v20)),
% 7.12/1.72 $product(12, v19)),
% 7.12/1.72 $product(24, v18)),
% 7.12/1.72 $product(12, v17)), $product(12,
% 7.12/1.72 v16)), $product(12, v15)), v14),
% 7.12/1.72 $product(4, v13)), $product(6, v12)),
% 7.12/1.72 $product(4, v11)), $product(4, v10)),
% 7.12/1.72 $product(12, v9)), $product(12, v8)),
% 7.12/1.72 $product(6, v7)), $product(12, v6)), v5),
% 7.12/1.72 $product(4, v4)), $product(6, v3)), v2), $product(4, v1)),
% 7.12/1.72 $product(6, v0)), $product(4, c)), $product(4, b)), $product(4,
% 7.12/1.72 a)) = -1) & $product(v21, b) = v28 & $product(v21, a) = v27 &
% 7.12/1.72 $product(v20, a) = v26 & $product(v19, b) = v25 & $product(v19, a) = v24 &
% 7.12/1.72 $product(v18, a) = v23 & $product(v17, a) = v22 & $product(v16, b) = v19 &
% 7.12/1.72 $product(v16, a) = v18 & $product(v15, a) = v17 & $product(v10, b) = v14 &
% 7.12/1.72 $product(v10, a) = v13 & $product(v9, a) = v12 & $product(v8, a) = v11 &
% 7.12/1.72 $product(v7, b) = v10 & $product(v7, a) = v9 & $product(v6, a) = v8 &
% 7.12/1.72 $product(v4, a) = v5 & $product(v3, a) = v4 & $product(v1, c) = v2 &
% 7.12/1.72 $product(v1, b) = v30 & $product(v1, a) = v29 & $product(v0, c) = v1 &
% 7.12/1.72 $product(v0, b) = v21 & $product(v0, a) = v20 & $product(c, c) = v0 &
% 7.12/1.72 $product(c, b) = v16 & $product(c, a) = v15 & $product(b, b) = v7 &
% 7.12/1.72 $product(b, a) = v6 & $product(a, a) = v3)
% 7.12/1.72
% 7.12/1.72 (eq)
% 7.12/1.73 ? [v0: int] : ? [v1: int] : ($product(v1, $sum($sum($sum(c, b), a), 1)) = 0
% 7.12/1.73 & $product(v0, $sum($sum($sum(c, b), a), 1)) = v1 &
% 7.12/1.73 $product($sum($sum($sum(c, b), a), 1), $sum($sum($sum(c, b), a), 1)) = v0)
% 7.12/1.73
% 7.12/1.73 Those formulas are unsatisfiable:
% 7.12/1.73 ---------------------------------
% 7.12/1.73
% 7.12/1.73 Begin of proof
% 7.12/1.73 |
% 7.12/1.73 | DELTA: instantiating (eq) with fresh symbols all_2_0, all_2_1 gives:
% 7.12/1.73 | (1) $product(all_2_0, $sum($sum($sum(c, b), a), 1)) = 0 & $product(all_2_1,
% 7.12/1.73 | $sum($sum($sum(c, b), a), 1)) = all_2_0 & $product($sum($sum($sum(c,
% 7.12/1.73 | b), a), 1), $sum($sum($sum(c, b), a), 1)) = all_2_1
% 7.12/1.73 |
% 7.12/1.73 | ALPHA: (1) implies:
% 7.12/1.73 | (2) $product($sum($sum($sum(c, b), a), 1), $sum($sum($sum(c, b), a), 1)) =
% 7.12/1.73 | all_2_1
% 7.12/1.73 | (3) $product(all_2_1, $sum($sum($sum(c, b), a), 1)) = all_2_0
% 7.12/1.73 | (4) $product(all_2_0, $sum($sum($sum(c, b), a), 1)) = 0
% 7.12/1.73 |
% 7.12/1.73 | DELTA: instantiating (conj) with fresh symbols all_4_0, all_4_1, all_4_2,
% 7.12/1.73 | all_4_3, all_4_4, all_4_5, all_4_6, all_4_7, all_4_8, all_4_9,
% 7.12/1.73 | all_4_10, all_4_11, all_4_12, all_4_13, all_4_14, all_4_15, all_4_16,
% 7.12/1.73 | all_4_17, all_4_18, all_4_19, all_4_20, all_4_21, all_4_22, all_4_23,
% 7.12/1.73 | all_4_24, all_4_25, all_4_26, all_4_27, all_4_28, all_4_29, all_4_30
% 7.12/1.73 | gives:
% 7.12/1.74 | (5) ~
% 7.12/1.74 | ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.12/1.74 | all_4_0),
% 7.12/1.74 | $product(4,
% 7.12/1.74 | all_4_1)),
% 7.12/1.74 | $product(6,
% 7.12/1.74 | all_4_2)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_3)),
% 7.12/1.74 | $product(6,
% 7.12/1.74 | all_4_4)),
% 7.12/1.74 | $product(4,
% 7.12/1.74 | all_4_5)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_6)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_7)),
% 7.12/1.74 | $product(4,
% 7.12/1.74 | all_4_8)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_9)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_10)),
% 7.12/1.74 | $product(12,
% 7.12/1.74 | all_4_11)),
% 7.12/1.74 | $product(24, all_4_12)),
% 7.12/1.74 | $product(12, all_4_13)),
% 7.12/1.74 | $product(12, all_4_14)),
% 7.12/1.74 | $product(12, all_4_15)),
% 7.12/1.74 | all_4_16), $product(4,
% 7.12/1.74 | all_4_17)), $product(6,
% 7.12/1.74 | all_4_18)), $product(4, all_4_19)),
% 7.12/1.74 | $product(4, all_4_20)), $product(12,
% 7.12/1.74 | all_4_21)), $product(12, all_4_22)),
% 7.12/1.74 | $product(6, all_4_23)), $product(12,
% 7.12/1.74 | all_4_24)), all_4_25), $product(4, all_4_26)),
% 7.12/1.74 | $product(6, all_4_27)), all_4_28), $product(4,
% 7.12/1.74 | all_4_29)), $product(6, all_4_30)), $product(4, c)),
% 7.12/1.74 | $product(4, b)), $product(4, a)) = -1) & $product(all_4_9, b) =
% 7.12/1.74 | all_4_2 & $product(all_4_9, a) = all_4_3 & $product(all_4_10, a) =
% 7.12/1.74 | all_4_4 & $product(all_4_11, b) = all_4_5 & $product(all_4_11, a) =
% 7.12/1.74 | all_4_6 & $product(all_4_12, a) = all_4_7 & $product(all_4_13, a) =
% 7.12/1.74 | all_4_8 & $product(all_4_14, b) = all_4_11 & $product(all_4_14, a) =
% 7.12/1.74 | all_4_12 & $product(all_4_15, a) = all_4_13 & $product(all_4_20, b) =
% 7.12/1.74 | all_4_16 & $product(all_4_20, a) = all_4_17 & $product(all_4_21, a) =
% 7.12/1.74 | all_4_18 & $product(all_4_22, a) = all_4_19 & $product(all_4_23, b) =
% 7.12/1.74 | all_4_20 & $product(all_4_23, a) = all_4_21 & $product(all_4_24, a) =
% 7.12/1.74 | all_4_22 & $product(all_4_26, a) = all_4_25 & $product(all_4_27, a) =
% 7.12/1.74 | all_4_26 & $product(all_4_29, c) = all_4_28 & $product(all_4_29, b) =
% 7.12/1.74 | all_4_0 & $product(all_4_29, a) = all_4_1 & $product(all_4_30, c) =
% 7.12/1.74 | all_4_29 & $product(all_4_30, b) = all_4_9 & $product(all_4_30, a) =
% 7.12/1.74 | all_4_10 & $product(c, c) = all_4_30 & $product(c, b) = all_4_14 &
% 7.12/1.75 | $product(c, a) = all_4_15 & $product(b, b) = all_4_23 & $product(b, a)
% 7.12/1.75 | = all_4_24 & $product(a, a) = all_4_27
% 7.12/1.75 |
% 7.12/1.75 | ALPHA: (5) implies:
% 7.12/1.75 | (6) ~
% 7.12/1.75 | ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.12/1.75 | all_4_0),
% 7.12/1.75 | $product(4,
% 7.12/1.75 | all_4_1)),
% 7.12/1.75 | $product(6,
% 7.12/1.75 | all_4_2)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_3)),
% 7.12/1.75 | $product(6,
% 7.12/1.75 | all_4_4)),
% 7.12/1.75 | $product(4,
% 7.12/1.75 | all_4_5)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_6)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_7)),
% 7.12/1.75 | $product(4,
% 7.12/1.75 | all_4_8)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_9)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_10)),
% 7.12/1.75 | $product(12,
% 7.12/1.75 | all_4_11)),
% 7.12/1.75 | $product(24, all_4_12)),
% 7.12/1.75 | $product(12, all_4_13)),
% 7.12/1.75 | $product(12, all_4_14)),
% 7.12/1.75 | $product(12, all_4_15)),
% 7.12/1.75 | all_4_16), $product(4,
% 7.12/1.75 | all_4_17)), $product(6,
% 7.12/1.75 | all_4_18)), $product(4, all_4_19)),
% 7.12/1.75 | $product(4, all_4_20)), $product(12,
% 7.12/1.75 | all_4_21)), $product(12, all_4_22)),
% 7.12/1.75 | $product(6, all_4_23)), $product(12,
% 7.12/1.75 | all_4_24)), all_4_25), $product(4, all_4_26)),
% 7.12/1.75 | $product(6, all_4_27)), all_4_28), $product(4,
% 7.12/1.75 | all_4_29)), $product(6, all_4_30)), $product(4, c)),
% 7.12/1.75 | $product(4, b)), $product(4, a)) = -1)
% 7.12/1.75 | (7) $product(a, a) = all_4_27
% 7.12/1.75 | (8) $product(b, a) = all_4_24
% 7.12/1.75 | (9) $product(b, b) = all_4_23
% 7.12/1.75 | (10) $product(c, a) = all_4_15
% 7.12/1.75 | (11) $product(c, b) = all_4_14
% 7.12/1.75 | (12) $product(c, c) = all_4_30
% 7.12/1.75 | (13) $product(all_4_30, a) = all_4_10
% 7.12/1.75 | (14) $product(all_4_30, b) = all_4_9
% 7.12/1.75 | (15) $product(all_4_30, c) = all_4_29
% 7.12/1.75 | (16) $product(all_4_29, a) = all_4_1
% 7.12/1.75 | (17) $product(all_4_29, b) = all_4_0
% 7.12/1.75 | (18) $product(all_4_29, c) = all_4_28
% 7.12/1.75 | (19) $product(all_4_27, a) = all_4_26
% 7.12/1.75 | (20) $product(all_4_26, a) = all_4_25
% 7.12/1.75 | (21) $product(all_4_24, a) = all_4_22
% 7.12/1.75 | (22) $product(all_4_23, a) = all_4_21
% 7.12/1.75 | (23) $product(all_4_23, b) = all_4_20
% 7.12/1.75 | (24) $product(all_4_22, a) = all_4_19
% 7.12/1.75 | (25) $product(all_4_21, a) = all_4_18
% 7.12/1.75 | (26) $product(all_4_20, a) = all_4_17
% 7.12/1.75 | (27) $product(all_4_20, b) = all_4_16
% 7.12/1.75 | (28) $product(all_4_15, a) = all_4_13
% 7.12/1.76 | (29) $product(all_4_14, a) = all_4_12
% 7.12/1.76 | (30) $product(all_4_14, b) = all_4_11
% 7.12/1.76 | (31) $product(all_4_13, a) = all_4_8
% 7.12/1.76 | (32) $product(all_4_12, a) = all_4_7
% 7.12/1.76 | (33) $product(all_4_11, a) = all_4_6
% 7.12/1.76 | (34) $product(all_4_11, b) = all_4_5
% 7.12/1.76 | (35) $product(all_4_10, a) = all_4_4
% 7.12/1.76 | (36) $product(all_4_9, a) = all_4_3
% 7.12/1.76 | (37) $product(all_4_9, b) = all_4_2
% 7.12/1.76 |
% 7.12/1.76 | THEORY_AXIOM GroebnerMultiplication:
% 7.12/1.76 | (38) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 7.12/1.76 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 7.12/1.76 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 7.12/1.76 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 7.12/1.76 | : ! [v18: int] : ! [v19: int] : ! [v20: int] : ! [v21: int] : !
% 7.12/1.76 | [v22: int] : ! [v23: int] : ! [v24: int] : ! [v25: int] : ! [v26:
% 7.12/1.76 | int] : ! [v27: int] : ! [v28: int] : ! [v29: int] : ! [v30: int]
% 7.12/1.76 | : ! [v31: int] : ! [v32: int] : ! [v33: int] : ! [v34: int] : !
% 7.12/1.76 | [v35: int] :
% 7.12/1.76 | ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.12/1.76 | v35),
% 7.12/1.76 | $product(4,
% 7.12/1.76 | v34)),
% 7.12/1.76 | $product(6,
% 7.12/1.76 | v33)),
% 7.12/1.76 | $product(12,
% 7.12/1.76 | v32)),
% 7.12/1.76 | $product(6,
% 7.12/1.76 | v31)),
% 7.12/1.76 | $product(4,
% 7.12/1.76 | v30)),
% 7.12/1.76 | $product(12,
% 7.12/1.76 | v29)),
% 7.12/1.76 | $product(12,
% 7.12/1.76 | v28)),
% 7.12/1.76 | $product(4,
% 7.12/1.76 | v27)),
% 7.12/1.76 | $product(9,
% 7.12/1.76 | v26)),
% 7.12/1.76 | $product(9, v25)),
% 7.12/1.76 | $product(9, v24)),
% 7.12/1.76 | $product(18, v23)),
% 7.12/1.76 | $product(9, v22)),
% 7.12/1.76 | $product(6, v21)),
% 7.12/1.76 | $product(6, v20)), v19),
% 7.12/1.76 | $product(4, v18)), $product(6,
% 7.12/1.76 | v17)), $product(4, v16)),
% 7.12/1.76 | $product(3, v15)), $product(9, v14)),
% 7.12/1.76 | $product(9, v13)), $product(3, v12)),
% 7.12/1.76 | $product(6, v11)), v10), $product(3, v9)),
% 7.12/1.76 | $product(3, v8)), v7), $product(3, v6)), $product(3,
% 7.12/1.76 | v5)), v4), v2), v1), v0) = 0 | ~ ($product(v26, v1) =
% 7.12/1.76 | v33) | ~ ($product(v26, v0) = v32) | ~ ($product(v25, v0) = v31)
% 7.12/1.76 | | ~ ($product(v24, v1) = v30) | ~ ($product(v24, v0) = v29) | ~
% 7.12/1.76 | ($product(v23, v0) = v28) | ~ ($product(v22, v0) = v27) | ~
% 7.12/1.76 | ($product(v21, v1) = v24) | ~ ($product(v21, v0) = v23) | ~
% 7.12/1.76 | ($product(v20, v0) = v22) | ~ ($product(v15, v1) = v19) | ~
% 7.12/1.76 | ($product(v15, v0) = v18) | ~ ($product(v14, v0) = v17) | ~
% 7.12/1.76 | ($product(v13, v0) = v16) | ~ ($product(v12, v1) = v15) | ~
% 7.12/1.76 | ($product(v12, v0) = v14) | ~ ($product(v11, v0) = v13) | ~
% 7.12/1.76 | ($product(v9, v0) = v10) | ~ ($product(v8, v0) = v9) | ~
% 7.12/1.76 | ($product(v6, v2) = v7) | ~ ($product(v6, v1) = v35) | ~
% 7.12/1.76 | ($product(v6, v0) = v34) | ~ ($product(v5, v2) = v6) | ~
% 7.12/1.76 | ($product(v5, v1) = v26) | ~ ($product(v5, v0) = v25) | ~
% 7.12/1.76 | ($product(v4, $sum($sum($sum(v2, v1), v0), 1)) = 0) | ~
% 7.12/1.76 | ($product(v3, $sum($sum($sum(v2, v1), v0), 1)) = v4) | ~
% 7.12/1.76 | ($product($sum($sum($sum(v2, v1), v0), 1), $sum($sum($sum(v2, v1),
% 7.12/1.76 | v0), 1)) = v3) | ~ ($product(v2, v2) = v5) | ~
% 7.12/1.76 | ($product(v2, v1) = v21) | ~ ($product(v2, v0) = v20) | ~
% 7.12/1.76 | ($product(v1, v1) = v12) | ~ ($product(v1, v0) = v11) | ~
% 7.12/1.76 | ($product(v0, v0) = v8))
% 7.12/1.76 |
% 7.12/1.77 | GROUND_INST: instantiating (38) with a, b, c, all_2_1, all_2_0, all_4_30,
% 7.12/1.77 | all_4_29, all_4_28, all_4_27, all_4_26, all_4_25, all_4_24,
% 7.12/1.77 | all_4_23, all_4_22, all_4_21, all_4_20, all_4_19, all_4_18,
% 7.12/1.77 | all_4_17, all_4_16, all_4_15, all_4_14, all_4_13, all_4_12,
% 7.12/1.77 | all_4_11, all_4_10, all_4_9, all_4_8, all_4_7, all_4_6, all_4_5,
% 7.12/1.77 | all_4_4, all_4_3, all_4_2, all_4_1, all_4_0, simplifying with
% 7.59/1.77 | (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 7.59/1.77 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 7.59/1.77 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37)
% 7.59/1.77 | gives:
% 7.59/1.77 | (39) $sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.59/1.77 | all_4_0),
% 7.59/1.77 | $product(4,
% 7.59/1.77 | all_4_1)),
% 7.59/1.77 | $product(6,
% 7.59/1.77 | all_4_2)),
% 7.59/1.77 | $product(12,
% 7.59/1.77 | all_4_3)),
% 7.59/1.77 | $product(6,
% 7.59/1.77 | all_4_4)),
% 7.59/1.77 | $product(4,
% 7.59/1.77 | all_4_5)),
% 7.59/1.77 | $product(12,
% 7.59/1.77 | all_4_6)),
% 7.59/1.77 | $product(12,
% 7.59/1.77 | all_4_7)),
% 7.59/1.77 | $product(4,
% 7.59/1.77 | all_4_8)),
% 7.59/1.77 | $product(9,
% 7.59/1.77 | all_4_9)),
% 7.59/1.77 | $product(9,
% 7.59/1.77 | all_4_10)),
% 7.59/1.77 | $product(9,
% 7.59/1.77 | all_4_11)),
% 7.59/1.77 | $product(18, all_4_12)),
% 7.59/1.77 | $product(9, all_4_13)),
% 7.59/1.77 | $product(6, all_4_14)),
% 7.59/1.77 | $product(6, all_4_15)),
% 7.59/1.77 | all_4_16), $product(4,
% 7.59/1.77 | all_4_17)), $product(6,
% 7.59/1.77 | all_4_18)), $product(4,
% 7.59/1.77 | all_4_19)), $product(3, all_4_20)),
% 7.59/1.77 | $product(9, all_4_21)), $product(9,
% 7.59/1.77 | all_4_22)), $product(3, all_4_23)),
% 7.59/1.77 | $product(6, all_4_24)), all_4_25), $product(3,
% 7.59/1.77 | all_4_26)), $product(3, all_4_27)), all_4_28),
% 7.59/1.77 | $product(3, all_4_29)), $product(3, all_4_30)), all_2_0),
% 7.59/1.77 | c), b), a) = 0
% 7.59/1.77 |
% 7.59/1.77 | THEORY_AXIOM GroebnerMultiplication:
% 7.59/1.78 | (40) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 7.59/1.78 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 7.59/1.78 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 7.59/1.78 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 7.59/1.78 | : ! [v18: int] : ! [v19: int] : ! [v20: int] : ! [v21: int] : !
% 7.59/1.78 | [v22: int] : ! [v23: int] : ! [v24: int] : ! [v25: int] : ! [v26:
% 7.59/1.78 | int] : ! [v27: int] : ! [v28: int] : ! [v29: int] : ! [v30: int]
% 7.59/1.78 | : ! [v31: int] : ! [v32: int] : ! [v33: int] : ! [v34: int] : !
% 7.59/1.78 | [v35: int] :
% 7.59/1.78 | ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(12,
% 7.59/1.78 | v35),
% 7.59/1.78 | $product(12,
% 7.59/1.78 | v34)),
% 7.59/1.78 | $product(18,
% 7.59/1.78 | v33)),
% 7.59/1.78 | $product(36,
% 7.59/1.78 | v32)),
% 7.59/1.78 | $product(18,
% 7.59/1.78 | v31)),
% 7.59/1.78 | $product(12,
% 7.59/1.78 | v30)),
% 7.59/1.78 | $product(36,
% 7.59/1.78 | v29)),
% 7.59/1.78 | $product(36,
% 7.59/1.78 | v28)),
% 7.59/1.78 | $product(12, v27)),
% 7.59/1.78 | $product(24, v26)),
% 7.59/1.78 | $product(24, v25)),
% 7.59/1.78 | $product(24, v24)),
% 7.59/1.78 | $product(48, v23)),
% 7.59/1.78 | $product(24, v22)),
% 7.59/1.78 | $product(12, v21)), $product(12,
% 7.59/1.78 | v20)), $product(3, v19)),
% 7.59/1.78 | $product(12, v18)), $product(18,
% 7.59/1.78 | v17)), $product(12, v16)), $product(8,
% 7.59/1.78 | v15)), $product(24, v14)), $product(24,
% 7.59/1.78 | v13)), $product(6, v12)), $product(12, v11)),
% 7.59/1.78 | $product(3, v10)), $product(8, v9)), $product(6, v8)),
% 7.59/1.78 | $product(3, v7)), $product(8, v6)), $product(6, v5)),
% 7.59/1.78 | $product(4, v4)) = 1 | ~ ($product(v26, v1) = v33) | ~
% 7.59/1.78 | ($product(v26, v0) = v32) | ~ ($product(v25, v0) = v31) | ~
% 7.59/1.78 | ($product(v24, v1) = v30) | ~ ($product(v24, v0) = v29) | ~
% 7.59/1.78 | ($product(v23, v0) = v28) | ~ ($product(v22, v0) = v27) | ~
% 7.59/1.78 | ($product(v21, v1) = v24) | ~ ($product(v21, v0) = v23) | ~
% 7.59/1.78 | ($product(v20, v0) = v22) | ~ ($product(v15, v1) = v19) | ~
% 7.59/1.78 | ($product(v15, v0) = v18) | ~ ($product(v14, v0) = v17) | ~
% 7.59/1.78 | ($product(v13, v0) = v16) | ~ ($product(v12, v1) = v15) | ~
% 7.59/1.78 | ($product(v12, v0) = v14) | ~ ($product(v11, v0) = v13) | ~
% 7.59/1.78 | ($product(v9, v0) = v10) | ~ ($product(v8, v0) = v9) | ~
% 7.59/1.78 | ($product(v6, v2) = v7) | ~ ($product(v6, v1) = v35) | ~
% 7.59/1.78 | ($product(v6, v0) = v34) | ~ ($product(v5, v2) = v6) | ~
% 7.59/1.78 | ($product(v5, v1) = v26) | ~ ($product(v5, v0) = v25) | ~
% 7.59/1.78 | ($product(v4, $sum($sum($sum(v2, v1), v0), 1)) = 0) | ~
% 7.59/1.78 | ($product(v3, $sum($sum($sum(v2, v1), v0), 1)) = v4) | ~
% 7.59/1.78 | ($product($sum($sum($sum(v2, v1), v0), 1), $sum($sum($sum(v2, v1),
% 7.59/1.78 | v0), 1)) = v3) | ~ ($product(v2, v2) = v5) | ~
% 7.59/1.78 | ($product(v2, v1) = v21) | ~ ($product(v2, v0) = v20) | ~
% 7.59/1.78 | ($product(v1, v1) = v12) | ~ ($product(v1, v0) = v11) | ~
% 7.59/1.78 | ($product(v0, v0) = v8))
% 7.59/1.78 |
% 7.59/1.78 | GROUND_INST: instantiating (40) with a, b, c, all_2_1, all_2_0, all_4_30,
% 7.59/1.78 | all_4_29, all_4_28, all_4_27, all_4_26, all_4_25, all_4_24,
% 7.59/1.78 | all_4_23, all_4_22, all_4_21, all_4_20, all_4_19, all_4_18,
% 7.59/1.78 | all_4_17, all_4_16, all_4_15, all_4_14, all_4_13, all_4_12,
% 7.59/1.78 | all_4_11, all_4_10, all_4_9, all_4_8, all_4_7, all_4_6, all_4_5,
% 7.59/1.78 | all_4_4, all_4_3, all_4_2, all_4_1, all_4_0, simplifying with
% 7.59/1.78 | (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 7.59/1.78 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 7.59/1.78 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37)
% 7.59/1.78 | gives:
% 7.59/1.79 | (41) $sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(12,
% 7.59/1.79 | all_4_0),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | all_4_1)),
% 7.59/1.79 | $product(18,
% 7.59/1.79 | all_4_2)),
% 7.59/1.79 | $product(36,
% 7.59/1.79 | all_4_3)),
% 7.59/1.79 | $product(18,
% 7.59/1.79 | all_4_4)),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | all_4_5)),
% 7.59/1.79 | $product(36,
% 7.59/1.79 | all_4_6)),
% 7.59/1.79 | $product(36,
% 7.59/1.79 | all_4_7)),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | all_4_8)),
% 7.59/1.79 | $product(24, all_4_9)),
% 7.59/1.79 | $product(24, all_4_10)),
% 7.59/1.79 | $product(24, all_4_11)),
% 7.59/1.79 | $product(48, all_4_12)),
% 7.59/1.79 | $product(24, all_4_13)),
% 7.59/1.79 | $product(12, all_4_14)),
% 7.59/1.79 | $product(12, all_4_15)), $product(3,
% 7.59/1.79 | all_4_16)), $product(12, all_4_17)),
% 7.59/1.79 | $product(18, all_4_18)), $product(12,
% 7.59/1.79 | all_4_19)), $product(8, all_4_20)),
% 7.59/1.79 | $product(24, all_4_21)), $product(24,
% 7.59/1.79 | all_4_22)), $product(6, all_4_23)), $product(12,
% 7.59/1.79 | all_4_24)), $product(3, all_4_25)), $product(8,
% 7.59/1.79 | all_4_26)), $product(6, all_4_27)), $product(3,
% 7.59/1.79 | all_4_28)), $product(8, all_4_29)), $product(6, all_4_30)),
% 7.59/1.79 | $product(4, all_2_0)) = 1
% 7.59/1.79 |
% 7.59/1.79 | THEORY_AXIOM GroebnerMultiplication:
% 7.59/1.79 | (42) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 7.59/1.79 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 7.59/1.79 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 7.59/1.79 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 7.59/1.79 | : ! [v18: int] : ! [v19: int] : ! [v20: int] : ! [v21: int] : !
% 7.59/1.79 | [v22: int] : ! [v23: int] : ! [v24: int] : ! [v25: int] : ! [v26:
% 7.59/1.79 | int] : ! [v27: int] : ! [v28: int] : ! [v29: int] : ! [v30: int]
% 7.59/1.79 | : ! [v31: int] : ! [v32: int] : ! [v33: int] : ! [v34: int] : !
% 7.59/1.79 | [v35: int] :
% 7.59/1.79 | ($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.59/1.79 | v35),
% 7.59/1.79 | $product(4,
% 7.59/1.79 | v34)),
% 7.59/1.79 | $product(6,
% 7.59/1.79 | v33)),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | v32)),
% 7.59/1.79 | $product(6,
% 7.59/1.79 | v31)),
% 7.59/1.79 | $product(4,
% 7.59/1.79 | v30)),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | v29)),
% 7.59/1.79 | $product(12,
% 7.59/1.79 | v28)),
% 7.59/1.79 | $product(4, v27)),
% 7.59/1.79 | $product(6, v26)),
% 7.59/1.79 | $product(6, v25)),
% 7.59/1.79 | $product(6, v24)),
% 7.59/1.79 | $product(12, v23)),
% 7.59/1.79 | $product(6, v22)), $product(2,
% 7.59/1.79 | v21)), $product(2, v20)),
% 7.59/1.79 | v19), $product(4, v18)), $product(6,
% 7.59/1.79 | v17)), $product(4, v16)), $product(2,
% 7.59/1.79 | v15)), $product(6, v14)), $product(6,
% 7.59/1.79 | v13)), v12), $product(2, v11)), v10),
% 7.59/1.79 | $product(2, v9)), v8), v7), $product(2, v6)), v5),
% 7.59/1.79 | $product(2, v4)) = v3 | ~ ($product(v26, v1) = v33) | ~
% 7.59/1.79 | ($product(v26, v0) = v32) | ~ ($product(v25, v0) = v31) | ~
% 7.59/1.79 | ($product(v24, v1) = v30) | ~ ($product(v24, v0) = v29) | ~
% 7.59/1.79 | ($product(v23, v0) = v28) | ~ ($product(v22, v0) = v27) | ~
% 7.59/1.79 | ($product(v21, v1) = v24) | ~ ($product(v21, v0) = v23) | ~
% 7.59/1.79 | ($product(v20, v0) = v22) | ~ ($product(v15, v1) = v19) | ~
% 7.59/1.79 | ($product(v15, v0) = v18) | ~ ($product(v14, v0) = v17) | ~
% 7.59/1.79 | ($product(v13, v0) = v16) | ~ ($product(v12, v1) = v15) | ~
% 7.59/1.79 | ($product(v12, v0) = v14) | ~ ($product(v11, v0) = v13) | ~
% 7.59/1.79 | ($product(v9, v0) = v10) | ~ ($product(v8, v0) = v9) | ~
% 7.59/1.79 | ($product(v6, v2) = v7) | ~ ($product(v6, v1) = v35) | ~
% 7.59/1.79 | ($product(v6, v0) = v34) | ~ ($product(v5, v2) = v6) | ~
% 7.59/1.79 | ($product(v5, v1) = v26) | ~ ($product(v5, v0) = v25) | ~
% 7.59/1.79 | ($product(v4, $sum($sum($sum(v2, v1), v0), 1)) = 0) | ~
% 7.59/1.79 | ($product(v3, $sum($sum($sum(v2, v1), v0), 1)) = v4) | ~
% 7.59/1.79 | ($product($sum($sum($sum(v2, v1), v0), 1), $sum($sum($sum(v2, v1),
% 7.59/1.79 | v0), 1)) = v3) | ~ ($product(v2, v2) = v5) | ~
% 7.59/1.79 | ($product(v2, v1) = v21) | ~ ($product(v2, v0) = v20) | ~
% 7.59/1.79 | ($product(v1, v1) = v12) | ~ ($product(v1, v0) = v11) | ~
% 7.59/1.79 | ($product(v0, v0) = v8))
% 7.59/1.79 |
% 7.59/1.80 | GROUND_INST: instantiating (42) with a, b, c, all_2_1, all_2_0, all_4_30,
% 7.59/1.80 | all_4_29, all_4_28, all_4_27, all_4_26, all_4_25, all_4_24,
% 7.59/1.80 | all_4_23, all_4_22, all_4_21, all_4_20, all_4_19, all_4_18,
% 7.59/1.80 | all_4_17, all_4_16, all_4_15, all_4_14, all_4_13, all_4_12,
% 7.59/1.80 | all_4_11, all_4_10, all_4_9, all_4_8, all_4_7, all_4_6, all_4_5,
% 7.59/1.80 | all_4_4, all_4_3, all_4_2, all_4_1, all_4_0, simplifying with
% 7.59/1.80 | (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 7.59/1.80 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 7.59/1.80 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37)
% 7.59/1.80 | gives:
% 7.75/1.80 | (43) $sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.75/1.80 | all_4_0),
% 7.75/1.80 | $product(4,
% 7.75/1.80 | all_4_1)),
% 7.75/1.80 | $product(6,
% 7.75/1.80 | all_4_2)),
% 7.75/1.80 | $product(12,
% 7.75/1.80 | all_4_3)),
% 7.75/1.80 | $product(6,
% 7.75/1.80 | all_4_4)),
% 7.75/1.80 | $product(4,
% 7.75/1.80 | all_4_5)),
% 7.75/1.80 | $product(12,
% 7.75/1.80 | all_4_6)),
% 7.75/1.80 | $product(12,
% 7.75/1.80 | all_4_7)),
% 7.75/1.80 | $product(4, all_4_8)),
% 7.75/1.80 | $product(6, all_4_9)),
% 7.75/1.80 | $product(6, all_4_10)),
% 7.75/1.80 | $product(6, all_4_11)),
% 7.75/1.80 | $product(12, all_4_12)),
% 7.75/1.80 | $product(6, all_4_13)),
% 7.75/1.80 | $product(2, all_4_14)),
% 7.75/1.80 | $product(2, all_4_15)), all_4_16),
% 7.75/1.80 | $product(4, all_4_17)), $product(6,
% 7.75/1.80 | all_4_18)), $product(4, all_4_19)),
% 7.75/1.80 | $product(2, all_4_20)), $product(6,
% 7.75/1.80 | all_4_21)), $product(6, all_4_22)), all_4_23),
% 7.75/1.80 | $product(2, all_4_24)), all_4_25), $product(2,
% 7.75/1.80 | all_4_26)), all_4_27), all_4_28), $product(2,
% 7.75/1.80 | all_4_29)), all_4_30), $product(2, all_2_0)) = all_2_1
% 7.75/1.80 |
% 7.75/1.80 | COMBINE_EQS: (39), (43) imply:
% 7.75/1.80 | (44) $sum($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(3,
% 7.75/1.80 | all_4_9), $product(3,
% 7.75/1.80 | all_4_10)), $product(3,
% 7.75/1.80 | all_4_11)), $product(6,
% 7.75/1.80 | all_4_12)), $product(3,
% 7.75/1.80 | all_4_13)), $product(4,
% 7.75/1.80 | all_4_14)), $product(4, all_4_15)),
% 7.75/1.80 | all_4_20), $product(3, all_4_21)),
% 7.75/1.80 | $product(3, all_4_22)), $product(2,
% 7.75/1.80 | all_4_23)), $product(4, all_4_24)), all_4_26),
% 7.75/1.80 | $product(2, all_4_27)), all_4_29), $product(2,
% 7.75/1.80 | all_4_30)), all_2_0), all_2_1), c), b), a) = 0
% 7.75/1.80 |
% 7.75/1.80 | SIMP: (44) implies:
% 7.75/1.80 | (45) $sum($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(3,
% 7.75/1.80 | all_4_9), $product(3,
% 7.75/1.80 | all_4_10)), $product(3,
% 7.75/1.80 | all_4_11)), $product(6,
% 7.75/1.80 | all_4_12)), $product(3,
% 7.75/1.80 | all_4_13)), $product(4,
% 7.75/1.80 | all_4_14)), $product(4, all_4_15)),
% 7.75/1.80 | all_4_20), $product(3, all_4_21)),
% 7.75/1.80 | $product(3, all_4_22)), $product(2,
% 7.75/1.80 | all_4_23)), $product(4, all_4_24)), all_4_26),
% 7.75/1.80 | $product(2, all_4_27)), all_4_29), $product(2,
% 7.75/1.80 | all_4_30)), all_2_0), all_2_1), c), b), a) = 0
% 7.75/1.80 |
% 7.75/1.80 | COMBINE_EQS: (39), (41) imply:
% 7.75/1.80 | (46) $sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(3,
% 7.75/1.80 | all_4_9), $product(3,
% 7.75/1.80 | all_4_10)), $product(3,
% 7.75/1.80 | all_4_11)), $product(6,
% 7.75/1.80 | all_4_12)), $product(3,
% 7.75/1.80 | all_4_13)), $product(6, all_4_14)),
% 7.75/1.80 | $product(6, all_4_15)), all_4_20),
% 7.75/1.80 | $product(3, all_4_21)), $product(3,
% 7.75/1.80 | all_4_22)), $product(3, all_4_23)),
% 7.75/1.80 | $product(6, all_4_24)), all_4_26), $product(3,
% 7.75/1.80 | all_4_27)), all_4_29), $product(3, all_4_30)),
% 7.75/1.80 | all_2_0), $product(3, c)), $product(3, b)), $product(3, a)) =
% 7.75/1.80 | -1
% 7.75/1.80 |
% 7.75/1.80 | SIMP: (46) implies:
% 7.75/1.81 | (47) $sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(3,
% 7.75/1.81 | all_4_9), $product(3,
% 7.75/1.81 | all_4_10)), $product(3,
% 7.75/1.81 | all_4_11)), $product(6,
% 7.75/1.81 | all_4_12)), $product(3,
% 7.75/1.81 | all_4_13)), $product(6, all_4_14)),
% 7.75/1.81 | $product(6, all_4_15)), all_4_20),
% 7.75/1.81 | $product(3, all_4_21)), $product(3,
% 7.75/1.81 | all_4_22)), $product(3, all_4_23)),
% 7.75/1.81 | $product(6, all_4_24)), all_4_26), $product(3,
% 7.75/1.81 | all_4_27)), all_4_29), $product(3, all_4_30)),
% 7.75/1.81 | all_2_0), $product(3, c)), $product(3, b)), $product(3, a)) =
% 7.75/1.81 | -1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (45), (47) imply:
% 7.75/1.81 | (48) $sum($sum($sum($difference($sum($sum($sum($sum($sum($product(2,
% 7.75/1.81 | all_4_14), $product(2, all_4_15)), all_4_23),
% 7.75/1.81 | $product(2, all_4_24)), all_4_27), all_4_30), all_2_1),
% 7.75/1.81 | $product(2, c)), $product(2, b)), $product(2, a)) = -1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (45), (48) imply:
% 7.75/1.81 | (49) $difference($difference($difference($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(3,
% 7.75/1.81 | all_4_9), $product(3, all_4_10)),
% 7.75/1.81 | $product(3, all_4_11)), $product(6,
% 7.75/1.81 | all_4_12)), $product(3, all_4_13)),
% 7.75/1.81 | all_4_20), $product(3, all_4_21)), $product(3,
% 7.75/1.81 | all_4_22)), all_4_26), all_4_29), all_2_0),
% 7.75/1.81 | $product(3, all_2_1)), $product(3, c)), $product(3, b)),
% 7.75/1.81 | $product(3, a)) = 2
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (39), (48), (49) imply:
% 7.75/1.81 | (50) $sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($product(4,
% 7.75/1.81 | all_4_0), $product(4,
% 7.75/1.81 | all_4_1)), $product(6,
% 7.75/1.81 | all_4_2)), $product(12,
% 7.75/1.81 | all_4_3)), $product(6, all_4_4)),
% 7.75/1.81 | $product(4, all_4_5)), $product(12,
% 7.75/1.81 | all_4_6)), $product(12, all_4_7)),
% 7.75/1.81 | $product(4, all_4_8)), all_4_16), $product(4,
% 7.75/1.81 | all_4_17)), $product(6, all_4_18)), $product(4,
% 7.75/1.81 | all_4_19)), all_4_25), all_4_28), $product(4,
% 7.75/1.81 | all_2_0)), $product(6, all_2_1)), $product(4, c)),
% 7.75/1.81 | $product(4, b)), $product(4, a)) = -3
% 7.75/1.81 |
% 7.75/1.81 | COL_REDUCE: introducing fresh symbol sc_9_0_0 defined by:
% 7.75/1.81 | (51) $difference($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum($sum(all_4_0,
% 7.75/1.81 | all_4_1), all_4_2), $product(3,
% 7.75/1.81 | all_4_3)), all_4_4), all_4_5),
% 7.75/1.81 | $product(3, all_4_6)), $product(3, all_4_7)),
% 7.75/1.81 | all_4_8), all_4_17), all_4_18), all_4_19),
% 7.75/1.81 | all_2_0), $product(2, all_2_1)), c), b), a), sc_9_0_0) =
% 7.75/1.81 | -1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (50), (51) imply:
% 7.75/1.81 | (52) $sum($sum($sum($sum($sum($sum($sum($product(2, all_4_2), $product(2,
% 7.75/1.81 | all_4_4)), all_4_16), $product(2, all_4_18)),
% 7.75/1.81 | all_4_25), all_4_28), $product(2, all_2_1)), $product(4,
% 7.75/1.81 | sc_9_0_0)) = 1
% 7.75/1.81 |
% 7.75/1.81 | COL_REDUCE: introducing fresh symbol sc_9_0_1 defined by:
% 7.75/1.81 | (53) $difference($sum($sum($sum($sum(all_4_2, all_4_4), all_4_18),
% 7.75/1.81 | all_2_1), $product(2, sc_9_0_0)), sc_9_0_1) = 1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (52), (53) imply:
% 7.75/1.81 | (54) $sum($sum($sum(all_4_16, all_4_25), all_4_28), $product(2, sc_9_0_1))
% 7.75/1.81 | = -1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (51), (53) imply:
% 7.75/1.81 | (55) $sum($difference($sum($sum($sum($difference($sum($sum($sum($sum($sum($sum($sum($sum($sum(all_4_0,
% 7.75/1.81 | all_4_1), $product(3, all_4_3)),
% 7.75/1.81 | all_4_5), $product(3, all_4_6)), $product(3,
% 7.75/1.81 | all_4_7)), all_4_8), all_4_17), all_4_19),
% 7.75/1.81 | all_2_0), $product(3, all_2_1)), c), b), a), $product(3,
% 7.75/1.81 | sc_9_0_0)), sc_9_0_1) = -2
% 7.75/1.81 |
% 7.75/1.81 | COL_REDUCE: introducing fresh symbol sc_9_0_2 defined by:
% 7.75/1.81 | (56) $difference($difference($difference($difference($sum($sum($sum($sum($sum($sum($sum(all_4_9,
% 7.75/1.81 | all_4_10), all_4_11), $product(2, all_4_12)),
% 7.75/1.81 | all_4_13), all_4_21), all_4_22), all_2_1), c), b), a),
% 7.75/1.81 | sc_9_0_2) = 1
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (49), (56) imply:
% 7.75/1.81 | (57) $sum($difference($sum($sum(all_4_20, all_4_26), all_4_29), all_2_0),
% 7.75/1.81 | $product(3, sc_9_0_2)) = -1
% 7.75/1.81 |
% 7.75/1.81 | COL_REDUCE: introducing fresh symbol sc_9_0_3 defined by:
% 7.75/1.81 | (58) $sum($sum($sum($difference($sum($sum(all_4_14, all_4_15), all_4_24),
% 7.75/1.81 | all_2_1), c), b), a) = sc_9_0_3
% 7.75/1.81 |
% 7.75/1.81 | COMBINE_EQS: (48), (58) imply:
% 7.75/1.81 | (59) $sum($sum($sum($sum(all_4_23, all_4_27), all_4_30), all_2_1),
% 7.75/1.81 | $product(2, sc_9_0_3)) = -1
% 7.75/1.81 |
% 7.75/1.81 | REDUCE: (6), (53), (54), (55), (56), (57), (58), (59) imply:
% 7.75/1.81 | (60) $false
% 7.75/1.81 |
% 7.75/1.81 | CLOSE: (60) is inconsistent.
% 7.75/1.81 |
% 7.75/1.81 End of proof
% 7.75/1.81 % SZS output end Proof for theBenchmark
% 7.75/1.81
% 7.75/1.81 1249ms
%------------------------------------------------------------------------------