TSTP Solution File: ARI712_1 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------