TSTP Solution File: ARI687_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI687_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 : n027.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 17:48:49 EDT 2023
% Result : Theorem 5.19s 1.58s
% Output : Proof 6.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI687_1 : TPTP v8.1.2. Released v6.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n027.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 18:24:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/1.09 Prover 5: Preprocessing ...
% 2.13/1.09 Prover 1: Preprocessing ...
% 2.13/1.09 Prover 0: Preprocessing ...
% 2.13/1.09 Prover 3: Preprocessing ...
% 2.13/1.09 Prover 2: Preprocessing ...
% 2.13/1.09 Prover 4: Preprocessing ...
% 2.13/1.09 Prover 6: Preprocessing ...
% 2.89/1.18 Prover 2: Constructing countermodel ...
% 2.89/1.18 Prover 6: Constructing countermodel ...
% 2.89/1.18 Prover 4: Constructing countermodel ...
% 2.89/1.18 Prover 3: Constructing countermodel ...
% 2.89/1.18 Prover 0: Constructing countermodel ...
% 2.89/1.18 Prover 5: Constructing countermodel ...
% 2.89/1.18 Prover 1: Constructing countermodel ...
% 5.19/1.58 Prover 3: proved (907ms)
% 5.19/1.58
% 5.19/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.58
% 5.19/1.58 Prover 6: stopped
% 5.19/1.58 Prover 5: stopped
% 5.19/1.58 Prover 0: proved (910ms)
% 5.19/1.58
% 5.19/1.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/1.58
% 5.19/1.58 Prover 2: stopped
% 5.19/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.19/1.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.19/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.19/1.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.19/1.60 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.19/1.61 Prover 7: Preprocessing ...
% 5.91/1.61 Prover 8: Preprocessing ...
% 5.91/1.62 Prover 11: Preprocessing ...
% 5.91/1.62 Prover 13: Preprocessing ...
% 5.91/1.63 Prover 10: Preprocessing ...
% 5.91/1.63 Prover 8: Constructing countermodel ...
% 5.91/1.65 Prover 11: Constructing countermodel ...
% 5.91/1.66 Prover 7: Constructing countermodel ...
% 5.91/1.66 Prover 10: Constructing countermodel ...
% 5.91/1.67 Prover 13: Constructing countermodel ...
% 5.91/1.68 Prover 1: Found proof (size 37)
% 5.91/1.68 Prover 1: proved (1014ms)
% 5.91/1.68 Prover 7: stopped
% 5.91/1.68 Prover 10: stopped
% 5.91/1.68 Prover 11: stopped
% 5.91/1.68 Prover 13: stopped
% 5.91/1.68 Prover 4: stopped
% 6.52/1.72 Prover 8: stopped
% 6.52/1.72
% 6.52/1.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.52/1.72
% 6.52/1.72 % SZS output start Proof for theBenchmark
% 6.52/1.73 Assumptions after simplification:
% 6.52/1.73 ---------------------------------
% 6.52/1.73
% 6.52/1.73 (conj)
% 6.52/1.73 ? [v0: int] : ? [v1: int] : ( ~ ($difference($product(2, v1), $product(5,
% 6.52/1.73 v0)) = $product(5, x)) & $product(v0, x) = v1 & $product(x, x) = v0)
% 6.52/1.73
% 6.52/1.73 (eq1)
% 6.52/1.74 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] : ?
% 6.52/1.74 [v5: int] : ($product(v4, x) = v5 & $product(v1, y) = v2 & $product(v0, y) =
% 6.52/1.74 v3 & $product(v0, x) = v1 & $product($product(3, x), x) = v4 &
% 6.52/1.74 $product($product(2, x), x) = $difference($difference($product(-1, v5), v3),
% 6.52/1.74 v2) & $product(x, x) = v0)
% 6.52/1.74
% 6.52/1.74 (eq2)
% 6.52/1.74 ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ? [v4: int] :
% 6.52/1.74 ($product(v4, x) = $sum($sum($sum($sum($difference(v3, v2), v0), y),
% 6.52/1.74 $product(3, x)), -3) & $product(v1, y) = v2 & $product(v0, x) = v1 &
% 6.52/1.74 $product($product(6, x), x) = v4 & $product($product(2, x), x) = v0 &
% 6.52/1.74 $product(x, y) = v3)
% 6.52/1.74
% 6.52/1.74 (eq3)
% 6.52/1.74 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($product(v0, y) = v1 &
% 6.52/1.74 $product($product(9, x), x) =
% 6.52/1.74 $sum($difference($difference($difference($product(-1, v2), v1), y),
% 6.52/1.74 $product(5, x)), 3) & $product($product(3, x), x) = v0 &
% 6.52/1.74 $product($product(2, x), y) = v2)
% 6.52/1.74
% 6.52/1.74 Those formulas are unsatisfiable:
% 6.52/1.74 ---------------------------------
% 6.52/1.74
% 6.52/1.74 Begin of proof
% 6.52/1.74 |
% 6.52/1.74 | DELTA: instantiating (conj) with fresh symbols all_2_0, all_2_1 gives:
% 6.52/1.75 | (1) ~ ($difference($product(2, all_2_0), $product(5, all_2_1)) =
% 6.52/1.75 | $product(5, x)) & $product(all_2_1, x) = all_2_0 & $product(x, x) =
% 6.52/1.75 | all_2_1
% 6.52/1.75 |
% 6.52/1.75 | ALPHA: (1) implies:
% 6.52/1.75 | (2) ~ ($difference($product(2, all_2_0), $product(5, all_2_1)) =
% 6.52/1.75 | $product(5, x))
% 6.52/1.75 | (3) $product(x, x) = all_2_1
% 6.52/1.75 | (4) $product(all_2_1, x) = all_2_0
% 6.52/1.75 |
% 6.52/1.75 | DELTA: instantiating (eq3) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 6.52/1.75 | (5) $product(all_4_2, y) = all_4_1 & $product($product(9, x), x) =
% 6.52/1.75 | $sum($difference($difference($difference($product(-1, all_4_0),
% 6.52/1.75 | all_4_1), y), $product(5, x)), 3) & $product($product(3, x), x)
% 6.52/1.75 | = all_4_2 & $product($product(2, x), y) = all_4_0
% 6.52/1.75 |
% 6.52/1.75 | ALPHA: (5) implies:
% 6.52/1.75 | (6) $product($product(2, x), y) = all_4_0
% 6.52/1.75 | (7) $product($product(3, x), x) = all_4_2
% 6.52/1.75 | (8) $product($product(9, x), x) =
% 6.52/1.75 | $sum($difference($difference($difference($product(-1, all_4_0),
% 6.52/1.75 | all_4_1), y), $product(5, x)), 3)
% 6.52/1.75 | (9) $product(all_4_2, y) = all_4_1
% 6.52/1.75 |
% 6.52/1.75 | DELTA: instantiating (eq2) with fresh symbols all_6_0, all_6_1, all_6_2,
% 6.52/1.75 | all_6_3, all_6_4 gives:
% 6.52/1.75 | (10) $product(all_6_0, x) = $sum($sum($sum($sum($difference(all_6_1,
% 6.52/1.75 | all_6_2), all_6_4), y), $product(3, x)), -3) &
% 6.52/1.75 | $product(all_6_3, y) = all_6_2 & $product(all_6_4, x) = all_6_3 &
% 6.52/1.75 | $product($product(6, x), x) = all_6_0 & $product($product(2, x), x) =
% 6.52/1.75 | all_6_4 & $product(x, y) = all_6_1
% 6.52/1.75 |
% 6.52/1.75 | ALPHA: (10) implies:
% 6.52/1.75 | (11) $product(x, y) = all_6_1
% 6.52/1.75 | (12) $product($product(2, x), x) = all_6_4
% 6.52/1.75 | (13) $product($product(6, x), x) = all_6_0
% 6.52/1.75 | (14) $product(all_6_4, x) = all_6_3
% 6.52/1.75 | (15) $product(all_6_3, y) = all_6_2
% 6.52/1.76 | (16) $product(all_6_0, x) = $sum($sum($sum($sum($difference(all_6_1,
% 6.52/1.76 | all_6_2), all_6_4), y), $product(3, x)), -3)
% 6.52/1.76 |
% 6.52/1.76 | DELTA: instantiating (eq1) with fresh symbols all_8_0, all_8_1, all_8_2,
% 6.52/1.76 | all_8_3, all_8_4, all_8_5 gives:
% 6.52/1.76 | (17) $product(all_8_1, x) = all_8_0 & $product(all_8_4, y) = all_8_3 &
% 6.52/1.76 | $product(all_8_5, y) = all_8_2 & $product(all_8_5, x) = all_8_4 &
% 6.52/1.76 | $product($product(3, x), x) = all_8_1 & $product($product(2, x), x) =
% 6.52/1.76 | $difference($difference($product(-1, all_8_0), all_8_2), all_8_3) &
% 6.52/1.76 | $product(x, x) = all_8_5
% 6.52/1.76 |
% 6.52/1.76 | ALPHA: (17) implies:
% 6.52/1.76 | (18) $product(x, x) = all_8_5
% 6.52/1.76 | (19) $product($product(2, x), x) = $difference($difference($product(-1,
% 6.52/1.76 | all_8_0), all_8_2), all_8_3)
% 6.52/1.76 | (20) $product($product(3, x), x) = all_8_1
% 6.52/1.76 | (21) $product(all_8_5, x) = all_8_4
% 6.52/1.76 | (22) $product(all_8_5, y) = all_8_2
% 6.52/1.76 | (23) $product(all_8_4, y) = all_8_3
% 6.52/1.76 | (24) $product(all_8_1, x) = all_8_0
% 6.52/1.76 |
% 6.52/1.76 | THEORY_AXIOM GroebnerMultiplication:
% 6.52/1.76 | (25) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 6.52/1.76 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 6.52/1.76 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 6.52/1.76 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] :
% 6.52/1.76 | ($difference($difference($sum($product(7, v9), $product(6, v2)), v1),
% 6.52/1.76 | $product(2, v0)) = -3 | ~ ($product(v15, v0) = v16) | ~
% 6.52/1.76 | ($product(v12, v1) = v13) | ~ ($product(v11, v1) = v14) | ~
% 6.52/1.76 | ($product(v11, v0) = v12) | ~ ($product(v10, v0) =
% 6.52/1.76 | $sum($sum($sum($sum($difference(v9, v8), v6), v1), $product(3,
% 6.52/1.76 | v0)), -3)) | ~ ($product(v7, v1) = v8) | ~ ($product(v6,
% 6.52/1.76 | v0) = v7) | ~ ($product(v3, v1) = v4) | ~
% 6.52/1.76 | ($product($product(9, v0), v0) =
% 6.52/1.76 | $sum($difference($difference($difference($product(-1, v5), v4),
% 6.52/1.76 | v1), $product(5, v0)), 3)) | ~ ($product($product(6, v0),
% 6.52/1.76 | v0) = v10) | ~ ($product($product(3, v0), v0) = v15) | ~
% 6.52/1.76 | ($product($product(3, v0), v0) = v3) | ~ ($product($product(2, v0),
% 6.52/1.76 | v1) = v5) | ~ ($product($product(2, v0), v0) =
% 6.52/1.76 | $difference($difference($product(-1, v16), v14), v13)) | ~
% 6.52/1.76 | ($product($product(2, v0), v0) = v6) | ~ ($product(v0, v1) = v9) |
% 6.52/1.76 | ~ ($product(v0, v0) = v11) | ~ ($product(v0, v0) = v2))
% 6.52/1.76 |
% 6.52/1.76 | GROUND_INST: instantiating (25) with x, y, all_2_1, all_4_2, all_4_1, all_4_0,
% 6.52/1.76 | all_6_4, all_6_3, all_6_2, all_6_1, all_6_0, all_8_5, all_8_4,
% 6.52/1.76 | all_8_3, all_8_2, all_8_1, all_8_0, simplifying with (3), (6),
% 6.52/1.76 | (7), (8), (9), (11), (12), (13), (14), (15), (16), (18), (19),
% 6.52/1.77 | (20), (21), (22), (23), (24) gives:
% 6.52/1.77 | (26) $difference($difference($sum($product(7, all_6_1), $product(6,
% 6.52/1.77 | all_2_1)), y), $product(2, x)) = -3
% 6.52/1.77 |
% 6.52/1.77 | THEORY_AXIOM GroebnerMultiplication:
% 6.52/1.77 | (27) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 6.52/1.77 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 6.52/1.77 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 6.52/1.77 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] :
% 6.52/1.77 | ($sum($product(2, v9), $product(2, v2)) = v0 | ~ ($product(v15, v0) =
% 6.52/1.77 | v16) | ~ ($product(v12, v1) = v13) | ~ ($product(v11, v1) = v14)
% 6.52/1.77 | | ~ ($product(v11, v0) = v12) | ~ ($product(v10, v0) =
% 6.52/1.77 | $sum($sum($sum($sum($difference(v9, v8), v6), v1), $product(3,
% 6.52/1.77 | v0)), -3)) | ~ ($product(v7, v1) = v8) | ~ ($product(v6,
% 6.52/1.77 | v0) = v7) | ~ ($product(v3, v1) = v4) | ~
% 6.52/1.77 | ($product($product(9, v0), v0) =
% 6.52/1.77 | $sum($difference($difference($difference($product(-1, v5), v4),
% 6.52/1.77 | v1), $product(5, v0)), 3)) | ~ ($product($product(6, v0),
% 6.52/1.77 | v0) = v10) | ~ ($product($product(3, v0), v0) = v15) | ~
% 6.52/1.77 | ($product($product(3, v0), v0) = v3) | ~ ($product($product(2, v0),
% 6.52/1.77 | v1) = v5) | ~ ($product($product(2, v0), v0) =
% 6.52/1.77 | $difference($difference($product(-1, v16), v14), v13)) | ~
% 6.52/1.77 | ($product($product(2, v0), v0) = v6) | ~ ($product(v0, v1) = v9) |
% 6.52/1.77 | ~ ($product(v0, v0) = v11) | ~ ($product(v0, v0) = v2))
% 6.52/1.77 |
% 6.52/1.77 | GROUND_INST: instantiating (27) with x, y, all_2_1, all_4_2, all_4_1, all_4_0,
% 6.52/1.77 | all_6_4, all_6_3, all_6_2, all_6_1, all_6_0, all_8_5, all_8_4,
% 6.52/1.77 | all_8_3, all_8_2, all_8_1, all_8_0, simplifying with (3), (6),
% 6.52/1.77 | (7), (8), (9), (11), (12), (13), (14), (15), (16), (18), (19),
% 6.52/1.77 | (20), (21), (22), (23), (24) gives:
% 6.52/1.77 | (28) $sum($product(2, all_6_1), $product(2, all_2_1)) = x
% 6.52/1.77 |
% 6.52/1.77 | THEORY_AXIOM GroebnerMultiplication:
% 6.52/1.77 | (29) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 6.52/1.77 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 6.52/1.77 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 6.52/1.77 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] :
% 6.52/1.77 | ($sum($sum(v14, $product(5, v9)), $product(7, v2)) = 0 | ~
% 6.52/1.77 | ($product(v15, v0) = v16) | ~ ($product(v12, v1) = v13) | ~
% 6.52/1.77 | ($product(v11, v1) = v14) | ~ ($product(v11, v0) = v12) | ~
% 6.52/1.77 | ($product(v10, v0) = $sum($sum($sum($sum($difference(v9, v8), v6),
% 6.52/1.77 | v1), $product(3, v0)), -3)) | ~ ($product(v7, v1) = v8) |
% 6.52/1.77 | ~ ($product(v6, v0) = v7) | ~ ($product(v3, v1) = v4) | ~
% 6.52/1.77 | ($product($product(9, v0), v0) =
% 6.52/1.77 | $sum($difference($difference($difference($product(-1, v5), v4),
% 6.52/1.77 | v1), $product(5, v0)), 3)) | ~ ($product($product(6, v0),
% 6.52/1.77 | v0) = v10) | ~ ($product($product(3, v0), v0) = v15) | ~
% 6.52/1.77 | ($product($product(3, v0), v0) = v3) | ~ ($product($product(2, v0),
% 6.52/1.77 | v1) = v5) | ~ ($product($product(2, v0), v0) =
% 6.52/1.77 | $difference($difference($product(-1, v16), v14), v13)) | ~
% 6.52/1.77 | ($product($product(2, v0), v0) = v6) | ~ ($product(v0, v1) = v9) |
% 6.52/1.77 | ~ ($product(v0, v0) = v11) | ~ ($product(v0, v0) = v2))
% 6.52/1.77 |
% 6.52/1.78 | GROUND_INST: instantiating (29) with x, y, all_2_1, all_4_2, all_4_1, all_4_0,
% 6.52/1.78 | all_6_4, all_6_3, all_6_2, all_6_1, all_6_0, all_8_5, all_8_4,
% 6.52/1.78 | all_8_3, all_8_2, all_8_1, all_8_0, simplifying with (3), (6),
% 6.52/1.78 | (7), (8), (9), (11), (12), (13), (14), (15), (16), (18), (19),
% 6.52/1.78 | (20), (21), (22), (23), (24) gives:
% 6.52/1.78 | (30) $sum($sum(all_8_2, $product(5, all_6_1)), $product(7, all_2_1)) = 0
% 6.52/1.78 |
% 6.52/1.78 | THEORY_AXIOM GroebnerMultiplication:
% 6.52/1.78 | (31) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 6.52/1.78 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 6.52/1.78 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 6.52/1.78 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 6.52/1.78 | : ($sum($product(2, v15), $product(2, v3)) = v2 | ~ ($product(v16,
% 6.52/1.78 | v0) = v17) | ~ ($product(v13, v1) = v14) | ~ ($product(v12,
% 6.52/1.78 | v1) = v15) | ~ ($product(v12, v0) = v13) | ~ ($product(v11,
% 6.52/1.78 | v0) = $sum($sum($sum($sum($difference(v10, v9), v7), v1),
% 6.52/1.78 | $product(3, v0)), -3)) | ~ ($product(v8, v1) = v9) | ~
% 6.52/1.78 | ($product(v7, v0) = v8) | ~ ($product(v4, v1) = v5) | ~
% 6.52/1.78 | ($product(v2, v0) = v3) | ~ ($product($product(9, v0), v0) =
% 6.52/1.78 | $sum($difference($difference($difference($product(-1, v6), v5),
% 6.52/1.78 | v1), $product(5, v0)), 3)) | ~ ($product($product(6, v0),
% 6.52/1.78 | v0) = v11) | ~ ($product($product(3, v0), v0) = v16) | ~
% 6.52/1.78 | ($product($product(3, v0), v0) = v4) | ~ ($product($product(2, v0),
% 6.52/1.78 | v1) = v6) | ~ ($product($product(2, v0), v0) =
% 6.52/1.78 | $difference($difference($product(-1, v17), v15), v14)) | ~
% 6.52/1.78 | ($product($product(2, v0), v0) = v7) | ~ ($product(v0, v1) = v10) |
% 6.52/1.78 | ~ ($product(v0, v0) = v12) | ~ ($product(v0, v0) = v2))
% 6.52/1.78 |
% 6.93/1.78 | GROUND_INST: instantiating (31) with x, y, all_2_1, all_2_0, all_4_2, all_4_1,
% 6.93/1.78 | all_4_0, all_6_4, all_6_3, all_6_2, all_6_1, all_6_0, all_8_5,
% 6.93/1.78 | all_8_4, all_8_3, all_8_2, all_8_1, all_8_0, simplifying with
% 6.93/1.78 | (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), (16),
% 6.93/1.78 | (18), (19), (20), (21), (22), (23), (24) gives:
% 6.93/1.78 | (32) $sum($product(2, all_8_2), $product(2, all_2_0)) = all_2_1
% 6.93/1.78 |
% 6.93/1.78 | THEORY_AXIOM GroebnerMultiplication:
% 6.93/1.79 | (33) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 6.93/1.79 | int] : ! [v5: int] : ! [v6: int] : ! [v7: int] : ! [v8: int] :
% 6.93/1.79 | ! [v9: int] : ! [v10: int] : ! [v11: int] : ! [v12: int] : ! [v13:
% 6.93/1.79 | int] : ! [v14: int] : ! [v15: int] : ! [v16: int] : ! [v17: int]
% 6.93/1.79 | : ($sum($sum($product(2, v14), $product(4, v3)), $product(5, v2)) = 0
% 6.93/1.79 | | ~ ($product(v16, v0) = v17) | ~ ($product(v13, v1) = v14) | ~
% 6.93/1.79 | ($product(v12, v1) = v15) | ~ ($product(v12, v0) = v13) | ~
% 6.93/1.79 | ($product(v11, v0) = $sum($sum($sum($sum($difference(v10, v9), v7),
% 6.93/1.79 | v1), $product(3, v0)), -3)) | ~ ($product(v8, v1) = v9) |
% 6.93/1.79 | ~ ($product(v7, v0) = v8) | ~ ($product(v4, v1) = v5) | ~
% 6.93/1.79 | ($product(v2, v0) = v3) | ~ ($product($product(9, v0), v0) =
% 6.93/1.79 | $sum($difference($difference($difference($product(-1, v6), v5),
% 6.93/1.79 | v1), $product(5, v0)), 3)) | ~ ($product($product(6, v0),
% 6.93/1.79 | v0) = v11) | ~ ($product($product(3, v0), v0) = v16) | ~
% 6.93/1.79 | ($product($product(3, v0), v0) = v4) | ~ ($product($product(2, v0),
% 6.93/1.79 | v1) = v6) | ~ ($product($product(2, v0), v0) =
% 6.93/1.79 | $difference($difference($product(-1, v17), v15), v14)) | ~
% 6.93/1.79 | ($product($product(2, v0), v0) = v7) | ~ ($product(v0, v1) = v10) |
% 6.93/1.79 | ~ ($product(v0, v0) = v12) | ~ ($product(v0, v0) = v2))
% 6.93/1.79 |
% 6.93/1.79 | GROUND_INST: instantiating (33) with x, y, all_2_1, all_2_0, all_4_2, all_4_1,
% 6.93/1.79 | all_4_0, all_6_4, all_6_3, all_6_2, all_6_1, all_6_0, all_8_5,
% 6.93/1.79 | all_8_4, all_8_3, all_8_2, all_8_1, all_8_0, simplifying with
% 6.93/1.79 | (3), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), (16),
% 6.93/1.79 | (18), (19), (20), (21), (22), (23), (24) gives:
% 6.93/1.79 | (34) $sum($sum($product(2, all_8_3), $product(4, all_2_0)), $product(5,
% 6.93/1.79 | all_2_1)) = 0
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (30), (32) imply:
% 6.93/1.79 | (35) $sum($difference($product(10, all_6_1), $product(2, all_2_0)),
% 6.93/1.79 | $product(15, all_2_1)) = 0
% 6.93/1.79 |
% 6.93/1.79 | SIMP: (35) implies:
% 6.93/1.79 | (36) $sum($difference($product(10, all_6_1), $product(2, all_2_0)),
% 6.93/1.79 | $product(15, all_2_1)) = 0
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (26), (28) imply:
% 6.93/1.79 | (37) $sum($difference(all_6_1, y), x) = -3
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (26), (37) imply:
% 6.93/1.79 | (38) $difference($sum($product(2, all_2_1), $product(2, y)), $product(3,
% 6.93/1.79 | x)) = 6
% 6.93/1.79 |
% 6.93/1.79 | SIMP: (38) implies:
% 6.93/1.79 | (39) $difference($sum($product(2, all_2_1), $product(2, y)), $product(3,
% 6.93/1.79 | x)) = 6
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (36), (37) imply:
% 6.93/1.79 | (40) $sum($difference($difference($product(2, all_2_0), $product(15,
% 6.93/1.79 | all_2_1)), $product(10, y)), $product(10, x)) = -30
% 6.93/1.79 |
% 6.93/1.79 | SIMP: (40) implies:
% 6.93/1.79 | (41) $sum($difference($difference($product(2, all_2_0), $product(15,
% 6.93/1.79 | all_2_1)), $product(10, y)), $product(10, x)) = -30
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (39), (41) imply:
% 6.93/1.79 | (42) $difference($sum($sum($product(2, all_2_0), all_2_1), $product(6, y)),
% 6.93/1.79 | $product(14, x)) = 18
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (34), (39), (42) imply:
% 6.93/1.79 | (43) $sum($difference($sum($product(2, all_8_3), all_2_1), $product(14,
% 6.93/1.79 | y)), $product(31, x)) = -42
% 6.93/1.79 |
% 6.93/1.79 | COL_REDUCE: introducing fresh symbol sc_13_0_0 defined by:
% 6.93/1.79 | (44) $difference($sum($difference(all_8_3, $product(7, y)), $product(15,
% 6.93/1.79 | x)), sc_13_0_0) = -21
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (43), (44) imply:
% 6.93/1.79 | (45) $sum($sum(all_2_1, x), $product(2, sc_13_0_0)) = 0
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (39), (45) imply:
% 6.93/1.79 | (46) $difference($difference($product(2, y), $product(5, x)), $product(4,
% 6.93/1.79 | sc_13_0_0)) = 6
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (42), (45), (46) imply:
% 6.93/1.79 | (47) $sum(all_2_0, $product(5, sc_13_0_0)) = 0
% 6.93/1.79 |
% 6.93/1.79 | SIMP: (47) implies:
% 6.93/1.79 | (48) $sum(all_2_0, $product(5, sc_13_0_0)) = 0
% 6.93/1.79 |
% 6.93/1.79 | COL_REDUCE: introducing fresh symbol sc_13_0_1 defined by:
% 6.93/1.79 | (49) $difference($difference($difference(y, $product(3, x)), $product(2,
% 6.93/1.79 | sc_13_0_0)), sc_13_0_1) = 3
% 6.93/1.79 |
% 6.93/1.79 | COMBINE_EQS: (46), (49) imply:
% 6.93/1.79 | (50) $sum(x, $product(2, sc_13_0_1)) = 0
% 6.93/1.79 |
% 6.93/1.80 | COMBINE_EQS: (45), (50) imply:
% 6.93/1.80 | (51) $sum(all_2_1, $product(2, sc_13_0_0)) = $product(2, sc_13_0_1)
% 6.93/1.80 |
% 6.93/1.80 | REDUCE: (2), (48), (50), (51) imply:
% 6.93/1.80 | (52) $false
% 6.93/1.80 |
% 6.93/1.80 | CLOSE: (52) is inconsistent.
% 6.93/1.80 |
% 6.93/1.80 End of proof
% 6.93/1.80 % SZS output end Proof for theBenchmark
% 6.93/1.80
% 6.93/1.80 1153ms
%------------------------------------------------------------------------------