TSTP Solution File: ARI698_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI698_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 : n020.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 17:48:51 EDT 2023
% Result : Theorem 3.01s 1.25s
% Output : Proof 5.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ARI698_1 : TPTP v8.1.2. Released v6.3.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 18:51:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.70/1.11 Prover 2: Preprocessing ...
% 2.70/1.11 Prover 5: Preprocessing ...
% 2.70/1.11 Prover 4: Preprocessing ...
% 2.70/1.12 Prover 3: Preprocessing ...
% 2.70/1.12 Prover 6: Preprocessing ...
% 2.70/1.12 Prover 1: Preprocessing ...
% 2.70/1.12 Prover 0: Preprocessing ...
% 3.01/1.22 Prover 6: Constructing countermodel ...
% 3.01/1.22 Prover 3: Constructing countermodel ...
% 3.01/1.22 Prover 2: Constructing countermodel ...
% 3.01/1.23 Prover 0: Constructing countermodel ...
% 3.01/1.24 Prover 4: Constructing countermodel ...
% 3.01/1.25 Prover 1: Constructing countermodel ...
% 3.01/1.25 Prover 3: proved (605ms)
% 3.01/1.25 Prover 6: proved (602ms)
% 3.01/1.25 Prover 0: proved (609ms)
% 3.01/1.25
% 3.01/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.01/1.25
% 3.01/1.25 Prover 2: proved (606ms)
% 3.01/1.25
% 3.01/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.01/1.25
% 3.01/1.26
% 3.01/1.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.01/1.26
% 3.01/1.27
% 3.01/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.01/1.27
% 3.01/1.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.01/1.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.01/1.27 Prover 5: Constructing countermodel ...
% 3.01/1.27 Prover 5: stopped
% 3.01/1.27 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.01/1.27 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.01/1.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.96/1.31 Prover 7: Preprocessing ...
% 3.96/1.32 Prover 13: Preprocessing ...
% 3.96/1.32 Prover 8: Preprocessing ...
% 3.96/1.34 Prover 11: Preprocessing ...
% 3.96/1.34 Prover 10: Preprocessing ...
% 3.96/1.36 Prover 13: Constructing countermodel ...
% 3.96/1.36 Prover 8: Constructing countermodel ...
% 4.49/1.36 Prover 11: Constructing countermodel ...
% 4.49/1.39 Prover 7: Constructing countermodel ...
% 4.49/1.40 Prover 10: Constructing countermodel ...
% 5.20/1.51 Prover 13: Found proof (size 35)
% 5.20/1.51 Prover 1: Found proof (size 35)
% 5.20/1.51 Prover 13: proved (242ms)
% 5.20/1.52 Prover 1: proved (873ms)
% 5.20/1.52 Prover 11: stopped
% 5.20/1.52 Prover 4: Found proof (size 35)
% 5.20/1.52 Prover 4: proved (871ms)
% 5.20/1.52 Prover 7: stopped
% 5.20/1.52 Prover 8: Found proof (size 35)
% 5.20/1.52 Prover 8: proved (253ms)
% 5.20/1.52 Prover 10: Found proof (size 35)
% 5.20/1.52 Prover 10: proved (251ms)
% 5.20/1.52
% 5.20/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.20/1.52
% 5.20/1.53 % SZS output start Proof for theBenchmark
% 5.70/1.53 Assumptions after simplification:
% 5.70/1.53 ---------------------------------
% 5.70/1.53
% 5.70/1.53 (conj)
% 5.70/1.54 ~ (x1 = 0) | ~ (x2 = 0) | ~ (x3 = 0) | ~ (x4 = 0) | ~ (x5 = 0) | ~ (x6 =
% 5.70/1.54 0)
% 5.70/1.54
% 5.70/1.54 (eq1)
% 5.70/1.54 n = 1000
% 5.70/1.54
% 5.70/1.54 (eq10)
% 5.70/1.54 $product(n, x6) = $difference(x2, x1)
% 5.70/1.54
% 5.70/1.54 (eq11)
% 5.70/1.54 $product(n, x6) = x1
% 5.70/1.54
% 5.70/1.54 (eq4)
% 5.70/1.54 $product(n, x6) = $difference($sum($sum($sum(x1, x2), x3), x4), x5)
% 5.70/1.54
% 5.70/1.54 (eq5)
% 5.70/1.54 $product(n, x6) = $difference($difference($difference($product(-1, x1), x2),
% 5.70/1.54 x3), x4)
% 5.70/1.54
% 5.70/1.54 (eq8)
% 5.70/1.54 $product(n, x6) = $difference($sum(x1, x2), x3)
% 5.70/1.54
% 5.70/1.54 (eq9)
% 5.70/1.54 $product(n, x6) = $difference($product(-1, x1), x2)
% 5.70/1.54
% 5.70/1.54 Further assumptions not needed in the proof:
% 5.70/1.54 --------------------------------------------
% 5.70/1.54 eq2, eq3, eq6, eq7
% 5.70/1.54
% 5.70/1.54 Those formulas are unsatisfiable:
% 5.70/1.54 ---------------------------------
% 5.70/1.54
% 5.70/1.54 Begin of proof
% 5.70/1.54 |
% 5.70/1.55 | REDUCE: (eq1), (eq5) imply:
% 5.70/1.55 | (1) $product(1000, x6) = $difference($difference($difference($product(-1,
% 5.70/1.55 | x1), x2), x3), x4)
% 5.70/1.55 |
% 5.70/1.55 | REDUCE: (eq1), (eq9) imply:
% 5.70/1.55 | (2) $product(1000, x6) = $difference($product(-1, x1), x2)
% 5.70/1.55 |
% 5.70/1.55 | REDUCE: (eq1), (eq10) imply:
% 5.70/1.55 | (3) $product(1000, x6) = $difference(x2, x1)
% 5.70/1.55 |
% 5.70/1.55 | REDUCE: (eq1), (eq8) imply:
% 5.70/1.55 | (4) $product(1000, x6) = $difference($sum(x1, x2), x3)
% 5.70/1.55 |
% 5.70/1.55 | REDUCE: (eq1), (eq4) imply:
% 5.70/1.55 | (5) $product(1000, x6) = $difference($sum($sum($sum(x1, x2), x3), x4), x5)
% 5.70/1.55 |
% 5.70/1.55 | REDUCE: (eq1), (eq11) imply:
% 5.70/1.55 | (6) $product(1000, x6) = x1
% 5.70/1.55 |
% 5.70/1.55 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.55 | (7) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v0 = 0 | ~
% 5.70/1.55 | ($product(1000, v0) = $difference($product(-1, v2), v1)) | ~
% 5.70/1.55 | ($product(1000, v0) = $difference(v1, v2)) | ~ ($product(1000, v0) =
% 5.70/1.55 | v2))
% 5.70/1.55 |
% 5.70/1.55 | GROUND_INST: instantiating (7) with x6, x2, x1, simplifying with (2), (3), (6)
% 5.70/1.55 | gives:
% 5.70/1.56 | (8) x6 = 0
% 5.70/1.56 |
% 5.70/1.56 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.56 | (9) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.70/1.56 | int] : ! [v5: int] : (v1 = 0 | ~ ($product(1000, v0) =
% 5.70/1.56 | $difference($difference($difference($product(-1, v5), v4), v3),
% 5.70/1.56 | v2)) | ~ ($product(1000, v0) = $difference($product(-1, v5),
% 5.70/1.56 | v4)) | ~ ($product(1000, v0) = $difference(v4, v5)) | ~
% 5.70/1.56 | ($product(1000, v0) = $difference($sum(v5, v4), v3)) | ~
% 5.70/1.56 | ($product(1000, v0) = $difference($sum($sum($sum(v5, v4), v3), v2),
% 5.70/1.56 | v1)) | ~ ($product(1000, v0) = v5))
% 5.70/1.56 |
% 5.70/1.56 | GROUND_INST: instantiating (9) with x6, x5, x4, x3, x2, x1, simplifying with
% 5.70/1.56 | (1), (2), (3), (4), (5), (6) gives:
% 5.70/1.56 | (10) x5 = 0
% 5.70/1.56 |
% 5.70/1.56 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.56 | (11) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4:
% 5.70/1.56 | int] : (v1 = 0 | ~ ($product(1000, v0) =
% 5.70/1.56 | $difference($difference($difference($product(-1, v4), v3), v2),
% 5.70/1.56 | v1)) | ~ ($product(1000, v0) = $difference($product(-1, v4),
% 5.70/1.56 | v3)) | ~ ($product(1000, v0) = $difference(v3, v4)) | ~
% 5.70/1.56 | ($product(1000, v0) = $difference($sum(v4, v3), v2)) | ~
% 5.70/1.56 | ($product(1000, v0) = v4))
% 5.70/1.56 |
% 5.70/1.56 | GROUND_INST: instantiating (11) with x6, x4, x3, x2, x1, simplifying with (1),
% 5.70/1.56 | (2), (3), (4), (6) gives:
% 5.70/1.56 | (12) x4 = 0
% 5.70/1.56 |
% 5.70/1.56 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.56 | (13) ! [v0: int] : ! [v1: int] : ! [v2: int] : ! [v3: int] : (v1 = 0 |
% 5.70/1.56 | ~ ($product(1000, v0) = $difference($product(-1, v3), v2)) | ~
% 5.70/1.56 | ($product(1000, v0) = $difference(v2, v3)) | ~ ($product(1000, v0)
% 5.70/1.56 | = $difference($sum(v3, v2), v1)) | ~ ($product(1000, v0) = v3))
% 5.70/1.56 |
% 5.70/1.57 | GROUND_INST: instantiating (13) with x6, x3, x2, x1, simplifying with (2),
% 5.70/1.57 | (3), (4), (6) gives:
% 5.70/1.57 | (14) x3 = 0
% 5.70/1.57 |
% 5.70/1.57 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.57 | (15) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~
% 5.70/1.57 | ($product(1000, v0) = $difference($product(-1, v2), v1)) | ~
% 5.70/1.57 | ($product(1000, v0) = $difference(v1, v2)) | ~ ($product(1000, v0)
% 5.70/1.57 | = v2))
% 5.70/1.57 |
% 5.70/1.57 | GROUND_INST: instantiating (15) with x6, x2, x1, simplifying with (2), (3),
% 5.70/1.57 | (6) gives:
% 5.70/1.57 | (16) x2 = 0
% 5.70/1.57 |
% 5.70/1.57 | THEORY_AXIOM GroebnerMultiplication:
% 5.70/1.57 | (17) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v2 = 0 | ~
% 5.70/1.57 | ($product(1000, v0) = $difference($product(-1, v2), v1)) | ~
% 5.70/1.57 | ($product(1000, v0) = $difference(v1, v2)) | ~ ($product(1000, v0)
% 5.70/1.57 | = v2))
% 5.70/1.57 |
% 5.70/1.57 | GROUND_INST: instantiating (17) with x6, x2, x1, simplifying with (2), (3),
% 5.70/1.57 | (6) gives:
% 5.70/1.57 | (18) x1 = 0
% 5.70/1.57 |
% 5.70/1.57 | BETA: splitting (conj) gives:
% 5.70/1.57 |
% 5.70/1.57 | Case 1:
% 5.70/1.57 | |
% 5.70/1.57 | | (19) ~ (x1 = 0)
% 5.70/1.57 | |
% 5.70/1.57 | | REDUCE: (18), (19) imply:
% 5.70/1.57 | | (20) $false
% 5.70/1.57 | |
% 5.70/1.57 | | CLOSE: (20) is inconsistent.
% 5.70/1.57 | |
% 5.70/1.57 | Case 2:
% 5.70/1.57 | |
% 5.70/1.57 | | (21) ~ (x2 = 0) | ~ (x3 = 0) | ~ (x4 = 0) | ~ (x5 = 0) | ~ (x6 = 0)
% 5.70/1.57 | |
% 5.70/1.57 | | BETA: splitting (21) gives:
% 5.70/1.57 | |
% 5.70/1.57 | | Case 1:
% 5.70/1.57 | | |
% 5.70/1.57 | | | (22) ~ (x6 = 0)
% 5.70/1.57 | | |
% 5.70/1.57 | | | REDUCE: (8), (22) imply:
% 5.70/1.57 | | | (23) $false
% 5.70/1.57 | | |
% 5.70/1.57 | | | CLOSE: (23) is inconsistent.
% 5.70/1.57 | | |
% 5.70/1.57 | | Case 2:
% 5.70/1.57 | | |
% 5.70/1.57 | | | (24) ~ (x2 = 0) | ~ (x3 = 0) | ~ (x4 = 0) | ~ (x5 = 0)
% 5.70/1.57 | | |
% 5.70/1.57 | | | BETA: splitting (24) gives:
% 5.70/1.57 | | |
% 5.70/1.57 | | | Case 1:
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | (25) ~ (x2 = 0)
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | REDUCE: (16), (25) imply:
% 5.70/1.57 | | | | (26) $false
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | CLOSE: (26) is inconsistent.
% 5.70/1.57 | | | |
% 5.70/1.57 | | | Case 2:
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | (27) ~ (x3 = 0) | ~ (x4 = 0) | ~ (x5 = 0)
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | BETA: splitting (27) gives:
% 5.70/1.57 | | | |
% 5.70/1.57 | | | | Case 1:
% 5.70/1.57 | | | | |
% 5.84/1.57 | | | | | (28) ~ (x3 = 0)
% 5.84/1.57 | | | | |
% 5.84/1.57 | | | | | REDUCE: (14), (28) imply:
% 5.84/1.57 | | | | | (29) $false
% 5.84/1.57 | | | | |
% 5.84/1.57 | | | | | CLOSE: (29) is inconsistent.
% 5.84/1.57 | | | | |
% 5.84/1.57 | | | | Case 2:
% 5.84/1.58 | | | | |
% 5.84/1.58 | | | | | (30) ~ (x4 = 0) | ~ (x5 = 0)
% 5.84/1.58 | | | | |
% 5.84/1.58 | | | | | BETA: splitting (30) gives:
% 5.84/1.58 | | | | |
% 5.84/1.58 | | | | | Case 1:
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | (31) ~ (x4 = 0)
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | REDUCE: (12), (31) imply:
% 5.84/1.58 | | | | | | (32) $false
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | CLOSE: (32) is inconsistent.
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | Case 2:
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | (33) ~ (x5 = 0)
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | REDUCE: (10), (33) imply:
% 5.84/1.58 | | | | | | (34) $false
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | | CLOSE: (34) is inconsistent.
% 5.84/1.58 | | | | | |
% 5.84/1.58 | | | | | End of split
% 5.84/1.58 | | | | |
% 5.84/1.58 | | | | End of split
% 5.84/1.58 | | | |
% 5.84/1.58 | | | End of split
% 5.84/1.58 | | |
% 5.84/1.58 | | End of split
% 5.84/1.58 | |
% 5.84/1.58 | End of split
% 5.84/1.58 |
% 5.84/1.58 End of proof
% 5.84/1.58 % SZS output end Proof for theBenchmark
% 5.84/1.58
% 5.84/1.58 964ms
%------------------------------------------------------------------------------