TSTP Solution File: ARI682_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ARI682_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 : n007.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 17:48:47 EDT 2023
% Result : Theorem 3.11s 1.21s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ARI682_1 : TPTP v8.1.2. Released v6.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 18:10:14 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.48/0.62 ________ _____
% 0.48/0.62 ___ __ \_________(_)________________________________
% 0.48/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.48/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.48/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.48/0.62
% 0.48/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.48/0.62 (2023-06-19)
% 0.48/0.62
% 0.48/0.62 (c) Philipp Rümmer, 2009-2023
% 0.48/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.48/0.62 Amanda Stjerna.
% 0.48/0.62 Free software under BSD-3-Clause.
% 0.48/0.62
% 0.48/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.48/0.62
% 0.48/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.48/0.63 Running up to 7 provers in parallel.
% 0.69/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.69/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.69/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.69/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.69/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.69/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.69/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.20/1.02 Prover 4: Preprocessing ...
% 2.20/1.02 Prover 6: Preprocessing ...
% 2.20/1.02 Prover 2: Preprocessing ...
% 2.20/1.02 Prover 5: Preprocessing ...
% 2.20/1.02 Prover 1: Preprocessing ...
% 2.20/1.02 Prover 0: Preprocessing ...
% 2.20/1.02 Prover 3: Preprocessing ...
% 2.65/1.07 Prover 4: Constructing countermodel ...
% 2.65/1.07 Prover 6: Constructing countermodel ...
% 2.65/1.07 Prover 5: Constructing countermodel ...
% 2.65/1.07 Prover 2: Constructing countermodel ...
% 2.65/1.07 Prover 0: Constructing countermodel ...
% 2.65/1.07 Prover 3: Constructing countermodel ...
% 2.65/1.07 Prover 1: Constructing countermodel ...
% 3.11/1.21 Prover 6: proved (567ms)
% 3.11/1.21 Prover 5: proved (569ms)
% 3.11/1.21 Prover 3: proved (571ms)
% 3.11/1.21 Prover 0: proved (571ms)
% 3.11/1.21
% 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21
% 3.11/1.21 Prover 2: proved (572ms)
% 3.11/1.21
% 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21
% 3.11/1.21
% 3.11/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.21
% 3.11/1.22
% 3.11/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.22
% 3.11/1.22
% 3.11/1.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.11/1.22
% 3.11/1.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.11/1.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.11/1.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.11/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.11/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.11/1.23 Prover 7: Preprocessing ...
% 3.11/1.23 Prover 8: Preprocessing ...
% 3.62/1.23 Prover 11: Preprocessing ...
% 3.62/1.24 Prover 10: Preprocessing ...
% 3.62/1.24 Prover 8: Constructing countermodel ...
% 3.62/1.24 Prover 7: Constructing countermodel ...
% 3.62/1.24 Prover 11: Constructing countermodel ...
% 3.62/1.24 Prover 13: Preprocessing ...
% 3.62/1.24 Prover 10: Constructing countermodel ...
% 3.62/1.24 Prover 1: Found proof (size 20)
% 3.62/1.24 Prover 1: proved (605ms)
% 3.62/1.25 Prover 10: stopped
% 3.62/1.25 Prover 11: stopped
% 3.62/1.25 Prover 8: stopped
% 3.62/1.25 Prover 7: stopped
% 3.62/1.25 Prover 4: Found proof (size 20)
% 3.62/1.25 Prover 4: proved (607ms)
% 3.62/1.25 Prover 13: Constructing countermodel ...
% 3.62/1.25 Prover 13: stopped
% 3.62/1.25
% 3.62/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.62/1.25
% 3.62/1.26 % SZS output start Proof for theBenchmark
% 3.62/1.26 Assumptions after simplification:
% 3.62/1.26 ---------------------------------
% 3.62/1.26
% 3.62/1.26 (conj)
% 3.62/1.26 $lesseq(1, $difference(b, a))
% 3.62/1.26
% 3.62/1.26 (conj_001)
% 3.62/1.27 $lesseq(0, a)
% 3.62/1.27
% 3.62/1.27 (conj_002)
% 3.62/1.27 ? [v0: int] : ($lesseq(b, $difference(a, v0)) & $product(a, b) = v0)
% 3.62/1.27
% 3.62/1.27 Those formulas are unsatisfiable:
% 3.62/1.27 ---------------------------------
% 3.62/1.27
% 3.62/1.27 Begin of proof
% 3.62/1.27 |
% 3.62/1.27 | DELTA: instantiating (conj_002) with fresh symbol all_3_0 gives:
% 3.62/1.27 | (1) $lesseq(b, $difference(a, all_3_0)) & $product(a, b) = all_3_0
% 3.62/1.27 |
% 3.62/1.27 | ALPHA: (1) implies:
% 3.85/1.27 | (2) $lesseq(b, $difference(a, all_3_0))
% 3.85/1.28 | (3) $product(a, b) = all_3_0
% 3.85/1.28 |
% 3.85/1.28 | COMBINE_INEQS: (conj), (conj_001) imply:
% 3.85/1.28 | (4) $lesseq(1, b)
% 3.85/1.28 |
% 3.85/1.28 | THEORY_AXIOM GroebnerMultiplication:
% 3.85/1.28 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(v0,
% 3.85/1.28 | $difference(v1, v2))) | ~ ($lesseq(v2, 457651)) | ~ ($lesseq(1,
% 3.85/1.28 | $difference(v0, v1))) | ~ ($lesseq(0, v1)) | ~ ($product(v1,
% 3.85/1.28 | v0) = v2))
% 3.85/1.28 |
% 3.85/1.28 | GROUND_INST: instantiating (5) with b, a, all_3_0, simplifying with (3) gives:
% 3.85/1.28 | (6) ~ ($lesseq(b, $difference(a, all_3_0))) | ~ ($lesseq(all_3_0,
% 3.85/1.28 | 457651)) | ~ ($lesseq(1, $difference(b, a))) | ~ ($lesseq(0, a))
% 3.85/1.28 |
% 3.85/1.28 | BETA: splitting (6) gives:
% 3.85/1.28 |
% 3.85/1.28 | Case 1:
% 3.85/1.28 | |
% 3.85/1.28 | | (7) ~ ($lesseq(b, $difference(a, all_3_0))) | ~ ($lesseq(1,
% 3.85/1.28 | | $difference(b, a)))
% 3.85/1.28 | |
% 3.85/1.28 | | BETA: splitting (7) gives:
% 3.85/1.28 | |
% 3.85/1.28 | | Case 1:
% 3.85/1.28 | | |
% 3.85/1.28 | | | (8) $lesseq(1, $sum($difference(all_3_0, a), b))
% 3.85/1.28 | | |
% 3.85/1.28 | | | COMBINE_INEQS: (2), (8) imply:
% 3.85/1.28 | | | (9) $false
% 3.85/1.28 | | |
% 3.85/1.28 | | | CLOSE: (9) is inconsistent.
% 3.85/1.28 | | |
% 3.85/1.28 | | Case 2:
% 3.85/1.28 | | |
% 3.85/1.28 | | | (10) $lesseq(b, a)
% 3.85/1.28 | | |
% 3.85/1.29 | | | COMBINE_INEQS: (10), (conj) imply:
% 3.85/1.29 | | | (11) $false
% 3.85/1.29 | | |
% 3.85/1.29 | | | CLOSE: (11) is inconsistent.
% 3.85/1.29 | | |
% 3.85/1.29 | | End of split
% 3.85/1.29 | |
% 3.85/1.29 | Case 2:
% 3.85/1.29 | |
% 3.85/1.29 | | (12) ~ ($lesseq(all_3_0, 457651)) | ~ ($lesseq(0, a)) | ~ ($lesseq(1,
% 3.85/1.29 | | b))
% 3.85/1.29 | |
% 3.85/1.29 | | BETA: splitting (12) gives:
% 3.85/1.29 | |
% 3.85/1.29 | | Case 1:
% 3.85/1.29 | | |
% 3.85/1.29 | | | (13) $lesseq(a, -1)
% 3.85/1.29 | | |
% 3.85/1.29 | | | COMBINE_INEQS: (13), (conj_001) imply:
% 3.85/1.29 | | | (14) $false
% 3.85/1.29 | | |
% 3.85/1.29 | | | CLOSE: (14) is inconsistent.
% 3.85/1.29 | | |
% 3.85/1.29 | | Case 2:
% 3.85/1.29 | | |
% 3.85/1.29 | | | (15) ~ ($lesseq(all_3_0, 457651)) | ~ ($lesseq(1, b))
% 3.85/1.29 | | |
% 3.85/1.29 | | | BETA: splitting (15) gives:
% 3.85/1.29 | | |
% 3.85/1.29 | | | Case 1:
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | (16) $lesseq(b, 0)
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | COMBINE_INEQS: (4), (16) imply:
% 3.85/1.29 | | | | (17) $false
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | CLOSE: (17) is inconsistent.
% 3.85/1.29 | | | |
% 3.85/1.29 | | | Case 2:
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | (18) $lesseq(457652, all_3_0)
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | COMBINE_INEQS: (2), (18) imply:
% 3.85/1.29 | | | | (19) $lesseq(457652, $difference(a, b))
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | COMBINE_INEQS: (19), (conj) imply:
% 3.85/1.29 | | | | (20) $false
% 3.85/1.29 | | | |
% 3.85/1.29 | | | | CLOSE: (20) is inconsistent.
% 3.85/1.29 | | | |
% 3.85/1.29 | | | End of split
% 3.85/1.29 | | |
% 3.85/1.29 | | End of split
% 3.85/1.29 | |
% 3.85/1.29 | End of split
% 3.85/1.29 |
% 3.85/1.29 End of proof
% 3.85/1.29 % SZS output end Proof for theBenchmark
% 3.85/1.29
% 3.85/1.29 670ms
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