TSTP Solution File: DAT055_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT055_1 : TPTP v8.1.2. Released v5.0.0.
% 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 22:19:02 EDT 2023
% Result : Theorem 3.28s 1.20s
% Output : Proof 3.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT055_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 15:06:01 EDT 2023
% 0.14/0.34 % 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 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 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 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 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 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
% 1.91/0.98 Prover 4: Preprocessing ...
% 1.91/0.98 Prover 1: Preprocessing ...
% 2.26/1.02 Prover 3: Preprocessing ...
% 2.26/1.02 Prover 0: Preprocessing ...
% 2.26/1.03 Prover 6: Preprocessing ...
% 2.26/1.03 Prover 2: Preprocessing ...
% 2.26/1.03 Prover 5: Preprocessing ...
% 2.74/1.09 Prover 4: Constructing countermodel ...
% 2.74/1.09 Prover 1: Constructing countermodel ...
% 2.74/1.10 Prover 6: Proving ...
% 2.74/1.10 Prover 2: Proving ...
% 2.74/1.10 Prover 3: Constructing countermodel ...
% 3.03/1.10 Prover 0: Proving ...
% 3.03/1.10 Prover 5: Proving ...
% 3.28/1.19 Prover 3: proved (560ms)
% 3.28/1.20
% 3.28/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.20
% 3.28/1.20 Prover 2: proved (565ms)
% 3.28/1.20 Prover 0: proved (566ms)
% 3.28/1.20
% 3.28/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.20
% 3.28/1.20
% 3.28/1.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.20
% 3.28/1.21 Prover 5: proved (559ms)
% 3.28/1.21
% 3.28/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/1.21
% 3.28/1.21 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.28/1.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.28/1.21 Prover 6: stopped
% 3.28/1.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.28/1.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.28/1.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.28/1.22 Prover 8: Preprocessing ...
% 3.28/1.22 Prover 7: Preprocessing ...
% 3.28/1.22 Prover 4: Found proof (size 13)
% 3.28/1.22 Prover 4: proved (597ms)
% 3.28/1.22 Prover 1: Found proof (size 13)
% 3.28/1.22 Prover 1: proved (600ms)
% 3.28/1.23 Prover 10: Preprocessing ...
% 3.28/1.23 Prover 13: Preprocessing ...
% 3.28/1.23 Prover 11: Preprocessing ...
% 3.85/1.24 Prover 8: Warning: ignoring some quantifiers
% 3.85/1.25 Prover 7: Constructing countermodel ...
% 3.85/1.25 Prover 8: Constructing countermodel ...
% 3.85/1.26 Prover 10: Constructing countermodel ...
% 3.85/1.26 Prover 7: stopped
% 3.85/1.26 Prover 13: Warning: ignoring some quantifiers
% 3.85/1.26 Prover 8: stopped
% 3.85/1.26 Prover 11: Constructing countermodel ...
% 3.85/1.26 Prover 10: stopped
% 3.85/1.26 Prover 13: Constructing countermodel ...
% 3.85/1.26 Prover 11: stopped
% 3.85/1.26 Prover 13: stopped
% 3.85/1.26
% 3.85/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.85/1.26
% 3.85/1.27 % SZS output start Proof for theBenchmark
% 3.85/1.27 Assumptions after simplification:
% 3.85/1.27 ---------------------------------
% 3.85/1.27
% 3.85/1.27 (boyer_moore_max_min)
% 3.85/1.29 list(a) & ? [v0: int] : ? [v1: int] : ($lesseq(0,
% 3.85/1.29 $sum($difference($product(-1, v1), k), l)) & $lesseq(l, v0) & $lesseq(1,
% 3.85/1.29 k) & min(a) = v0 & max(a) = v1 & ! [v2: list] : ! [v3: int] : ( ~
% 3.85/1.29 (min(v2) = v3) | ~ list(v2) | ? [v4: int] : ($lesseq(v3, v4) & max(v2) =
% 3.85/1.29 v4)) & ! [v2: list] : ! [v3: int] : ( ~ (max(v2) = v3) | ~ list(v2) |
% 3.85/1.29 ? [v4: int] : ($lesseq(v4, v3) & min(v2) = v4)))
% 3.85/1.29
% 3.85/1.29 (function-axioms)
% 3.85/1.30 ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (min(v2) = v1) |
% 3.85/1.30 ~ (min(v2) = v0)) & ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 |
% 3.85/1.30 ~ (max(v2) = v1) | ~ (max(v2) = v0))
% 3.85/1.30
% 3.85/1.30 Those formulas are unsatisfiable:
% 3.85/1.30 ---------------------------------
% 3.85/1.30
% 3.85/1.30 Begin of proof
% 3.85/1.30 |
% 3.85/1.30 | ALPHA: (boyer_moore_max_min) implies:
% 3.85/1.30 | (1) list(a)
% 3.85/1.30 | (2) ? [v0: int] : ? [v1: int] : ($lesseq(0, $sum($difference($product(-1,
% 3.85/1.30 | v1), k), l)) & $lesseq(l, v0) & $lesseq(1, k) & min(a) = v0 &
% 3.85/1.30 | max(a) = v1 & ! [v2: list] : ! [v3: int] : ( ~ (min(v2) = v3) | ~
% 3.85/1.30 | list(v2) | ? [v4: int] : ($lesseq(v3, v4) & max(v2) = v4)) & !
% 3.85/1.30 | [v2: list] : ! [v3: int] : ( ~ (max(v2) = v3) | ~ list(v2) | ?
% 3.85/1.30 | [v4: int] : ($lesseq(v4, v3) & min(v2) = v4)))
% 3.85/1.30 |
% 3.85/1.30 | ALPHA: (function-axioms) implies:
% 3.85/1.31 | (3) ! [v0: int] : ! [v1: int] : ! [v2: list] : (v1 = v0 | ~ (max(v2) =
% 3.85/1.31 | v1) | ~ (max(v2) = v0))
% 3.85/1.31 |
% 3.85/1.31 | DELTA: instantiating (2) with fresh symbols all_6_0, all_6_1 gives:
% 3.85/1.31 | (4) $lesseq(0, $sum($difference($product(-1, all_6_0), k), l)) & $lesseq(l,
% 3.85/1.31 | all_6_1) & $lesseq(1, k) & min(a) = all_6_1 & max(a) = all_6_0 & !
% 3.85/1.31 | [v0: list] : ! [v1: int] : ( ~ (min(v0) = v1) | ~ list(v0) | ? [v2:
% 3.85/1.31 | int] : ($lesseq(v1, v2) & max(v0) = v2)) & ! [v0: list] : ! [v1:
% 3.85/1.31 | int] : ( ~ (max(v0) = v1) | ~ list(v0) | ? [v2: int] : ($lesseq(v2,
% 3.85/1.31 | v1) & min(v0) = v2))
% 3.85/1.31 |
% 3.85/1.31 | ALPHA: (4) implies:
% 3.85/1.31 | (5) $lesseq(1, k)
% 3.85/1.31 | (6) $lesseq(l, all_6_1)
% 3.85/1.31 | (7) $lesseq(0, $sum($difference($product(-1, all_6_0), k), l))
% 3.85/1.31 | (8) max(a) = all_6_0
% 3.85/1.31 | (9) min(a) = all_6_1
% 3.85/1.31 | (10) ! [v0: list] : ! [v1: int] : ( ~ (min(v0) = v1) | ~ list(v0) | ?
% 3.85/1.31 | [v2: int] : ($lesseq(v1, v2) & max(v0) = v2))
% 3.85/1.31 |
% 3.85/1.31 | COMBINE_INEQS: (6), (7) imply:
% 3.85/1.31 | (11) $lesseq(k, $difference(all_6_1, all_6_0))
% 3.85/1.31 |
% 3.85/1.31 | COMBINE_INEQS: (5), (11) imply:
% 3.85/1.31 | (12) $lesseq(1, $difference(all_6_1, all_6_0))
% 3.85/1.31 |
% 3.85/1.32 | GROUND_INST: instantiating (10) with a, all_6_1, simplifying with (1), (9)
% 3.85/1.32 | gives:
% 3.85/1.32 | (13) ? [v0: int] : ($lesseq(all_6_1, v0) & max(a) = v0)
% 3.85/1.32 |
% 3.85/1.32 | DELTA: instantiating (13) with fresh symbol all_20_0 gives:
% 3.85/1.32 | (14) $lesseq(all_6_1, all_20_0) & max(a) = all_20_0
% 3.85/1.32 |
% 3.85/1.32 | ALPHA: (14) implies:
% 3.85/1.32 | (15) $lesseq(all_6_1, all_20_0)
% 3.85/1.32 | (16) max(a) = all_20_0
% 3.85/1.32 |
% 3.85/1.32 | GROUND_INST: instantiating (3) with all_6_0, all_20_0, a, simplifying with
% 3.85/1.32 | (8), (16) gives:
% 3.85/1.32 | (17) all_20_0 = all_6_0
% 3.85/1.32 |
% 3.85/1.32 | REDUCE: (15), (17) imply:
% 3.85/1.32 | (18) $lesseq(all_6_1, all_6_0)
% 3.85/1.32 |
% 3.85/1.32 | COMBINE_INEQS: (12), (18) imply:
% 3.85/1.32 | (19) $false
% 3.85/1.32 |
% 3.85/1.32 | CLOSE: (19) is inconsistent.
% 3.85/1.32 |
% 3.85/1.32 End of proof
% 3.85/1.32 % SZS output end Proof for theBenchmark
% 3.85/1.32
% 3.85/1.32 715ms
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