TSTP Solution File: DAT011_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT011_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 : n013.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 22:18:52 EDT 2023
% Result : Theorem 3.79s 1.26s
% Output : Proof 4.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT011_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n013.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 : Thu Aug 24 14:22:17 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.56 ________ _____
% 0.19/0.56 ___ __ \_________(_)________________________________
% 0.19/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.56
% 0.19/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.56 (2023-06-19)
% 0.19/0.56
% 0.19/0.56 (c) Philipp Rümmer, 2009-2023
% 0.19/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.56 Amanda Stjerna.
% 0.19/0.56 Free software under BSD-3-Clause.
% 0.19/0.56
% 0.19/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.56
% 0.19/0.56 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.57 Running up to 7 provers in parallel.
% 0.19/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.36/0.99 Prover 4: Preprocessing ...
% 2.51/0.99 Prover 1: Preprocessing ...
% 2.71/1.02 Prover 5: Preprocessing ...
% 2.71/1.02 Prover 3: Preprocessing ...
% 2.71/1.02 Prover 2: Preprocessing ...
% 2.75/1.02 Prover 6: Preprocessing ...
% 2.75/1.02 Prover 0: Preprocessing ...
% 3.28/1.13 Prover 1: Constructing countermodel ...
% 3.28/1.13 Prover 6: Proving ...
% 3.28/1.13 Prover 0: Proving ...
% 3.28/1.13 Prover 3: Constructing countermodel ...
% 3.28/1.14 Prover 4: Constructing countermodel ...
% 3.28/1.16 Prover 2: Proving ...
% 3.28/1.16 Prover 5: Proving ...
% 3.79/1.25 Prover 3: proved (671ms)
% 3.79/1.26
% 3.79/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/1.26
% 3.79/1.26 Prover 0: stopped
% 3.79/1.26 Prover 6: stopped
% 3.79/1.26 Prover 2: stopped
% 3.79/1.26 Prover 5: stopped
% 3.79/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.79/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.79/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.79/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.79/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.48/1.28 Prover 8: Preprocessing ...
% 4.48/1.28 Prover 7: Preprocessing ...
% 4.48/1.28 Prover 11: Preprocessing ...
% 4.64/1.29 Prover 10: Preprocessing ...
% 4.64/1.29 Prover 13: Preprocessing ...
% 4.64/1.31 Prover 8: Warning: ignoring some quantifiers
% 4.64/1.31 Prover 8: Constructing countermodel ...
% 4.64/1.32 Prover 10: Constructing countermodel ...
% 4.64/1.33 Prover 7: Constructing countermodel ...
% 4.64/1.34 Prover 11: Constructing countermodel ...
% 4.64/1.35 Prover 13: Warning: ignoring some quantifiers
% 4.64/1.35 Prover 1: Found proof (size 31)
% 4.64/1.35 Prover 1: proved (767ms)
% 4.64/1.35 Prover 7: stopped
% 4.64/1.35 Prover 10: stopped
% 4.64/1.35 Prover 11: stopped
% 4.64/1.35 Prover 13: Constructing countermodel ...
% 4.64/1.36 Prover 4: Found proof (size 31)
% 4.64/1.36 Prover 4: proved (772ms)
% 4.64/1.36 Prover 8: stopped
% 4.64/1.36 Prover 13: stopped
% 4.64/1.36
% 4.64/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.64/1.36
% 4.64/1.36 % SZS output start Proof for theBenchmark
% 4.64/1.37 Assumptions after simplification:
% 4.64/1.37 ---------------------------------
% 4.64/1.37
% 4.64/1.37 (ax1)
% 4.64/1.39 ! [v0: array] : ! [v1: int] : ! [v2: int] : ! [v3: array] : ! [v4: int] :
% 4.64/1.39 (v4 = v2 | ~ (write(v0, v1, v2) = v3) | ~ (read(v3, v1) = v4) | ~
% 4.64/1.39 array(v0))
% 4.64/1.39
% 4.64/1.39 (ax2)
% 4.64/1.39 ! [v0: array] : ! [v1: int] : ! [v2: int] : ! [v3: int] : ! [v4: array] :
% 4.64/1.39 ! [v5: int] : (v2 = v1 | ~ (write(v0, v1, v3) = v4) | ~ (read(v4, v2) = v5)
% 4.64/1.39 | ~ array(v0) | read(v0, v2) = v5)
% 4.64/1.39
% 4.64/1.39 (co1)
% 4.64/1.40 ? [v0: array] : ? [v1: array] : ? [v2: int] : ? [v3: int] : (write(v1,
% 4.64/1.40 $sum(v3, 1), 3) = v0 & array(v1) & array(v0) & ! [v4: int] : ! [v5: int]
% 4.64/1.40 : ( ~ ($lesseq(v5, 0) | ~ ($lesseq(v4, v3)) | ~ ($lesseq(v2, v4)) | ~
% 4.64/1.40 (read(v1, v4) = v5)) & ? [v4: int] : ? [v5: int] : ($lesseq(v5,
% 4.64/1.40 0)$lesseq(-1, $difference(v3, v4)) & $lesseq(v2, v4) & read(v0, v4) =
% 4.64/1.40 v5))
% 4.64/1.40
% 4.64/1.40 Those formulas are unsatisfiable:
% 4.64/1.40 ---------------------------------
% 4.64/1.40
% 4.64/1.40 Begin of proof
% 4.64/1.40 |
% 4.64/1.40 | DELTA: instantiating (co1) with fresh symbols all_7_0, all_7_1, all_7_2,
% 4.64/1.40 | all_7_3 gives:
% 4.64/1.40 | (1) write(all_7_2, $sum(all_7_0, 1), 3) = all_7_3 & array(all_7_2) &
% 4.64/1.40 | array(all_7_3) & ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~
% 4.64/1.40 | ($lesseq(v0, all_7_0)) | ~ ($lesseq(all_7_1, v0)) | ~
% 4.64/1.40 | (read(all_7_2, v0) = v1)) & ? [v0: int] : ? [v1: int] :
% 4.64/1.40 | ($lesseq(v1, 0)$lesseq(-1, $difference(all_7_0, v0)) &
% 4.64/1.40 | $lesseq(all_7_1, v0) & read(all_7_3, v0) = v1)
% 4.64/1.40 |
% 4.64/1.40 | ALPHA: (1) implies:
% 4.64/1.40 | (2) array(all_7_2)
% 4.64/1.41 | (3) write(all_7_2, $sum(all_7_0, 1), 3) = all_7_3
% 4.64/1.41 | (4) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(v1, 0) | ~ ($lesseq(v0,
% 4.64/1.41 | all_7_0)) | ~ ($lesseq(all_7_1, v0)) | ~ (read(all_7_2, v0) =
% 4.64/1.41 | v1))
% 4.64/1.41 | (5) ? [v0: int] : ? [v1: int] : ($lesseq(v1, 0)$lesseq(-1,
% 4.64/1.41 | $difference(all_7_0, v0)) & $lesseq(all_7_1, v0) & read(all_7_3,
% 4.64/1.41 | v0) = v1)
% 4.64/1.41 |
% 4.64/1.41 | DELTA: instantiating (5) with fresh symbols all_10_0, all_10_1 gives:
% 4.64/1.41 | (6) $lesseq(all_10_0, 0)$lesseq(-1, $difference(all_7_0, all_10_1)) &
% 4.64/1.41 | $lesseq(all_7_1, all_10_1) & read(all_7_3, all_10_1) = all_10_0
% 4.64/1.41 |
% 4.64/1.41 | ALPHA: (6) implies:
% 4.64/1.41 | (7) $lesseq(all_7_1, all_10_1)
% 4.64/1.41 | (8) $lesseq(-1, $difference(all_7_0, all_10_1))
% 4.64/1.41 | (9) $lesseq(all_10_0, 0)
% 4.64/1.41 | (10) read(all_7_3, all_10_1) = all_10_0
% 4.64/1.41 |
% 4.64/1.41 | GROUND_INST: instantiating (ax1) with all_7_2, $sum(all_7_0, 1), 3, all_7_3,
% 4.64/1.41 | all_10_0, simplifying with (2), (3) gives:
% 4.64/1.41 | (11) all_10_0 = 3 | ~ (read(all_7_3, $sum(all_7_0, 1)) = all_10_0)
% 4.64/1.41 |
% 4.64/1.41 | GROUND_INST: instantiating (ax2) with all_7_2, $sum(all_7_0, 1), all_10_1, 3,
% 4.64/1.41 | all_7_3, all_10_0, simplifying with (2), (3), (10) gives:
% 4.64/1.41 | (12) $difference(all_10_1, all_7_0) = 1 | read(all_7_2, all_10_1) =
% 4.64/1.41 | all_10_0
% 4.64/1.41 |
% 4.64/1.41 | BETA: splitting (12) gives:
% 4.64/1.41 |
% 4.64/1.41 | Case 1:
% 4.64/1.41 | |
% 4.64/1.41 | | (13) read(all_7_2, all_10_1) = all_10_0
% 4.64/1.41 | |
% 4.64/1.41 | | BETA: splitting (11) gives:
% 4.64/1.41 | |
% 4.64/1.41 | | Case 1:
% 4.64/1.41 | | |
% 4.64/1.41 | | | (14) ~ (read(all_7_3, $sum(all_7_0, 1)) = all_10_0)
% 4.64/1.41 | | |
% 4.64/1.41 | | | GROUND_INST: instantiating (4) with all_10_1, all_10_0, simplifying with
% 4.64/1.41 | | | (13) gives:
% 4.64/1.41 | | | (15) ~ ($lesseq(all_10_0, 0) | ~ ($lesseq(all_10_1, all_7_0)) | ~
% 4.64/1.41 | | | ($lesseq(all_7_1, all_10_1))
% 4.64/1.41 | | |
% 4.64/1.42 | | | PRED_UNIFY: (10), (14) imply:
% 4.64/1.42 | | | (16) ~ ($difference(all_10_1, all_7_0) = 1)
% 4.64/1.42 | | |
% 4.64/1.42 | | | STRENGTHEN: (8), (16) imply:
% 4.64/1.42 | | | (17) $lesseq(all_10_1, all_7_0)
% 4.64/1.42 | | |
% 4.64/1.42 | | | BETA: splitting (15) gives:
% 4.64/1.42 | | |
% 4.64/1.42 | | | Case 1:
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | (18) $lesseq(1, all_10_0)
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | COMBINE_INEQS: (9), (18) imply:
% 4.64/1.42 | | | | (19) $false
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | CLOSE: (19) is inconsistent.
% 4.64/1.42 | | | |
% 4.64/1.42 | | | Case 2:
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | (20) ~ ($lesseq(all_10_1, all_7_0)) | ~ ($lesseq(all_7_1,
% 4.64/1.42 | | | | all_10_1))
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | BETA: splitting (20) gives:
% 4.64/1.42 | | | |
% 4.64/1.42 | | | | Case 1:
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | (21) $lesseq(1, $difference(all_10_1, all_7_0))
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | COMBINE_INEQS: (17), (21) imply:
% 4.64/1.42 | | | | | (22) $false
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | CLOSE: (22) is inconsistent.
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | Case 2:
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | (23) $lesseq(1, $difference(all_7_1, all_10_1))
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | COMBINE_INEQS: (7), (23) imply:
% 4.64/1.42 | | | | | (24) $false
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | | CLOSE: (24) is inconsistent.
% 4.64/1.42 | | | | |
% 4.64/1.42 | | | | End of split
% 4.64/1.42 | | | |
% 4.64/1.42 | | | End of split
% 4.64/1.42 | | |
% 4.64/1.42 | | Case 2:
% 4.64/1.42 | | |
% 4.64/1.42 | | | (25) read(all_7_3, $sum(all_7_0, 1)) = all_10_0
% 4.64/1.42 | | |
% 4.64/1.42 | | | REF_CLOSE: (9), (11), (25) are inconsistent by sub-proof #1.
% 4.64/1.42 | | |
% 4.64/1.42 | | End of split
% 4.64/1.42 | |
% 4.64/1.42 | Case 2:
% 4.64/1.42 | |
% 4.64/1.42 | | (26) $difference(all_10_1, all_7_0) = 1
% 4.64/1.42 | |
% 4.64/1.42 | | REDUCE: (10), (26) imply:
% 4.64/1.42 | | (27) read(all_7_3, $sum(all_7_0, 1)) = all_10_0
% 4.64/1.42 | |
% 4.64/1.42 | | REF_CLOSE: (9), (11), (27) are inconsistent by sub-proof #1.
% 4.64/1.42 | |
% 4.64/1.42 | End of split
% 4.64/1.42 |
% 4.64/1.42 End of proof
% 4.64/1.42
% 4.64/1.42 Sub-proof #1 shows that the following formulas are inconsistent:
% 4.64/1.42 ----------------------------------------------------------------
% 4.64/1.42 (1) all_10_0 = 3 | ~ (read(all_7_3, $sum(all_7_0, 1)) = all_10_0)
% 4.64/1.42 (2) read(all_7_3, $sum(all_7_0, 1)) = all_10_0
% 4.64/1.42 (3) $lesseq(all_10_0, 0)
% 4.64/1.42
% 4.64/1.42 Begin of proof
% 4.64/1.42 |
% 4.64/1.42 | BETA: splitting (1) gives:
% 4.64/1.42 |
% 4.64/1.42 | Case 1:
% 4.64/1.42 | |
% 4.64/1.42 | | (4) ~ (read(all_7_3, $sum(all_7_0, 1)) = all_10_0)
% 4.64/1.42 | |
% 4.64/1.42 | | PRED_UNIFY: (2), (4) imply:
% 4.64/1.42 | | (5) $false
% 4.64/1.42 | |
% 4.64/1.42 | | CLOSE: (5) is inconsistent.
% 4.64/1.42 | |
% 4.64/1.42 | Case 2:
% 4.64/1.42 | |
% 4.64/1.42 | | (6) all_10_0 = 3
% 4.64/1.42 | |
% 4.64/1.42 | | REDUCE: (3), (6) imply:
% 4.64/1.42 | | (7) $false
% 4.64/1.42 | |
% 4.64/1.42 | | CLOSE: (7) is inconsistent.
% 4.64/1.42 | |
% 4.64/1.42 | End of split
% 4.64/1.42 |
% 4.64/1.42 End of proof
% 4.64/1.42 % SZS output end Proof for theBenchmark
% 4.64/1.43
% 4.64/1.43 863ms
%------------------------------------------------------------------------------