TSTP Solution File: DAT024_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT024_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 : n028.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 22:18:55 EDT 2023
% Result : Theorem 4.34s 1.25s
% Output : Proof 5.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT024_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 15:03:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 ________ _____
% 0.19/0.57 ___ __ \_________(_)________________________________
% 0.19/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.57
% 0.19/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.57 (2023-06-19)
% 0.19/0.57
% 0.19/0.57 (c) Philipp Rümmer, 2009-2023
% 0.19/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.57 Amanda Stjerna.
% 0.19/0.57 Free software under BSD-3-Clause.
% 0.19/0.57
% 0.19/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.57
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/0.97 Prover 4: Preprocessing ...
% 2.26/0.97 Prover 1: Preprocessing ...
% 2.26/1.00 Prover 6: Preprocessing ...
% 2.26/1.00 Prover 5: Preprocessing ...
% 2.26/1.00 Prover 2: Preprocessing ...
% 2.26/1.00 Prover 0: Preprocessing ...
% 2.26/1.00 Prover 3: Preprocessing ...
% 3.64/1.16 Prover 6: Proving ...
% 3.64/1.16 Prover 1: Constructing countermodel ...
% 3.64/1.17 Prover 0: Proving ...
% 3.64/1.17 Prover 5: Proving ...
% 3.64/1.17 Prover 3: Constructing countermodel ...
% 3.64/1.18 Prover 2: Proving ...
% 3.64/1.18 Prover 4: Constructing countermodel ...
% 4.34/1.25 Prover 5: proved (647ms)
% 4.34/1.25 Prover 2: proved (651ms)
% 4.34/1.25
% 4.34/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.34/1.25
% 4.34/1.25
% 4.34/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.34/1.25
% 4.34/1.25 Prover 3: stopped
% 4.34/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.34/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.34/1.25 Prover 6: stopped
% 4.34/1.25 Prover 0: stopped
% 4.34/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.34/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.34/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.34/1.29 Prover 8: Preprocessing ...
% 4.34/1.30 Prover 11: Preprocessing ...
% 4.34/1.30 Prover 7: Preprocessing ...
% 4.34/1.30 Prover 10: Preprocessing ...
% 4.34/1.31 Prover 13: Preprocessing ...
% 4.34/1.34 Prover 4: Found proof (size 18)
% 4.34/1.34 Prover 1: Found proof (size 20)
% 4.34/1.34 Prover 4: proved (746ms)
% 4.34/1.34 Prover 1: proved (747ms)
% 4.34/1.36 Prover 13: Warning: ignoring some quantifiers
% 4.34/1.36 Prover 8: Warning: ignoring some quantifiers
% 4.34/1.36 Prover 13: Constructing countermodel ...
% 4.34/1.37 Prover 13: stopped
% 4.34/1.37 Prover 8: Constructing countermodel ...
% 4.34/1.37 Prover 7: Constructing countermodel ...
% 4.34/1.37 Prover 10: Constructing countermodel ...
% 4.34/1.38 Prover 7: stopped
% 4.34/1.38 Prover 8: stopped
% 4.34/1.39 Prover 11: Constructing countermodel ...
% 4.34/1.39 Prover 10: stopped
% 4.34/1.39 Prover 11: stopped
% 4.34/1.39
% 4.34/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.34/1.39
% 4.34/1.40 % SZS output start Proof for theBenchmark
% 4.34/1.40 Assumptions after simplification:
% 4.34/1.40 ---------------------------------
% 4.34/1.40
% 4.34/1.40 (co1)
% 5.02/1.43 ? [v0: collection] : ? [v1: int] : ? [v2: int] : ? [v3: int] : ( ~ (v2 =
% 5.02/1.43 0) & ~ (v1 = 0) & $lesseq(v3, 1) & in(v3, v0) = 0 & in(1, v0) = v2 &
% 5.02/1.43 in(0, v0) = v1 & collection(v0) & ! [v4: int] : ( ~ ($lesseq(v4, -1)) | ~
% 5.02/1.43 (in(v4, v0) = 0)))
% 5.02/1.43
% 5.02/1.43 (function-axioms)
% 5.02/1.43 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 5.02/1.43 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 5.02/1.43 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 5.02/1.43 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 5.02/1.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 5.02/1.43 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 5.02/1.43
% 5.02/1.43 Further assumptions not needed in the proof:
% 5.02/1.43 --------------------------------------------
% 5.02/1.43 ax1, ax2, ax3, ax4, ax5
% 5.02/1.43
% 5.02/1.43 Those formulas are unsatisfiable:
% 5.02/1.43 ---------------------------------
% 5.02/1.43
% 5.02/1.43 Begin of proof
% 5.02/1.43 |
% 5.02/1.43 | ALPHA: (function-axioms) implies:
% 5.02/1.43 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 5.02/1.43 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 5.02/1.43 | (in(v3, v2) = v0))
% 5.02/1.43 |
% 5.02/1.43 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2,
% 5.02/1.43 | all_11_3 gives:
% 5.02/1.44 | (2) ~ (all_11_1 = 0) & ~ (all_11_2 = 0) & $lesseq(all_11_0, 1) &
% 5.02/1.44 | in(all_11_0, all_11_3) = 0 & in(1, all_11_3) = all_11_1 & in(0,
% 5.02/1.44 | all_11_3) = all_11_2 & collection(all_11_3) & ! [v0: int] : ( ~
% 5.02/1.44 | ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0))
% 5.02/1.44 |
% 5.02/1.44 | ALPHA: (2) implies:
% 5.02/1.44 | (3) ~ (all_11_2 = 0)
% 5.02/1.44 | (4) ~ (all_11_1 = 0)
% 5.02/1.44 | (5) $lesseq(all_11_0, 1)
% 5.02/1.44 | (6) in(0, all_11_3) = all_11_2
% 5.02/1.44 | (7) in(1, all_11_3) = all_11_1
% 5.02/1.44 | (8) in(all_11_0, all_11_3) = 0
% 5.02/1.44 | (9) ! [v0: int] : ( ~ ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0))
% 5.02/1.44 |
% 5.02/1.44 | GROUND_INST: instantiating (1) with all_11_1, 0, all_11_3, 1, simplifying with
% 5.02/1.44 | (7) gives:
% 5.02/1.44 | (10) all_11_1 = 0 | ~ (in(1, all_11_3) = 0)
% 5.02/1.44 |
% 5.02/1.44 | GROUND_INST: instantiating (1) with all_11_2, 0, all_11_3, 0, simplifying with
% 5.02/1.44 | (6) gives:
% 5.02/1.44 | (11) all_11_2 = 0 | ~ (in(0, all_11_3) = 0)
% 5.02/1.44 |
% 5.02/1.44 | GROUND_INST: instantiating (9) with all_11_0, simplifying with (8) gives:
% 5.02/1.44 | (12) $lesseq(0, all_11_0)
% 5.02/1.44 |
% 5.02/1.44 | BETA: splitting (11) gives:
% 5.02/1.44 |
% 5.02/1.44 | Case 1:
% 5.02/1.44 | |
% 5.02/1.44 | | (13) ~ (in(0, all_11_3) = 0)
% 5.02/1.44 | |
% 5.02/1.44 | | PRED_UNIFY: (8), (13) imply:
% 5.02/1.44 | | (14) ~ (all_11_0 = 0)
% 5.02/1.44 | |
% 5.02/1.44 | | STRENGTHEN: (12), (14) imply:
% 5.02/1.44 | | (15) $lesseq(1, all_11_0)
% 5.02/1.44 | |
% 5.02/1.44 | | ANTI_SYMM: (5), (15) imply:
% 5.02/1.44 | | (16) all_11_0 = 1
% 5.02/1.44 | |
% 5.02/1.45 | | REDUCE: (8), (16) imply:
% 5.02/1.45 | | (17) in(1, all_11_3) = 0
% 5.02/1.45 | |
% 5.02/1.45 | | BETA: splitting (10) gives:
% 5.02/1.45 | |
% 5.02/1.45 | | Case 1:
% 5.02/1.45 | | |
% 5.02/1.45 | | | (18) ~ (in(1, all_11_3) = 0)
% 5.02/1.45 | | |
% 5.02/1.45 | | | PRED_UNIFY: (17), (18) imply:
% 5.02/1.45 | | | (19) $false
% 5.02/1.45 | | |
% 5.02/1.45 | | | CLOSE: (19) is inconsistent.
% 5.02/1.45 | | |
% 5.02/1.45 | | Case 2:
% 5.02/1.45 | | |
% 5.02/1.45 | | | (20) all_11_1 = 0
% 5.02/1.45 | | |
% 5.02/1.45 | | | REDUCE: (4), (20) imply:
% 5.02/1.45 | | | (21) $false
% 5.02/1.45 | | |
% 5.02/1.45 | | | CLOSE: (21) is inconsistent.
% 5.02/1.45 | | |
% 5.02/1.45 | | End of split
% 5.02/1.45 | |
% 5.02/1.45 | Case 2:
% 5.02/1.45 | |
% 5.02/1.45 | | (22) all_11_2 = 0
% 5.02/1.45 | |
% 5.02/1.45 | | REDUCE: (3), (22) imply:
% 5.02/1.45 | | (23) $false
% 5.02/1.45 | |
% 5.02/1.45 | | CLOSE: (23) is inconsistent.
% 5.02/1.45 | |
% 5.02/1.45 | End of split
% 5.02/1.45 |
% 5.02/1.45 End of proof
% 5.02/1.45 % SZS output end Proof for theBenchmark
% 5.02/1.45
% 5.02/1.45 873ms
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