TSTP Solution File: DAT025_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT025_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 : n012.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 5.06s 1.50s
% Output : Proof 6.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT025_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 14:27:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 1.96/1.04 Prover 1: Preprocessing ...
% 2.51/1.04 Prover 4: Preprocessing ...
% 2.51/1.08 Prover 0: Preprocessing ...
% 2.51/1.08 Prover 5: Preprocessing ...
% 2.51/1.08 Prover 6: Preprocessing ...
% 2.51/1.08 Prover 2: Preprocessing ...
% 2.51/1.08 Prover 3: Preprocessing ...
% 4.05/1.27 Prover 6: Proving ...
% 4.05/1.27 Prover 5: Proving ...
% 4.05/1.28 Prover 3: Constructing countermodel ...
% 4.05/1.29 Prover 2: Proving ...
% 4.05/1.29 Prover 4: Constructing countermodel ...
% 4.05/1.31 Prover 1: Constructing countermodel ...
% 4.05/1.32 Prover 0: Proving ...
% 4.67/1.39 Prover 1: gave up
% 4.67/1.40 Prover 3: gave up
% 4.67/1.41 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.67/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.67/1.42 Prover 7: Preprocessing ...
% 4.67/1.45 Prover 8: Preprocessing ...
% 4.67/1.47 Prover 7: Constructing countermodel ...
% 5.06/1.50 Prover 5: proved (828ms)
% 5.06/1.50 Prover 0: proved (845ms)
% 5.06/1.50
% 5.06/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.50
% 5.06/1.50
% 5.06/1.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/1.50
% 5.06/1.50 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.06/1.50 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.06/1.50 Prover 6: stopped
% 5.06/1.50 Prover 2: stopped
% 5.06/1.50 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.06/1.50 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 5.06/1.52 Prover 4: Found proof (size 22)
% 5.06/1.52 Prover 4: proved (863ms)
% 5.06/1.52 Prover 7: stopped
% 5.06/1.52 Prover 11: Preprocessing ...
% 5.06/1.52 Prover 8: Warning: ignoring some quantifiers
% 5.06/1.53 Prover 16: Preprocessing ...
% 5.06/1.53 Prover 8: Constructing countermodel ...
% 5.06/1.53 Prover 10: Preprocessing ...
% 5.06/1.53 Prover 13: Preprocessing ...
% 5.06/1.54 Prover 8: stopped
% 5.06/1.55 Prover 11: stopped
% 5.06/1.55 Prover 16: stopped
% 6.07/1.55 Prover 10: stopped
% 6.07/1.55 Prover 13: stopped
% 6.07/1.55
% 6.07/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.07/1.55
% 6.07/1.56 % SZS output start Proof for theBenchmark
% 6.07/1.56 Assumptions after simplification:
% 6.07/1.56 ---------------------------------
% 6.07/1.56
% 6.07/1.56 (ax3)
% 6.17/1.58 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1)
% 6.17/1.58 = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2) =
% 6.17/1.58 v3))
% 6.17/1.58
% 6.17/1.58 (ax5)
% 6.17/1.59 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 6.17/1.59 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) =
% 6.17/1.59 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 6.17/1.59 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (
% 6.17/1.59 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0,
% 6.17/1.59 v1) = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 6.17/1.59 (remove(v0, v1) = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1))
% 6.17/1.59
% 6.17/1.59 (co1)
% 6.17/1.60 ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : ? [v3: int]
% 6.17/1.60 : ($lesseq(v3, 1) & remove(1, v0) = v1 & remove(0, v1) = v2 & in(v3, v0) = 0 &
% 6.17/1.60 collection(v2) & collection(v1) & collection(v0) & ! [v4: int] : ! [v5:
% 6.17/1.60 int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 6.17/1.60 in(v4, v0) = v6)) & ! [v4: int] : ! [v5: int] : (v5 = 0 | ~ (in(v4,
% 6.17/1.60 v0) = v5) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v2) = v6)) & ! [v4:
% 6.17/1.60 int] : ( ~ ($lesseq(v4, -1)) | ~ (in(v4, v0) = 0)) & ! [v4: int] : ( ~
% 6.17/1.60 (in(v4, v2) = 0) | in(v4, v0) = 0) & ! [v4: int] : ( ~ (in(v4, v0) = 0) |
% 6.17/1.60 in(v4, v2) = 0))
% 6.17/1.60
% 6.17/1.60 (function-axioms)
% 6.17/1.60 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 6.17/1.60 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 6.17/1.60 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 6.17/1.60 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 6.17/1.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 6.17/1.60 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 6.17/1.60
% 6.17/1.60 Further assumptions not needed in the proof:
% 6.17/1.60 --------------------------------------------
% 6.17/1.60 ax1, ax2, ax4
% 6.17/1.60
% 6.17/1.60 Those formulas are unsatisfiable:
% 6.17/1.60 ---------------------------------
% 6.17/1.60
% 6.17/1.60 Begin of proof
% 6.17/1.60 |
% 6.17/1.60 | ALPHA: (ax5) implies:
% 6.17/1.61 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 6.17/1.61 | (remove(v0, v1) = v2) | ~ (in(v0, v2) = 0) | ~ collection(v1))
% 6.17/1.61 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 6.17/1.61 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) |
% 6.17/1.61 | in(v0, v1) = 0)
% 6.17/1.61 |
% 6.17/1.61 | ALPHA: (function-axioms) implies:
% 6.17/1.61 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 6.17/1.61 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 6.17/1.61 | (in(v3, v2) = v0))
% 6.17/1.61 |
% 6.17/1.61 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2,
% 6.17/1.61 | all_11_3 gives:
% 6.17/1.61 | (4) $lesseq(all_11_0, 1) & remove(1, all_11_3) = all_11_2 & remove(0,
% 6.17/1.61 | all_11_2) = all_11_1 & in(all_11_0, all_11_3) = 0 &
% 6.17/1.61 | collection(all_11_1) & collection(all_11_2) & collection(all_11_3) & !
% 6.17/1.61 | [v0: int] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_11_1) = v1) | ?
% 6.17/1.61 | [v2: int] : ( ~ (v2 = 0) & in(v0, all_11_3) = v2)) & ! [v0: int] :
% 6.17/1.61 | ! [v1: int] : (v1 = 0 | ~ (in(v0, all_11_3) = v1) | ? [v2: int] : ( ~
% 6.17/1.61 | (v2 = 0) & in(v0, all_11_1) = v2)) & ! [v0: int] : ( ~
% 6.17/1.61 | ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0)) & ! [v0: int] : ( ~
% 6.17/1.61 | (in(v0, all_11_1) = 0) | in(v0, all_11_3) = 0) & ! [v0: int] : ( ~
% 6.17/1.61 | (in(v0, all_11_3) = 0) | in(v0, all_11_1) = 0)
% 6.17/1.61 |
% 6.41/1.61 | ALPHA: (4) implies:
% 6.41/1.62 | (5) $lesseq(all_11_0, 1)
% 6.41/1.62 | (6) collection(all_11_3)
% 6.41/1.62 | (7) collection(all_11_2)
% 6.41/1.62 | (8) in(all_11_0, all_11_3) = 0
% 6.41/1.62 | (9) remove(0, all_11_2) = all_11_1
% 6.41/1.62 | (10) remove(1, all_11_3) = all_11_2
% 6.41/1.62 | (11) ! [v0: int] : ( ~ (in(v0, all_11_3) = 0) | in(v0, all_11_1) = 0)
% 6.41/1.62 | (12) ! [v0: int] : ( ~ ($lesseq(v0, -1)) | ~ (in(v0, all_11_3) = 0))
% 6.41/1.62 |
% 6.41/1.62 | GROUND_INST: instantiating (12) with all_11_0, simplifying with (8) gives:
% 6.41/1.62 | (13) $lesseq(0, all_11_0)
% 6.41/1.62 |
% 6.41/1.62 | GROUND_INST: instantiating (11) with all_11_0, simplifying with (8) gives:
% 6.41/1.62 | (14) in(all_11_0, all_11_1) = 0
% 6.41/1.62 |
% 6.41/1.62 | GROUND_INST: instantiating (ax3) with 1, all_11_3, all_11_2, simplifying with
% 6.41/1.62 | (6), (10) gives:
% 6.41/1.62 | (15) ? [v0: int] : ( ~ (v0 = 0) & in(1, all_11_2) = v0)
% 6.41/1.62 |
% 6.41/1.62 | DELTA: instantiating (15) with fresh symbol all_25_0 gives:
% 6.41/1.62 | (16) ~ (all_25_0 = 0) & in(1, all_11_2) = all_25_0
% 6.41/1.62 |
% 6.41/1.62 | ALPHA: (16) implies:
% 6.41/1.62 | (17) ~ (all_25_0 = 0)
% 6.41/1.62 | (18) in(1, all_11_2) = all_25_0
% 6.41/1.62 |
% 6.41/1.62 | GROUND_INST: instantiating (1) with 0, all_11_2, all_11_1, simplifying with
% 6.41/1.62 | (7), (9) gives:
% 6.41/1.62 | (19) ~ (in(0, all_11_1) = 0)
% 6.41/1.62 |
% 6.41/1.62 | GROUND_INST: instantiating (2) with all_11_0, all_11_2, 0, all_11_1,
% 6.41/1.62 | simplifying with (7), (9), (14) gives:
% 6.41/1.63 | (20) in(all_11_0, all_11_2) = 0
% 6.41/1.63 |
% 6.41/1.63 | GROUND_INST: instantiating (3) with all_25_0, 0, all_11_2, 1, simplifying with
% 6.41/1.63 | (18) gives:
% 6.41/1.63 | (21) all_25_0 = 0 | ~ (in(1, all_11_2) = 0)
% 6.41/1.63 |
% 6.41/1.63 | PRED_UNIFY: (14), (19) imply:
% 6.41/1.63 | (22) ~ (all_11_0 = 0)
% 6.41/1.63 |
% 6.41/1.63 | STRENGTHEN: (13), (22) imply:
% 6.41/1.63 | (23) $lesseq(1, all_11_0)
% 6.41/1.63 |
% 6.41/1.63 | ANTI_SYMM: (5), (23) imply:
% 6.41/1.63 | (24) all_11_0 = 1
% 6.41/1.63 |
% 6.41/1.63 | REDUCE: (20), (24) imply:
% 6.41/1.63 | (25) in(1, all_11_2) = 0
% 6.41/1.63 |
% 6.41/1.63 | BETA: splitting (21) gives:
% 6.41/1.63 |
% 6.41/1.63 | Case 1:
% 6.41/1.63 | |
% 6.41/1.63 | | (26) ~ (in(1, all_11_2) = 0)
% 6.41/1.63 | |
% 6.41/1.63 | | PRED_UNIFY: (25), (26) imply:
% 6.41/1.63 | | (27) $false
% 6.41/1.63 | |
% 6.41/1.63 | | CLOSE: (27) is inconsistent.
% 6.41/1.63 | |
% 6.41/1.63 | Case 2:
% 6.41/1.63 | |
% 6.41/1.63 | | (28) all_25_0 = 0
% 6.41/1.63 | |
% 6.41/1.63 | | REDUCE: (17), (28) imply:
% 6.41/1.63 | | (29) $false
% 6.41/1.63 | |
% 6.41/1.63 | | CLOSE: (29) is inconsistent.
% 6.41/1.63 | |
% 6.41/1.63 | End of split
% 6.41/1.63 |
% 6.41/1.63 End of proof
% 6.41/1.63 % SZS output end Proof for theBenchmark
% 6.41/1.63
% 6.41/1.63 999ms
%------------------------------------------------------------------------------