TSTP Solution File: DAT022_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT022_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 : n023.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 22:18:54 EDT 2023
% Result : Theorem 5.03s 1.41s
% Output : Proof 6.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT022_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n023.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 14:56:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 ________ _____
% 0.20/0.56 ___ __ \_________(_)________________________________
% 0.20/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.56
% 0.20/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.56 (2023-06-19)
% 0.20/0.56
% 0.20/0.56 (c) Philipp Rümmer, 2009-2023
% 0.20/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.56 Amanda Stjerna.
% 0.20/0.56 Free software under BSD-3-Clause.
% 0.20/0.56
% 0.20/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.56
% 0.20/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.57 Running up to 7 provers in parallel.
% 0.20/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.33/1.01 Prover 1: Preprocessing ...
% 2.33/1.01 Prover 4: Preprocessing ...
% 2.33/1.05 Prover 0: Preprocessing ...
% 2.33/1.05 Prover 2: Preprocessing ...
% 2.33/1.05 Prover 6: Preprocessing ...
% 2.77/1.07 Prover 5: Preprocessing ...
% 2.77/1.07 Prover 3: Preprocessing ...
% 4.05/1.25 Prover 5: Proving ...
% 4.05/1.25 Prover 6: Proving ...
% 4.05/1.25 Prover 0: Proving ...
% 4.05/1.25 Prover 1: Constructing countermodel ...
% 4.05/1.26 Prover 4: Constructing countermodel ...
% 4.05/1.26 Prover 3: Constructing countermodel ...
% 4.05/1.27 Prover 2: Proving ...
% 5.03/1.40 Prover 3: proved (828ms)
% 5.03/1.41
% 5.03/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.41
% 5.03/1.41 Prover 6: stopped
% 5.03/1.41 Prover 0: stopped
% 5.03/1.41 Prover 2: stopped
% 5.03/1.41 Prover 5: stopped
% 5.03/1.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.03/1.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.03/1.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.03/1.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.03/1.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.03/1.44 Prover 1: Found proof (size 15)
% 5.03/1.44 Prover 1: proved (863ms)
% 5.03/1.44 Prover 4: stopped
% 5.49/1.45 Prover 7: Preprocessing ...
% 5.49/1.46 Prover 8: Preprocessing ...
% 5.49/1.46 Prover 11: Preprocessing ...
% 5.55/1.46 Prover 13: Preprocessing ...
% 5.55/1.46 Prover 10: Preprocessing ...
% 5.55/1.48 Prover 7: stopped
% 5.55/1.50 Prover 13: stopped
% 5.55/1.50 Prover 11: stopped
% 5.55/1.50 Prover 10: stopped
% 6.00/1.54 Prover 8: Warning: ignoring some quantifiers
% 6.00/1.55 Prover 8: Constructing countermodel ...
% 6.00/1.56 Prover 8: stopped
% 6.00/1.56
% 6.00/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.00/1.56
% 6.00/1.56 % SZS output start Proof for theBenchmark
% 6.00/1.56 Assumptions after simplification:
% 6.00/1.56 ---------------------------------
% 6.00/1.56
% 6.00/1.56 (ax4)
% 6.00/1.60 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 6.00/1.60 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 6.00/1.60 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 6.00/1.60 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 6.00/1.60 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 6.00/1.60 collection(v1) | in(v0, v1) = 0)
% 6.00/1.60
% 6.00/1.60 (ax5)
% 6.00/1.61 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 6.00/1.61 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) =
% 6.00/1.61 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 6.00/1.61 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (
% 6.00/1.61 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | ( ~ (v2
% 6.00/1.61 = v0) & in(v0, v1) = 0))
% 6.00/1.61
% 6.00/1.61 (co1)
% 6.00/1.61 ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : (remove(7,
% 6.00/1.61 v1) = v2 & add(2, v2) = v0 & collection(v2) & collection(v1) &
% 6.00/1.61 collection(v0) & ! [v3: int] : ( ~ ($lesseq(v3, 0) | ~ (in(v3, v1) = 0)) &
% 6.00/1.61 ? [v3: int] : ($lesseq(v3, 0)in(v3, v0) = 0))
% 6.00/1.61
% 6.00/1.61 Further assumptions not needed in the proof:
% 6.00/1.61 --------------------------------------------
% 6.00/1.61 ax1, ax2, ax3
% 6.00/1.61
% 6.00/1.61 Those formulas are unsatisfiable:
% 6.00/1.61 ---------------------------------
% 6.00/1.61
% 6.00/1.61 Begin of proof
% 6.00/1.61 |
% 6.00/1.61 | ALPHA: (ax4) implies:
% 6.00/1.62 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 6.00/1.62 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 6.00/1.62 | collection(v1) | in(v0, v1) = 0)
% 6.00/1.62 |
% 6.00/1.62 | ALPHA: (ax5) implies:
% 6.00/1.62 | (2) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 6.00/1.62 | : ( ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) |
% 6.00/1.62 | ( ~ (v2 = v0) & in(v0, v1) = 0))
% 6.00/1.62 |
% 6.00/1.62 | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2
% 6.00/1.62 | gives:
% 6.00/1.62 | (3) remove(7, all_11_1) = all_11_0 & add(2, all_11_0) = all_11_2 &
% 6.00/1.62 | collection(all_11_0) & collection(all_11_1) & collection(all_11_2) & !
% 6.00/1.62 | [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_1) = 0)) & ? [v0:
% 6.00/1.62 | int] : ($lesseq(v0, 0)in(v0, all_11_2) = 0)
% 6.00/1.62 |
% 6.00/1.62 | ALPHA: (3) implies:
% 6.00/1.63 | (4) collection(all_11_1)
% 6.00/1.63 | (5) collection(all_11_0)
% 6.00/1.63 | (6) add(2, all_11_0) = all_11_2
% 6.00/1.63 | (7) remove(7, all_11_1) = all_11_0
% 6.00/1.63 | (8) ! [v0: int] : ( ~ ($lesseq(v0, 0) | ~ (in(v0, all_11_1) = 0))
% 6.00/1.63 | (9) ? [v0: int] : ($lesseq(v0, 0)in(v0, all_11_2) = 0)
% 6.00/1.63 |
% 6.00/1.63 | DELTA: instantiating (9) with fresh symbol all_14_0 gives:
% 6.00/1.63 | (10) $lesseq(all_14_0, 0)in(all_14_0, all_11_2) = 0
% 6.00/1.63 |
% 6.00/1.63 | ALPHA: (10) implies:
% 6.00/1.63 | (11) $lesseq(all_14_0, 0)
% 6.00/1.63 | (12) in(all_14_0, all_11_2) = 0
% 6.00/1.63 |
% 6.38/1.63 | GROUND_INST: instantiating (1) with all_14_0, all_11_0, 2, all_11_2,
% 6.38/1.63 | simplifying with (5), (6), (12) gives:
% 6.38/1.63 | (13) all_14_0 = 2 | in(all_14_0, all_11_0) = 0
% 6.38/1.63 |
% 6.38/1.63 | BETA: splitting (13) gives:
% 6.38/1.63 |
% 6.38/1.63 | Case 1:
% 6.38/1.63 | |
% 6.38/1.63 | | (14) in(all_14_0, all_11_0) = 0
% 6.38/1.63 | |
% 6.38/1.64 | | GROUND_INST: instantiating (2) with all_14_0, all_11_1, 7, all_11_0,
% 6.38/1.64 | | simplifying with (4), (7), (14) gives:
% 6.38/1.64 | | (15) ~ (all_14_0 = 7) & in(all_14_0, all_11_1) = 0
% 6.38/1.64 | |
% 6.38/1.64 | | ALPHA: (15) implies:
% 6.38/1.64 | | (16) in(all_14_0, all_11_1) = 0
% 6.38/1.64 | |
% 6.38/1.64 | | GROUND_INST: instantiating (8) with all_14_0, simplifying with (16) gives:
% 6.38/1.64 | | (17) $lesseq(1, all_14_0)
% 6.38/1.64 | |
% 6.38/1.64 | | COMBINE_INEQS: (11), (17) imply:
% 6.38/1.64 | | (18) $false
% 6.38/1.64 | |
% 6.38/1.64 | | CLOSE: (18) is inconsistent.
% 6.38/1.64 | |
% 6.38/1.64 | Case 2:
% 6.38/1.64 | |
% 6.38/1.64 | | (19) all_14_0 = 2
% 6.38/1.64 | |
% 6.38/1.64 | | REDUCE: (11), (19) imply:
% 6.38/1.64 | | (20) $false
% 6.38/1.64 | |
% 6.38/1.64 | | CLOSE: (20) is inconsistent.
% 6.38/1.64 | |
% 6.38/1.64 | End of split
% 6.38/1.64 |
% 6.38/1.64 End of proof
% 6.38/1.64 % SZS output end Proof for theBenchmark
% 6.38/1.64
% 6.38/1.64 1083ms
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