TSTP Solution File: DAT019_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT019_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 : n004.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 4.08s 1.32s
% Output : Proof 5.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT019_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 : n004.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 14:02:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 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 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 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 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 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
% 2.53/1.01 Prover 1: Preprocessing ...
% 2.53/1.01 Prover 4: Preprocessing ...
% 2.53/1.06 Prover 5: Preprocessing ...
% 2.53/1.06 Prover 3: Preprocessing ...
% 2.53/1.06 Prover 0: Preprocessing ...
% 2.53/1.06 Prover 6: Preprocessing ...
% 2.53/1.06 Prover 2: Preprocessing ...
% 3.86/1.20 Prover 6: Constructing countermodel ...
% 3.86/1.20 Prover 3: Constructing countermodel ...
% 3.86/1.21 Prover 5: Proving ...
% 3.86/1.21 Prover 4: Constructing countermodel ...
% 3.86/1.21 Prover 0: Proving ...
% 3.86/1.21 Prover 1: Constructing countermodel ...
% 3.86/1.22 Prover 2: Proving ...
% 4.08/1.31 Prover 0: proved (686ms)
% 4.08/1.31
% 4.08/1.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.08/1.32
% 4.08/1.32 Prover 6: stopped
% 4.08/1.32 Prover 2: stopped
% 4.08/1.32 Prover 5: stopped
% 4.08/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.08/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.08/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.27/1.32 Prover 3: stopped
% 4.27/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.27/1.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.27/1.34 Prover 7: Preprocessing ...
% 4.27/1.34 Prover 11: Preprocessing ...
% 4.27/1.34 Prover 10: Preprocessing ...
% 4.27/1.35 Prover 8: Preprocessing ...
% 4.27/1.38 Prover 13: Preprocessing ...
% 4.27/1.39 Prover 1: Found proof (size 13)
% 4.27/1.39 Prover 4: Found proof (size 15)
% 4.27/1.39 Prover 4: proved (756ms)
% 4.27/1.39 Prover 1: proved (758ms)
% 5.12/1.40 Prover 13: stopped
% 5.12/1.40 Prover 7: Constructing countermodel ...
% 5.12/1.40 Prover 7: stopped
% 5.12/1.41 Prover 10: Constructing countermodel ...
% 5.12/1.41 Prover 10: stopped
% 5.12/1.42 Prover 11: Constructing countermodel ...
% 5.12/1.42 Prover 8: Warning: ignoring some quantifiers
% 5.12/1.43 Prover 8: Constructing countermodel ...
% 5.12/1.43 Prover 11: stopped
% 5.12/1.43 Prover 8: stopped
% 5.12/1.43
% 5.12/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.12/1.43
% 5.12/1.44 % SZS output start Proof for theBenchmark
% 5.12/1.44 Assumptions after simplification:
% 5.12/1.44 ---------------------------------
% 5.12/1.44
% 5.12/1.44 (ax2)
% 5.54/1.47 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3
% 5.54/1.47 = 0 | ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1))
% 5.54/1.47
% 5.54/1.47 (ax4)
% 5.54/1.48 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 5.54/1.48 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 5.54/1.48 collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) =
% 5.54/1.48 v5))) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3:
% 5.54/1.48 collection] : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 5.54/1.48 collection(v1) | in(v0, v1) = 0)
% 5.54/1.48
% 5.54/1.48 (co1)
% 5.54/1.48 collection(empty) & ? [v0: collection] : ? [v1: collection] : ? [v2:
% 5.54/1.48 collection] : ? [v3: int] : ( ~ (v3 = 0) & add(5, empty) = v0 & add(3, v0)
% 5.54/1.48 = v1 & add(1, v1) = v2 & in(3, v2) = v3 & collection(v2) & collection(v1) &
% 5.54/1.48 collection(v0))
% 5.54/1.48
% 5.54/1.48 Further assumptions not needed in the proof:
% 5.54/1.48 --------------------------------------------
% 5.54/1.48 ax1, ax3, ax5
% 5.54/1.48
% 5.54/1.48 Those formulas are unsatisfiable:
% 5.54/1.48 ---------------------------------
% 5.54/1.48
% 5.54/1.48 Begin of proof
% 5.54/1.48 |
% 5.54/1.48 | ALPHA: (ax4) implies:
% 5.54/1.48 | (1) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 5.54/1.48 | : ! [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4)
% 5.54/1.48 | | ~ collection(v1) | ( ~ (v2 = v0) & ? [v5: int] : ( ~ (v5 = 0) &
% 5.54/1.48 | in(v0, v1) = v5)))
% 5.54/1.48 |
% 5.54/1.48 | ALPHA: (co1) implies:
% 5.54/1.49 | (2) ? [v0: collection] : ? [v1: collection] : ? [v2: collection] : ?
% 5.54/1.49 | [v3: int] : ( ~ (v3 = 0) & add(5, empty) = v0 & add(3, v0) = v1 &
% 5.54/1.49 | add(1, v1) = v2 & in(3, v2) = v3 & collection(v2) & collection(v1) &
% 5.54/1.49 | collection(v0))
% 5.54/1.49 |
% 5.54/1.49 | DELTA: instantiating (2) with fresh symbols all_11_0, all_11_1, all_11_2,
% 5.54/1.49 | all_11_3 gives:
% 5.54/1.49 | (3) ~ (all_11_0 = 0) & add(5, empty) = all_11_3 & add(3, all_11_3) =
% 5.54/1.49 | all_11_2 & add(1, all_11_2) = all_11_1 & in(3, all_11_1) = all_11_0 &
% 5.54/1.49 | collection(all_11_1) & collection(all_11_2) & collection(all_11_3)
% 5.54/1.49 |
% 5.54/1.49 | ALPHA: (3) implies:
% 5.54/1.49 | (4) ~ (all_11_0 = 0)
% 5.54/1.49 | (5) collection(all_11_3)
% 5.54/1.49 | (6) collection(all_11_2)
% 5.54/1.49 | (7) in(3, all_11_1) = all_11_0
% 5.54/1.49 | (8) add(1, all_11_2) = all_11_1
% 5.54/1.49 | (9) add(3, all_11_3) = all_11_2
% 5.54/1.49 |
% 5.54/1.49 | GROUND_INST: instantiating (1) with 3, all_11_2, 1, all_11_1, all_11_0,
% 5.54/1.49 | simplifying with (6), (7), (8) gives:
% 5.54/1.49 | (10) all_11_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(3, all_11_2) = v0)
% 5.54/1.49 |
% 5.54/1.49 | BETA: splitting (10) gives:
% 5.54/1.49 |
% 5.54/1.49 | Case 1:
% 5.54/1.49 | |
% 5.54/1.49 | | (11) all_11_0 = 0
% 5.54/1.49 | |
% 5.54/1.49 | | REDUCE: (4), (11) imply:
% 5.54/1.49 | | (12) $false
% 5.54/1.50 | |
% 5.54/1.50 | | CLOSE: (12) is inconsistent.
% 5.54/1.50 | |
% 5.54/1.50 | Case 2:
% 5.54/1.50 | |
% 5.54/1.50 | | (13) ? [v0: int] : ( ~ (v0 = 0) & in(3, all_11_2) = v0)
% 5.54/1.50 | |
% 5.54/1.50 | | DELTA: instantiating (13) with fresh symbol all_20_0 gives:
% 5.54/1.50 | | (14) ~ (all_20_0 = 0) & in(3, all_11_2) = all_20_0
% 5.54/1.50 | |
% 5.54/1.50 | | ALPHA: (14) implies:
% 5.54/1.50 | | (15) ~ (all_20_0 = 0)
% 5.54/1.50 | | (16) in(3, all_11_2) = all_20_0
% 5.54/1.50 | |
% 5.54/1.50 | | GROUND_INST: instantiating (ax2) with 3, all_11_3, all_11_2, all_20_0,
% 5.54/1.50 | | simplifying with (5), (9), (16) gives:
% 5.54/1.50 | | (17) all_20_0 = 0
% 5.54/1.50 | |
% 5.54/1.50 | | REDUCE: (15), (17) imply:
% 5.54/1.50 | | (18) $false
% 5.54/1.50 | |
% 5.54/1.50 | | CLOSE: (18) is inconsistent.
% 5.54/1.50 | |
% 5.54/1.50 | End of split
% 5.54/1.50 |
% 5.54/1.50 End of proof
% 5.54/1.50 % SZS output end Proof for theBenchmark
% 5.54/1.50
% 5.54/1.50 890ms
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