TSTP Solution File: DAT029_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : DAT029_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 : n001.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 22:18:56 EDT 2023

% Result   : Theorem 4.48s 1.27s
% Output   : Proof 5.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT029_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug 24 15:18:27 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.57  ________       _____
% 0.20/0.57  ___  __ \_________(_)________________________________
% 0.20/0.57  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.57  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.57  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.57  
% 0.20/0.58  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58  (2023-06-19)
% 0.20/0.58  
% 0.20/0.58  (c) Philipp Rümmer, 2009-2023
% 0.20/0.58  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58                Amanda Stjerna.
% 0.20/0.58  Free software under BSD-3-Clause.
% 0.20/0.58  
% 0.20/0.58  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58  
% 0.20/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.59  Running up to 7 provers in parallel.
% 0.20/0.60  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.60  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.60  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.60  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.60  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.60  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.60  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.67/1.01  Prover 6: Preprocessing ...
% 2.67/1.01  Prover 2: Preprocessing ...
% 2.67/1.01  Prover 0: Preprocessing ...
% 2.67/1.01  Prover 4: Preprocessing ...
% 2.67/1.01  Prover 5: Preprocessing ...
% 2.67/1.01  Prover 1: Preprocessing ...
% 2.67/1.01  Prover 3: Preprocessing ...
% 3.49/1.18  Prover 5: Proving ...
% 3.49/1.18  Prover 2: Proving ...
% 3.49/1.18  Prover 6: Proving ...
% 3.95/1.19  Prover 4: Constructing countermodel ...
% 3.95/1.19  Prover 3: Constructing countermodel ...
% 3.95/1.19  Prover 0: Proving ...
% 3.95/1.19  Prover 1: Constructing countermodel ...
% 4.48/1.27  Prover 3: proved (671ms)
% 4.48/1.27  
% 4.48/1.27  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.48/1.27  
% 4.48/1.27  Prover 6: stopped
% 4.48/1.27  Prover 5: stopped
% 4.58/1.27  Prover 0: stopped
% 4.58/1.28  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.58/1.28  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.58/1.28  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.58/1.28  Prover 2: proved (682ms)
% 4.58/1.28  
% 4.58/1.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.58/1.28  
% 4.58/1.28  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.58/1.28  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.58/1.31  Prover 4: Found proof (size 10)
% 4.58/1.31  Prover 4: proved (710ms)
% 4.58/1.31  Prover 1: Found proof (size 12)
% 4.58/1.31  Prover 1: proved (713ms)
% 4.58/1.31  Prover 10: Preprocessing ...
% 4.58/1.31  Prover 13: Preprocessing ...
% 4.58/1.31  Prover 11: Preprocessing ...
% 4.58/1.31  Prover 7: Preprocessing ...
% 4.58/1.32  Prover 8: Preprocessing ...
% 4.58/1.33  Prover 10: stopped
% 4.58/1.33  Prover 7: stopped
% 4.58/1.34  Prover 13: stopped
% 4.58/1.34  Prover 11: stopped
% 4.58/1.38  Prover 8: Warning: ignoring some quantifiers
% 4.58/1.39  Prover 8: Constructing countermodel ...
% 4.58/1.39  Prover 8: stopped
% 4.58/1.39  
% 4.58/1.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.58/1.40  
% 4.58/1.40  % SZS output start Proof for theBenchmark
% 4.58/1.40  Assumptions after simplification:
% 4.58/1.40  ---------------------------------
% 4.58/1.40  
% 4.58/1.40    (co1)
% 5.15/1.43     ? [v0: collection] :  ? [v1: collection] :  ? [v2: int] : ($lesseq(v2, 2) &
% 5.15/1.43      in(v2, v0) = 0 & collection(v1) & collection(v0) &  ! [v3: int] : ( ~
% 5.15/1.43        ($lesseq(v3, 0) |  ~ (in(v3, v1) = 0)) &  ! [v3: int] : ( ~ (in(v3, v0) =
% 5.15/1.43            0) |  ? [v4: int] : ($lesseq(1, $difference($product(2, v3),
% 5.15/1.43                $product(5, v4))) & in(v4, v1) = 0)))
% 5.15/1.43  
% 5.15/1.43  Further assumptions not needed in the proof:
% 5.15/1.43  --------------------------------------------
% 5.15/1.43  ax1, ax2, ax3, ax4, ax5
% 5.15/1.43  
% 5.15/1.43  Those formulas are unsatisfiable:
% 5.15/1.43  ---------------------------------
% 5.15/1.43  
% 5.15/1.43  Begin of proof
% 5.15/1.43  | 
% 5.15/1.43  | DELTA: instantiating (co1) with fresh symbols all_11_0, all_11_1, all_11_2
% 5.15/1.43  |        gives:
% 5.15/1.43  |   (1)  $lesseq(all_11_0, 2) & in(all_11_0, all_11_2) = 0 &
% 5.15/1.43  |        collection(all_11_1) & collection(all_11_2) &  ! [v0: int] : ( ~
% 5.15/1.43  |          ($lesseq(v0, 0) |  ~ (in(v0, all_11_1) = 0)) &  ! [v0: int] : ( ~
% 5.15/1.43  |            (in(v0, all_11_2) = 0) |  ? [v1: int] : ($lesseq(1,
% 5.15/1.43  |                $difference($product(2, v0), $product(5, v1))) & in(v1,
% 5.15/1.43  |                all_11_1) = 0))
% 5.15/1.43  | 
% 5.15/1.43  | ALPHA: (1) implies:
% 5.15/1.43  |   (2)  $lesseq(all_11_0, 2)
% 5.15/1.43  |   (3)  in(all_11_0, all_11_2) = 0
% 5.15/1.44  |   (4)   ! [v0: int] : ( ~ (in(v0, all_11_2) = 0) |  ? [v1: int] : ($lesseq(1,
% 5.15/1.44  |              $difference($product(2, v0), $product(5, v1))) & in(v1, all_11_1)
% 5.15/1.44  |            = 0))
% 5.15/1.44  |   (5)   ! [v0: int] : ( ~ ($lesseq(v0, 0) |  ~ (in(v0, all_11_1) = 0))
% 5.15/1.44  | 
% 5.49/1.44  | GROUND_INST: instantiating (4) with all_11_0, simplifying with (3) gives:
% 5.49/1.44  |   (6)   ? [v0: int] : ($lesseq(1, $difference($product(2, all_11_0),
% 5.49/1.44  |              $product(5, v0))) & in(v0, all_11_1) = 0)
% 5.49/1.44  | 
% 5.49/1.44  | DELTA: instantiating (6) with fresh symbol all_20_0 gives:
% 5.49/1.44  |   (7)  $lesseq(1, $difference($product(2, all_11_0), $product(5, all_20_0))) &
% 5.49/1.44  |        in(all_20_0, all_11_1) = 0
% 5.49/1.44  | 
% 5.49/1.44  | ALPHA: (7) implies:
% 5.49/1.44  |   (8)  $lesseq(1, $difference($product(2, all_11_0), $product(5, all_20_0)))
% 5.49/1.44  |   (9)  in(all_20_0, all_11_1) = 0
% 5.49/1.44  | 
% 5.49/1.44  | GROUND_INST: instantiating (5) with all_20_0, simplifying with (9) gives:
% 5.49/1.44  |   (10)  $lesseq(1, all_20_0)
% 5.49/1.44  | 
% 5.49/1.44  | COMBINE_INEQS: (8), (10) imply:
% 5.49/1.44  |   (11)  $lesseq(3, all_11_0)
% 5.49/1.44  | 
% 5.49/1.44  | SIMP: (11) implies:
% 5.49/1.44  |   (12)  $lesseq(3, all_11_0)
% 5.49/1.44  | 
% 5.49/1.44  | COMBINE_INEQS: (2), (12) imply:
% 5.49/1.44  |   (13)  $false
% 5.49/1.44  | 
% 5.49/1.44  | CLOSE: (13) is inconsistent.
% 5.49/1.44  | 
% 5.49/1.44  End of proof
% 5.49/1.44  % SZS output end Proof for theBenchmark
% 5.49/1.44  
% 5.49/1.44  866ms
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