TSTP Solution File: DAT019_1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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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