TSTP Solution File: DAT025_1 by Princess---230619

View Problem - Process Solution

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