TSTP Solution File: SWB027+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWB027+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n007.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 : Thu Aug 31 20:11:52 EDT 2023

% Result   : Theorem 20.75s 3.54s
% Output   : Proof 23.45s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWB027+2 : TPTP v8.1.2. Released v5.2.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n007.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 : Sun Aug 27 07:23:12 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  ________       _____
% 0.19/0.59  ___  __ \_________(_)________________________________
% 0.19/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59  (2023-06-19)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2023
% 0.19/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59                Amanda Stjerna.
% 0.19/0.59  Free software under BSD-3-Clause.
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59  
% 0.19/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61  Running up to 7 provers in parallel.
% 0.19/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.13/0.96  Prover 1: Preprocessing ...
% 2.13/0.96  Prover 4: Preprocessing ...
% 2.43/1.01  Prover 6: Preprocessing ...
% 2.43/1.01  Prover 0: Preprocessing ...
% 2.43/1.01  Prover 5: Preprocessing ...
% 2.43/1.01  Prover 3: Preprocessing ...
% 2.43/1.01  Prover 2: Preprocessing ...
% 4.46/1.28  Prover 5: Proving ...
% 4.46/1.28  Prover 2: Proving ...
% 4.46/1.30  Prover 6: Proving ...
% 4.46/1.30  Prover 3: Constructing countermodel ...
% 4.46/1.33  Prover 1: Constructing countermodel ...
% 6.76/1.63  Prover 3: gave up
% 6.76/1.63  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.96/1.65  Prover 7: Preprocessing ...
% 6.96/1.68  Prover 7: Warning: ignoring some quantifiers
% 6.96/1.69  Prover 7: Constructing countermodel ...
% 6.96/1.69  Prover 4: Constructing countermodel ...
% 7.57/1.75  Prover 0: Proving ...
% 7.57/1.76  Prover 1: gave up
% 7.57/1.77  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.96/1.80  Prover 8: Preprocessing ...
% 8.64/1.88  Prover 8: Warning: ignoring some quantifiers
% 8.64/1.88  Prover 8: Constructing countermodel ...
% 10.25/2.11  Prover 8: gave up
% 10.25/2.12  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 10.25/2.13  Prover 9: Preprocessing ...
% 12.47/2.42  Prover 9: Constructing countermodel ...
% 20.75/3.53  Prover 0: proved (2919ms)
% 20.75/3.53  
% 20.75/3.54  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.75/3.54  
% 21.25/3.55  Prover 5: stopped
% 21.25/3.55  Prover 2: stopped
% 21.25/3.55  Prover 9: stopped
% 21.25/3.55  Prover 6: stopped
% 21.25/3.56  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.25/3.56  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.25/3.56  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 21.25/3.56  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.25/3.56  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 21.46/3.58  Prover 13: Preprocessing ...
% 21.46/3.58  Prover 11: Preprocessing ...
% 21.46/3.58  Prover 16: Preprocessing ...
% 21.46/3.58  Prover 10: Preprocessing ...
% 21.46/3.59  Prover 19: Preprocessing ...
% 21.46/3.60  Prover 16: Warning: ignoring some quantifiers
% 21.46/3.61  Prover 16: Constructing countermodel ...
% 21.46/3.62  Prover 10: Warning: ignoring some quantifiers
% 21.46/3.62  Prover 13: Warning: ignoring some quantifiers
% 21.46/3.62  Prover 13: Constructing countermodel ...
% 21.46/3.62  Prover 10: Constructing countermodel ...
% 21.93/3.71  Prover 19: Warning: ignoring some quantifiers
% 21.93/3.72  Prover 19: Constructing countermodel ...
% 23.20/3.81  Prover 13: Found proof (size 34)
% 23.20/3.81  Prover 13: proved (250ms)
% 23.20/3.81  Prover 19: stopped
% 23.20/3.81  Prover 16: stopped
% 23.20/3.82  Prover 10: stopped
% 23.20/3.82  Prover 7: stopped
% 23.20/3.82  Prover 4: stopped
% 23.20/3.83  Prover 11: Constructing countermodel ...
% 23.20/3.83  Prover 11: stopped
% 23.20/3.83  
% 23.20/3.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.20/3.83  
% 23.20/3.84  % SZS output start Proof for theBenchmark
% 23.20/3.84  Assumptions after simplification:
% 23.20/3.84  ---------------------------------
% 23.20/3.84  
% 23.20/3.84    (owl_chain_002)
% 23.45/3.85    $i(uri_owl_propertyChainAxiom) & $i(uri_rdf_nil) & $i(uri_rdf_rest) &
% 23.45/3.85    $i(uri_rdf_first) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  !
% 23.45/3.85    [v4: $i] :  ! [v5: $i] :  ! [v6: $i] :  ! [v7: $i] : ( ~ $i(v7) |  ~ $i(v6) | 
% 23.45/3.85      ~ $i(v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.85      iext(v4, v6, v7) |  ~ iext(v2, v5, v6) |  ~ iext(uri_owl_propertyChainAxiom,
% 23.45/3.85        v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest,
% 23.45/3.85        v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2)
% 23.45/3.85      | iext(v0, v5, v7)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 23.45/3.85    :  ! [v4: $i] : ( ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) | 
% 23.45/3.85      ~ ip(v4) |  ~ ip(v2) |  ~ ip(v0) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) | 
% 23.45/3.85      ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~
% 23.45/3.85      iext(uri_rdf_first, v1, v2) | iext(uri_owl_propertyChainAxiom, v0, v1) |  ?
% 23.45/3.85      [v5: $i] :  ? [v6: $i] :  ? [v7: $i] : ($i(v7) & $i(v6) & $i(v5) & iext(v4,
% 23.45/3.85          v6, v7) & iext(v2, v5, v6) &  ~ iext(v0, v5, v7))) &  ! [v0: $i] :  !
% 23.45/3.85    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ $i(v4) |  ~ $i(v3) | 
% 23.45/3.85      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ iext(uri_owl_propertyChainAxiom, v0,
% 23.45/3.85        v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1,
% 23.45/3.85        v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) |
% 23.45/3.85      ip(v4)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4:
% 23.45/3.85      $i] : ( ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.85      iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3,
% 23.45/3.85        uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3,
% 23.45/3.85        v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v2)) &  ! [v0: $i] :  ! [v1: $i]
% 23.45/3.85    :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2)
% 23.45/3.85      |  ~ $i(v1) |  ~ $i(v0) |  ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~
% 23.45/3.85      iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~
% 23.45/3.85      iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v0))
% 23.45/3.85  
% 23.45/3.85    (owl_char_inversefunctional)
% 23.45/3.86    $i(uri_owl_InverseFunctionalProperty) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 23.45/3.86      $i] :  ! [v3: $i] : (v2 = v1 |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)
% 23.45/3.86      |  ~ icext(uri_owl_InverseFunctionalProperty, v0) |  ~ iext(v0, v2, v3) |  ~
% 23.45/3.86      iext(v0, v1, v3)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ ip(v0) |
% 23.45/3.86      icext(uri_owl_InverseFunctionalProperty, v0) |  ? [v1: $i] :  ? [v2: $i] : 
% 23.45/3.86      ? [v3: $i] : ( ~ (v2 = v1) & $i(v3) & $i(v2) & $i(v1) & iext(v0, v2, v3) &
% 23.45/3.86        iext(v0, v1, v3))) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 23.45/3.86      icext(uri_owl_InverseFunctionalProperty, v0) | ip(v0))
% 23.45/3.86  
% 23.45/3.86    (owl_eqdis_sameas)
% 23.45/3.86    $i(uri_owl_sameAs) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~
% 23.45/3.86      $i(v0) |  ~ iext(uri_owl_sameAs, v0, v1)) &  ? [v0: $i] : ( ~ $i(v0) |
% 23.45/3.86      iext(uri_owl_sameAs, v0, v0))
% 23.45/3.86  
% 23.45/3.86    (owl_inv)
% 23.45/3.86    $i(uri_owl_inverseOf) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i]
% 23.45/3.86    : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ iext(v1, v3, v2) |  ~
% 23.45/3.86      iext(uri_owl_inverseOf, v0, v1) | iext(v0, v2, v3)) &  ! [v0: $i] :  ! [v1:
% 23.45/3.86      $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~
% 23.45/3.86      $i(v0) |  ~ iext(v0, v2, v3) |  ~ iext(uri_owl_inverseOf, v0, v1) | iext(v1,
% 23.45/3.86        v3, v2)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ ip(v1)
% 23.45/3.86      |  ~ ip(v0) | iext(uri_owl_inverseOf, v0, v1) |  ? [v2: $i] :  ? [v3: $i] :
% 23.45/3.86      ($i(v3) & $i(v2) & ( ~ iext(v1, v3, v2) |  ~ iext(v0, v2, v3)) & (iext(v1,
% 23.45/3.86            v3, v2) | iext(v0, v2, v3)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1)
% 23.45/3.86      |  ~ $i(v0) |  ~ iext(uri_owl_inverseOf, v0, v1) | ip(v1)) &  ! [v0: $i] : 
% 23.45/3.86    ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ iext(uri_owl_inverseOf, v0, v1) |
% 23.45/3.86      ip(v0))
% 23.45/3.86  
% 23.45/3.86    (rdfs_cext_def)
% 23.45/3.86    $i(uri_rdf_type) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.86      icext(v1, v0) | iext(uri_rdf_type, v0, v1)) &  ! [v0: $i] :  ! [v1: $i] : (
% 23.45/3.86      ~ $i(v1) |  ~ $i(v0) |  ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0))
% 23.45/3.86  
% 23.45/3.86    (testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II)
% 23.45/3.86    $i(uri_ex_p) & $i(uri_owl_InverseFunctionalProperty) & $i(uri_rdf_type) &  ~
% 23.45/3.86    iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)
% 23.45/3.86  
% 23.45/3.86    (testcase_premise_fullish_027_Inferred_Property_Characteristics_II)
% 23.45/3.86    $i(uri_ex_p) & $i(uri_owl_inverseOf) & $i(uri_owl_propertyChainAxiom) &
% 23.45/3.86    $i(uri_rdf_nil) & $i(uri_rdf_rest) & $i(uri_rdf_first) & $i(uri_owl_sameAs) & 
% 23.45/3.86    ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 23.45/3.86      iext(uri_owl_inverseOf, v2, uri_ex_p) & iext(uri_owl_propertyChainAxiom,
% 23.45/3.86        uri_owl_sameAs, v0) & iext(uri_rdf_rest, v1, uri_rdf_nil) &
% 23.45/3.86      iext(uri_rdf_rest, v0, v1) & iext(uri_rdf_first, v1, v2) &
% 23.45/3.86      iext(uri_rdf_first, v0, uri_ex_p))
% 23.45/3.86  
% 23.45/3.86  Those formulas are unsatisfiable:
% 23.45/3.86  ---------------------------------
% 23.45/3.86  
% 23.45/3.86  Begin of proof
% 23.45/3.86  | 
% 23.45/3.86  | ALPHA: (testcase_conclusion_fullish_027_Inferred_Property_Characteristics_II)
% 23.45/3.86  |        implies:
% 23.45/3.87  |   (1)   ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (testcase_premise_fullish_027_Inferred_Property_Characteristics_II)
% 23.45/3.87  |        implies:
% 23.45/3.87  |   (2)  $i(uri_ex_p)
% 23.45/3.87  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) &
% 23.45/3.87  |          iext(uri_owl_inverseOf, v2, uri_ex_p) &
% 23.45/3.87  |          iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, v0) &
% 23.45/3.87  |          iext(uri_rdf_rest, v1, uri_rdf_nil) & iext(uri_rdf_rest, v0, v1) &
% 23.45/3.87  |          iext(uri_rdf_first, v1, v2) & iext(uri_rdf_first, v0, uri_ex_p))
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (owl_inv) implies:
% 23.45/3.87  |   (4)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.87  |          iext(uri_owl_inverseOf, v0, v1) | ip(v1))
% 23.45/3.87  |   (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~
% 23.45/3.87  |          $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ iext(v1, v3, v2) |  ~
% 23.45/3.87  |          iext(uri_owl_inverseOf, v0, v1) | iext(v0, v2, v3))
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (owl_char_inversefunctional) implies:
% 23.45/3.87  |   (6)  $i(uri_owl_InverseFunctionalProperty)
% 23.45/3.87  |   (7)   ! [v0: $i] : ( ~ $i(v0) |  ~ ip(v0) |
% 23.45/3.87  |          icext(uri_owl_InverseFunctionalProperty, v0) |  ? [v1: $i] :  ? [v2:
% 23.45/3.87  |            $i] :  ? [v3: $i] : ( ~ (v2 = v1) & $i(v3) & $i(v2) & $i(v1) &
% 23.45/3.87  |            iext(v0, v2, v3) & iext(v0, v1, v3)))
% 23.45/3.87  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v2 = v1 |  ~
% 23.45/3.87  |          $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.87  |          icext(uri_owl_InverseFunctionalProperty, v0) |  ~ iext(v0, v2, v3) | 
% 23.45/3.87  |          ~ iext(v0, v1, v3))
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (owl_chain_002) implies:
% 23.45/3.87  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (
% 23.45/3.87  |          ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.87  |          iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3,
% 23.45/3.87  |            uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~
% 23.45/3.87  |          iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) |
% 23.45/3.87  |          ip(v0))
% 23.45/3.87  |   (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : 
% 23.45/3.87  |         ! [v5: $i] :  ! [v6: $i] :  ! [v7: $i] : ( ~ $i(v7) |  ~ $i(v6) |  ~
% 23.45/3.87  |           $i(v5) |  ~ $i(v4) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 23.45/3.87  |            ~ iext(v4, v6, v7) |  ~ iext(v2, v5, v6) |  ~
% 23.45/3.87  |           iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3,
% 23.45/3.87  |             uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~
% 23.45/3.87  |           iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) |
% 23.45/3.87  |           iext(v0, v5, v7))
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (owl_eqdis_sameas) implies:
% 23.45/3.87  |   (11)  $i(uri_owl_sameAs)
% 23.45/3.87  |   (12)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 23.45/3.87  |           iext(uri_owl_sameAs, v0, v1))
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (rdfs_cext_def) implies:
% 23.45/3.87  |   (13)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ icext(v1, v0)
% 23.45/3.87  |           | iext(uri_rdf_type, v0, v1))
% 23.45/3.87  | 
% 23.45/3.87  | DELTA: instantiating (3) with fresh symbols all_9_0, all_9_1, all_9_2 gives:
% 23.45/3.87  |   (14)  $i(all_9_0) & $i(all_9_1) & $i(all_9_2) & iext(uri_owl_inverseOf,
% 23.45/3.87  |           all_9_0, uri_ex_p) & iext(uri_owl_propertyChainAxiom,
% 23.45/3.87  |           uri_owl_sameAs, all_9_2) & iext(uri_rdf_rest, all_9_1, uri_rdf_nil)
% 23.45/3.87  |         & iext(uri_rdf_rest, all_9_2, all_9_1) & iext(uri_rdf_first, all_9_1,
% 23.45/3.87  |           all_9_0) & iext(uri_rdf_first, all_9_2, uri_ex_p)
% 23.45/3.87  | 
% 23.45/3.87  | ALPHA: (14) implies:
% 23.45/3.87  |   (15)  iext(uri_rdf_first, all_9_2, uri_ex_p)
% 23.45/3.87  |   (16)  iext(uri_rdf_first, all_9_1, all_9_0)
% 23.45/3.87  |   (17)  iext(uri_rdf_rest, all_9_2, all_9_1)
% 23.45/3.87  |   (18)  iext(uri_rdf_rest, all_9_1, uri_rdf_nil)
% 23.45/3.87  |   (19)  iext(uri_owl_propertyChainAxiom, uri_owl_sameAs, all_9_2)
% 23.45/3.87  |   (20)  iext(uri_owl_inverseOf, all_9_0, uri_ex_p)
% 23.45/3.87  |   (21)  $i(all_9_2)
% 23.45/3.87  |   (22)  $i(all_9_1)
% 23.45/3.87  |   (23)  $i(all_9_0)
% 23.45/3.87  | 
% 23.45/3.88  | GROUND_INST: instantiating (9) with uri_owl_sameAs, all_9_2, uri_ex_p,
% 23.45/3.88  |              all_9_1, all_9_0, simplifying with (2), (11), (15), (16), (17),
% 23.45/3.88  |              (18), (19), (21), (22), (23) gives:
% 23.45/3.88  |   (24)  ip(uri_owl_sameAs)
% 23.45/3.88  | 
% 23.45/3.88  | GROUND_INST: instantiating (4) with all_9_0, uri_ex_p, simplifying with (2),
% 23.45/3.88  |              (20), (23) gives:
% 23.45/3.88  |   (25)  ip(uri_ex_p)
% 23.45/3.88  | 
% 23.45/3.88  | GROUND_INST: instantiating (7) with uri_owl_sameAs, simplifying with (11),
% 23.45/3.88  |              (24) gives:
% 23.45/3.88  |   (26)  icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs) |  ? [v0: $i]
% 23.45/3.88  |         :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v1 = v0) & $i(v2) & $i(v1) & $i(v0)
% 23.45/3.88  |           & iext(uri_owl_sameAs, v1, v2) & iext(uri_owl_sameAs, v0, v2))
% 23.45/3.88  | 
% 23.45/3.88  | GROUND_INST: instantiating (7) with uri_ex_p, simplifying with (2), (25)
% 23.45/3.88  |              gives:
% 23.45/3.88  |   (27)  icext(uri_owl_InverseFunctionalProperty, uri_ex_p) |  ? [v0: $i] :  ?
% 23.45/3.88  |         [v1: $i] :  ? [v2: $i] : ( ~ (v1 = v0) & $i(v2) & $i(v1) & $i(v0) &
% 23.45/3.88  |           iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0, v2))
% 23.45/3.88  | 
% 23.45/3.88  | BETA: splitting (26) gives:
% 23.45/3.88  | 
% 23.45/3.88  | Case 1:
% 23.45/3.88  | | 
% 23.45/3.88  | |   (28)  icext(uri_owl_InverseFunctionalProperty, uri_owl_sameAs)
% 23.45/3.88  | | 
% 23.45/3.88  | | BETA: splitting (27) gives:
% 23.45/3.88  | | 
% 23.45/3.88  | | Case 1:
% 23.45/3.88  | | | 
% 23.45/3.88  | | |   (29)  icext(uri_owl_InverseFunctionalProperty, uri_ex_p)
% 23.45/3.88  | | | 
% 23.45/3.88  | | | GROUND_INST: instantiating (13) with uri_ex_p,
% 23.45/3.88  | | |              uri_owl_InverseFunctionalProperty, simplifying with (1), (2),
% 23.45/3.88  | | |              (6), (29) gives:
% 23.45/3.88  | | |   (30)  $false
% 23.45/3.88  | | | 
% 23.45/3.88  | | | CLOSE: (30) is inconsistent.
% 23.45/3.88  | | | 
% 23.45/3.88  | | Case 2:
% 23.45/3.88  | | | 
% 23.45/3.88  | | |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v1 = v0) & $i(v2) &
% 23.45/3.88  | | |           $i(v1) & $i(v0) & iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0,
% 23.45/3.88  | | |             v2))
% 23.45/3.88  | | | 
% 23.45/3.88  | | | DELTA: instantiating (31) with fresh symbols all_104_0, all_104_1,
% 23.45/3.88  | | |        all_104_2 gives:
% 23.45/3.88  | | |   (32)   ~ (all_104_1 = all_104_2) & $i(all_104_0) & $i(all_104_1) &
% 23.45/3.88  | | |         $i(all_104_2) & iext(uri_ex_p, all_104_1, all_104_0) &
% 23.45/3.88  | | |         iext(uri_ex_p, all_104_2, all_104_0)
% 23.45/3.88  | | | 
% 23.45/3.88  | | | ALPHA: (32) implies:
% 23.45/3.88  | | |   (33)   ~ (all_104_1 = all_104_2)
% 23.45/3.88  | | |   (34)  iext(uri_ex_p, all_104_2, all_104_0)
% 23.45/3.88  | | |   (35)  iext(uri_ex_p, all_104_1, all_104_0)
% 23.45/3.88  | | |   (36)  $i(all_104_2)
% 23.45/3.88  | | |   (37)  $i(all_104_1)
% 23.45/3.88  | | |   (38)  $i(all_104_0)
% 23.45/3.88  | | | 
% 23.45/3.88  | | | GROUND_INST: instantiating (5) with all_9_0, uri_ex_p, all_104_0,
% 23.45/3.88  | | |              all_104_1, simplifying with (2), (20), (23), (35), (37), (38)
% 23.45/3.88  | | |              gives:
% 23.45/3.88  | | |   (39)  iext(all_9_0, all_104_0, all_104_1)
% 23.45/3.88  | | | 
% 23.45/3.89  | | | GROUND_INST: instantiating (10) with uri_owl_sameAs, all_9_2, uri_ex_p,
% 23.45/3.89  | | |              all_9_1, all_9_0, all_104_1, all_104_0, all_104_1,
% 23.45/3.89  | | |              simplifying with (2), (11), (15), (16), (17), (18), (19),
% 23.45/3.89  | | |              (21), (22), (23), (35), (37), (38), (39) gives:
% 23.45/3.89  | | |   (40)  iext(uri_owl_sameAs, all_104_1, all_104_1)
% 23.45/3.89  | | | 
% 23.45/3.89  | | | GROUND_INST: instantiating (10) with uri_owl_sameAs, all_9_2, uri_ex_p,
% 23.45/3.89  | | |              all_9_1, all_9_0, all_104_2, all_104_0, all_104_1,
% 23.45/3.89  | | |              simplifying with (2), (11), (15), (16), (17), (18), (19),
% 23.45/3.89  | | |              (21), (22), (23), (34), (36), (37), (38), (39) gives:
% 23.45/3.89  | | |   (41)  iext(uri_owl_sameAs, all_104_2, all_104_1)
% 23.45/3.89  | | | 
% 23.45/3.89  | | | GROUND_INST: instantiating (8) with uri_owl_sameAs, all_104_2, all_104_1,
% 23.45/3.89  | | |              all_104_1, simplifying with (11), (28), (36), (37), (40),
% 23.45/3.89  | | |              (41) gives:
% 23.45/3.89  | | |   (42)  all_104_1 = all_104_2
% 23.45/3.89  | | | 
% 23.45/3.89  | | | REDUCE: (33), (42) imply:
% 23.45/3.89  | | |   (43)  $false
% 23.45/3.89  | | | 
% 23.45/3.89  | | | CLOSE: (43) is inconsistent.
% 23.45/3.89  | | | 
% 23.45/3.89  | | End of split
% 23.45/3.89  | | 
% 23.45/3.89  | Case 2:
% 23.45/3.89  | | 
% 23.45/3.89  | |   (44)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v1 = v0) & $i(v2) &
% 23.45/3.89  | |           $i(v1) & $i(v0) & iext(uri_owl_sameAs, v1, v2) &
% 23.45/3.89  | |           iext(uri_owl_sameAs, v0, v2))
% 23.45/3.89  | | 
% 23.45/3.89  | | DELTA: instantiating (44) with fresh symbols all_70_0, all_70_1, all_70_2
% 23.45/3.89  | |        gives:
% 23.45/3.89  | |   (45)   ~ (all_70_1 = all_70_2) & $i(all_70_0) & $i(all_70_1) &
% 23.45/3.89  | |         $i(all_70_2) & iext(uri_owl_sameAs, all_70_1, all_70_0) &
% 23.45/3.89  | |         iext(uri_owl_sameAs, all_70_2, all_70_0)
% 23.45/3.89  | | 
% 23.45/3.89  | | ALPHA: (45) implies:
% 23.45/3.89  | |   (46)   ~ (all_70_1 = all_70_2)
% 23.45/3.89  | |   (47)  iext(uri_owl_sameAs, all_70_2, all_70_0)
% 23.45/3.89  | |   (48)  iext(uri_owl_sameAs, all_70_1, all_70_0)
% 23.45/3.89  | |   (49)  $i(all_70_2)
% 23.45/3.89  | |   (50)  $i(all_70_1)
% 23.45/3.89  | |   (51)  $i(all_70_0)
% 23.45/3.89  | | 
% 23.45/3.89  | | GROUND_INST: instantiating (12) with all_70_2, all_70_0, simplifying with
% 23.45/3.89  | |              (47), (49), (51) gives:
% 23.45/3.89  | |   (52)  all_70_0 = all_70_2
% 23.45/3.89  | | 
% 23.45/3.89  | | GROUND_INST: instantiating (12) with all_70_1, all_70_0, simplifying with
% 23.45/3.89  | |              (48), (50), (51) gives:
% 23.45/3.89  | |   (53)  all_70_0 = all_70_1
% 23.45/3.89  | | 
% 23.45/3.89  | | COMBINE_EQS: (52), (53) imply:
% 23.45/3.89  | |   (54)  all_70_1 = all_70_2
% 23.45/3.89  | | 
% 23.45/3.89  | | REDUCE: (46), (54) imply:
% 23.45/3.89  | |   (55)  $false
% 23.45/3.89  | | 
% 23.45/3.89  | | CLOSE: (55) is inconsistent.
% 23.45/3.89  | | 
% 23.45/3.89  | End of split
% 23.45/3.89  | 
% 23.45/3.89  End of proof
% 23.45/3.89  % SZS output end Proof for theBenchmark
% 23.45/3.89  
% 23.45/3.89  3297ms
%------------------------------------------------------------------------------