TSTP Solution File: SWB023+2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SWB023+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 : n032.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 20:11:49 EDT 2023

% Result   : Theorem 5.09s 1.44s
% Output   : Proof 7.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SWB023+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Sun Aug 27 06:37:14 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.52  ________       _____
% 0.15/0.52  ___  __ \_________(_)________________________________
% 0.15/0.52  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.15/0.52  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.15/0.52  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.15/0.52  
% 0.15/0.52  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.52  (2023-06-19)
% 0.15/0.52  
% 0.15/0.52  (c) Philipp Rümmer, 2009-2023
% 0.15/0.52  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.52                Amanda Stjerna.
% 0.15/0.52  Free software under BSD-3-Clause.
% 0.15/0.52  
% 0.15/0.52  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.52  
% 0.15/0.52  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.53  Running up to 7 provers in parallel.
% 0.15/0.54  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.54  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.54  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.54  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.54  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.54  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.86/0.89  Prover 4: Preprocessing ...
% 0.86/0.89  Prover 1: Preprocessing ...
% 2.01/0.93  Prover 3: Preprocessing ...
% 2.01/0.93  Prover 6: Preprocessing ...
% 2.01/0.93  Prover 0: Preprocessing ...
% 2.01/0.93  Prover 5: Preprocessing ...
% 2.01/0.93  Prover 2: Preprocessing ...
% 3.13/1.13  Prover 5: Proving ...
% 3.13/1.14  Prover 2: Proving ...
% 3.64/1.18  Prover 6: Proving ...
% 3.64/1.19  Prover 1: Constructing countermodel ...
% 3.64/1.20  Prover 3: Constructing countermodel ...
% 3.98/1.23  Prover 0: Proving ...
% 3.98/1.23  Prover 4: Constructing countermodel ...
% 5.09/1.44  Prover 3: proved (897ms)
% 5.09/1.44  
% 5.09/1.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.09/1.44  
% 5.09/1.44  Prover 5: stopped
% 5.09/1.45  Prover 0: stopped
% 5.09/1.45  Prover 6: stopped
% 5.09/1.46  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.09/1.46  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.09/1.46  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.09/1.46  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.09/1.47  Prover 2: proved (929ms)
% 5.09/1.47  
% 5.09/1.47  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.09/1.47  
% 5.09/1.50  Prover 8: Preprocessing ...
% 5.09/1.51  Prover 7: Preprocessing ...
% 5.09/1.51  Prover 10: Preprocessing ...
% 5.09/1.51  Prover 11: Preprocessing ...
% 5.09/1.52  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.09/1.54  Prover 13: Preprocessing ...
% 5.09/1.54  Prover 7: Warning: ignoring some quantifiers
% 5.09/1.55  Prover 10: Warning: ignoring some quantifiers
% 5.09/1.55  Prover 7: Constructing countermodel ...
% 5.09/1.58  Prover 10: Constructing countermodel ...
% 5.09/1.59  Prover 13: Warning: ignoring some quantifiers
% 5.09/1.59  Prover 13: Constructing countermodel ...
% 5.09/1.60  Prover 1: Found proof (size 46)
% 5.09/1.60  Prover 1: proved (1067ms)
% 5.09/1.60  Prover 10: stopped
% 5.09/1.60  Prover 7: stopped
% 5.09/1.60  Prover 4: stopped
% 5.09/1.60  Prover 13: stopped
% 5.68/1.62  Prover 8: Warning: ignoring some quantifiers
% 5.68/1.62  Prover 8: Constructing countermodel ...
% 6.63/1.63  Prover 8: stopped
% 6.63/1.66  Prover 11: Constructing countermodel ...
% 6.63/1.67  Prover 11: stopped
% 6.63/1.67  
% 6.63/1.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.63/1.67  
% 6.85/1.69  % SZS output start Proof for theBenchmark
% 6.85/1.69  Assumptions after simplification:
% 6.85/1.69  ---------------------------------
% 6.85/1.69  
% 6.85/1.69    (owl_enum_class_001)
% 6.85/1.73    $i(uri_owl_oneOf) & $i(uri_rdf_nil) & $i(uri_rdf_rest) & $i(uri_rdf_first) & 
% 6.85/1.73    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 6.85/1.73      (iext(uri_owl_oneOf, v0, v1) = v3) |  ~ (iext(uri_rdf_first, v1, v2) = 0) | 
% 6.85/1.73      ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5: any] : (ic(v0) =
% 6.85/1.73        v5 & iext(uri_rdf_rest, v1, uri_rdf_nil) = v4 & ( ~ (v4 = 0) | (( ~ (v5 =
% 6.85/1.73                0) | v3 = 0 |  ? [v6: $i] :  ? [v7: any] : (icext(v0, v6) = v7 &
% 6.85/1.73                $i(v6) & ( ~ (v7 = 0) |  ~ (v6 = v2)) & (v7 = 0 | v6 = v2))) & ( ~
% 6.85/1.73              (v3 = 0) | (v5 = 0 &  ! [v6: $i] : (v6 = v2 |  ~ (icext(v0, v6) = 0)
% 6.85/1.73                  |  ~ $i(v6)) &  ! [v6: int] : (v6 = 0 |  ~ (icext(v0, v2) =
% 6.85/1.73                    v6))))))))
% 6.85/1.73  
% 6.85/1.73    (owl_eqdis_sameas)
% 6.85/1.74    $i(uri_owl_sameAs) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~
% 6.85/1.74      (iext(uri_owl_sameAs, v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] : 
% 6.85/1.74    ! [v1: int] : (v1 = 0 |  ~ (iext(uri_owl_sameAs, v0, v0) = v1) |  ~ $i(v0))
% 6.85/1.74  
% 6.85/1.74    (rdfs_cext_def)
% 6.85/1.74    $i(uri_rdf_type) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~
% 6.85/1.74      (iext(uri_rdf_type, v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : (
% 6.85/1.74        ~ (v3 = 0) & icext(v1, v0) = v3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 6.85/1.74      (iext(uri_rdf_type, v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) | icext(v1, v0) =
% 6.85/1.74      0)
% 6.85/1.74  
% 6.85/1.74    (testcase_conclusion_fullish_023_Unique_List_Components)
% 6.85/1.74    $i(uri_ex_v) & $i(uri_ex_u) & $i(uri_ex_w) & $i(uri_owl_sameAs) &  ? [v0: any]
% 6.85/1.74    :  ? [v1: any] : (iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = v1 &
% 6.85/1.74      iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 6.85/1.74  
% 6.85/1.74    (testcase_premise_fullish_023_Unique_List_Components)
% 7.17/1.74    $i(uri_owl_Class) & $i(uri_ex_v) & $i(uri_ex_u) & $i(uri_ex_w) &
% 7.17/1.74    $i(uri_owl_FunctionalProperty) & $i(uri_owl_oneOf) & $i(uri_rdf_nil) &
% 7.17/1.74    $i(uri_rdf_rest) & $i(uri_rdf_first) & $i(uri_rdf_type) &  ? [v0: any] :
% 7.17/1.74    (iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) = v0 &  ? [v1:
% 7.17/1.74        $i] :  ? [v2: $i] : (v0 = 0 & iext(uri_owl_oneOf, v1, v2) = 0 &
% 7.17/1.74        iext(uri_rdf_rest, v2, uri_rdf_nil) = 0 & iext(uri_rdf_first, v2,
% 7.17/1.74          uri_ex_v) = 0 & iext(uri_rdf_first, v2, uri_ex_u) = 0 &
% 7.17/1.74        iext(uri_rdf_type, v1, uri_owl_Class) = 0 & iext(uri_rdf_type, uri_ex_w,
% 7.17/1.74          v1) = 0 & $i(v2) & $i(v1)))
% 7.17/1.74  
% 7.17/1.74    (function-axioms)
% 7.17/1.75     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 7.17/1.75    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (iext(v4, v3, v2) = v1) |  ~ (iext(v4,
% 7.17/1.75          v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool]
% 7.17/1.75    :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (icext(v3, v2) = v1) |  ~
% 7.17/1.75      (icext(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.17/1.75      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (ip(v2) = v1) |  ~ (ip(v2)
% 7.17/1.75        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 7.17/1.75      $i] : (v1 = v0 |  ~ (ic(v2) = v1) |  ~ (ic(v2) = v0))
% 7.17/1.75  
% 7.17/1.75  Further assumptions not needed in the proof:
% 7.17/1.75  --------------------------------------------
% 7.17/1.75  owl_char_functional
% 7.17/1.75  
% 7.17/1.75  Those formulas are unsatisfiable:
% 7.17/1.75  ---------------------------------
% 7.17/1.75  
% 7.17/1.75  Begin of proof
% 7.17/1.75  | 
% 7.17/1.75  | ALPHA: (rdfs_cext_def) implies:
% 7.17/1.75  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) |  ~
% 7.17/1.75  |          $i(v1) |  ~ $i(v0) | icext(v1, v0) = 0)
% 7.17/1.75  | 
% 7.17/1.75  | ALPHA: (owl_enum_class_001) implies:
% 7.17/1.76  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~
% 7.17/1.76  |          (iext(uri_owl_oneOf, v0, v1) = v3) |  ~ (iext(uri_rdf_first, v1, v2)
% 7.17/1.76  |            = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ? [v5:
% 7.17/1.76  |            any] : (ic(v0) = v5 & iext(uri_rdf_rest, v1, uri_rdf_nil) = v4 & (
% 7.17/1.76  |              ~ (v4 = 0) | (( ~ (v5 = 0) | v3 = 0 |  ? [v6: $i] :  ? [v7: any]
% 7.17/1.76  |                  : (icext(v0, v6) = v7 & $i(v6) & ( ~ (v7 = 0) |  ~ (v6 = v2))
% 7.17/1.76  |                    & (v7 = 0 | v6 = v2))) & ( ~ (v3 = 0) | (v5 = 0 &  ! [v6:
% 7.17/1.76  |                      $i] : (v6 = v2 |  ~ (icext(v0, v6) = 0) |  ~ $i(v6)) &  !
% 7.17/1.76  |                    [v6: int] : (v6 = 0 |  ~ (icext(v0, v2) = v6))))))))
% 7.17/1.76  | 
% 7.17/1.76  | ALPHA: (owl_eqdis_sameas) implies:
% 7.17/1.76  |   (3)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (iext(uri_owl_sameAs, v0, v0)
% 7.17/1.76  |            = v1) |  ~ $i(v0))
% 7.17/1.76  | 
% 7.17/1.76  | ALPHA: (testcase_premise_fullish_023_Unique_List_Components) implies:
% 7.17/1.76  |   (4)   ? [v0: any] : (iext(uri_rdf_type, uri_rdf_first,
% 7.17/1.76  |            uri_owl_FunctionalProperty) = v0 &  ? [v1: $i] :  ? [v2: $i] : (v0
% 7.17/1.76  |            = 0 & iext(uri_owl_oneOf, v1, v2) = 0 & iext(uri_rdf_rest, v2,
% 7.17/1.76  |              uri_rdf_nil) = 0 & iext(uri_rdf_first, v2, uri_ex_v) = 0 &
% 7.17/1.76  |            iext(uri_rdf_first, v2, uri_ex_u) = 0 & iext(uri_rdf_type, v1,
% 7.17/1.76  |              uri_owl_Class) = 0 & iext(uri_rdf_type, uri_ex_w, v1) = 0 &
% 7.17/1.76  |            $i(v2) & $i(v1)))
% 7.17/1.76  | 
% 7.17/1.76  | ALPHA: (testcase_conclusion_fullish_023_Unique_List_Components) implies:
% 7.17/1.76  |   (5)  $i(uri_ex_w)
% 7.17/1.76  |   (6)  $i(uri_ex_u)
% 7.17/1.76  |   (7)  $i(uri_ex_v)
% 7.17/1.76  |   (8)   ? [v0: any] :  ? [v1: any] : (iext(uri_owl_sameAs, uri_ex_w, uri_ex_v)
% 7.17/1.76  |          = v1 & iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = v0 & ( ~ (v1 = 0) |
% 7.17/1.76  |             ~ (v0 = 0)))
% 7.17/1.76  | 
% 7.17/1.76  | ALPHA: (function-axioms) implies:
% 7.17/1.76  |   (9)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 7.17/1.76  |         ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (iext(v4, v3, v2) = v1) |  ~
% 7.17/1.76  |          (iext(v4, v3, v2) = v0))
% 7.17/1.76  | 
% 7.17/1.76  | DELTA: instantiating (8) with fresh symbols all_8_0, all_8_1 gives:
% 7.17/1.76  |   (10)  iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = all_8_0 &
% 7.17/1.76  |         iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_8_1 & ( ~ (all_8_0 = 0)
% 7.17/1.76  |           |  ~ (all_8_1 = 0))
% 7.17/1.76  | 
% 7.17/1.76  | ALPHA: (10) implies:
% 7.17/1.77  |   (11)  iext(uri_owl_sameAs, uri_ex_w, uri_ex_u) = all_8_1
% 7.17/1.77  |   (12)  iext(uri_owl_sameAs, uri_ex_w, uri_ex_v) = all_8_0
% 7.17/1.77  |   (13)   ~ (all_8_0 = 0) |  ~ (all_8_1 = 0)
% 7.17/1.77  | 
% 7.17/1.77  | DELTA: instantiating (4) with fresh symbol all_10_0 gives:
% 7.17/1.77  |   (14)  iext(uri_rdf_type, uri_rdf_first, uri_owl_FunctionalProperty) =
% 7.17/1.77  |         all_10_0 &  ? [v0: $i] :  ? [v1: $i] : (all_10_0 = 0 &
% 7.17/1.77  |           iext(uri_owl_oneOf, v0, v1) = 0 & iext(uri_rdf_rest, v1,
% 7.17/1.77  |             uri_rdf_nil) = 0 & iext(uri_rdf_first, v1, uri_ex_v) = 0 &
% 7.17/1.77  |           iext(uri_rdf_first, v1, uri_ex_u) = 0 & iext(uri_rdf_type, v0,
% 7.17/1.77  |             uri_owl_Class) = 0 & iext(uri_rdf_type, uri_ex_w, v0) = 0 & $i(v1)
% 7.17/1.77  |           & $i(v0))
% 7.17/1.77  | 
% 7.17/1.77  | ALPHA: (14) implies:
% 7.17/1.77  |   (15)   ? [v0: $i] :  ? [v1: $i] : (all_10_0 = 0 & iext(uri_owl_oneOf, v0,
% 7.17/1.77  |             v1) = 0 & iext(uri_rdf_rest, v1, uri_rdf_nil) = 0 &
% 7.17/1.77  |           iext(uri_rdf_first, v1, uri_ex_v) = 0 & iext(uri_rdf_first, v1,
% 7.17/1.77  |             uri_ex_u) = 0 & iext(uri_rdf_type, v0, uri_owl_Class) = 0 &
% 7.17/1.77  |           iext(uri_rdf_type, uri_ex_w, v0) = 0 & $i(v1) & $i(v0))
% 7.17/1.77  | 
% 7.17/1.77  | DELTA: instantiating (15) with fresh symbols all_12_0, all_12_1 gives:
% 7.17/1.77  |   (16)  all_10_0 = 0 & iext(uri_owl_oneOf, all_12_1, all_12_0) = 0 &
% 7.17/1.77  |         iext(uri_rdf_rest, all_12_0, uri_rdf_nil) = 0 & iext(uri_rdf_first,
% 7.17/1.77  |           all_12_0, uri_ex_v) = 0 & iext(uri_rdf_first, all_12_0, uri_ex_u) =
% 7.17/1.77  |         0 & iext(uri_rdf_type, all_12_1, uri_owl_Class) = 0 &
% 7.17/1.77  |         iext(uri_rdf_type, uri_ex_w, all_12_1) = 0 & $i(all_12_0) &
% 7.17/1.77  |         $i(all_12_1)
% 7.17/1.77  | 
% 7.17/1.77  | ALPHA: (16) implies:
% 7.17/1.77  |   (17)  $i(all_12_1)
% 7.17/1.77  |   (18)  $i(all_12_0)
% 7.17/1.77  |   (19)  iext(uri_rdf_type, uri_ex_w, all_12_1) = 0
% 7.30/1.77  |   (20)  iext(uri_rdf_first, all_12_0, uri_ex_u) = 0
% 7.30/1.77  |   (21)  iext(uri_rdf_first, all_12_0, uri_ex_v) = 0
% 7.30/1.77  |   (22)  iext(uri_rdf_rest, all_12_0, uri_rdf_nil) = 0
% 7.30/1.77  |   (23)  iext(uri_owl_oneOf, all_12_1, all_12_0) = 0
% 7.30/1.77  | 
% 7.30/1.77  | GROUND_INST: instantiating (1) with uri_ex_w, all_12_1, simplifying with (5),
% 7.30/1.77  |              (17), (19) gives:
% 7.30/1.77  |   (24)  icext(all_12_1, uri_ex_w) = 0
% 7.30/1.77  | 
% 7.30/1.77  | GROUND_INST: instantiating (2) with all_12_1, all_12_0, uri_ex_v, 0,
% 7.30/1.77  |              simplifying with (7), (17), (18), (21), (23) gives:
% 7.30/1.77  |   (25)   ? [v0: any] :  ? [v1: any] : (ic(all_12_1) = v1 & iext(uri_rdf_rest,
% 7.30/1.77  |             all_12_0, uri_rdf_nil) = v0 & ( ~ (v0 = 0) | (v1 = 0 &  ! [v2: $i]
% 7.30/1.77  |               : (v2 = uri_ex_v |  ~ (icext(all_12_1, v2) = 0) |  ~ $i(v2)) & 
% 7.30/1.77  |               ! [v2: int] : (v2 = 0 |  ~ (icext(all_12_1, uri_ex_v) = v2)))))
% 7.30/1.77  | 
% 7.30/1.78  | GROUND_INST: instantiating (2) with all_12_1, all_12_0, uri_ex_u, 0,
% 7.30/1.78  |              simplifying with (6), (17), (18), (20), (23) gives:
% 7.30/1.78  |   (26)   ? [v0: any] :  ? [v1: any] : (ic(all_12_1) = v1 & iext(uri_rdf_rest,
% 7.30/1.78  |             all_12_0, uri_rdf_nil) = v0 & ( ~ (v0 = 0) | (v1 = 0 &  ! [v2: $i]
% 7.30/1.78  |               : (v2 = uri_ex_u |  ~ (icext(all_12_1, v2) = 0) |  ~ $i(v2)) & 
% 7.30/1.78  |               ! [v2: int] : (v2 = 0 |  ~ (icext(all_12_1, uri_ex_u) = v2)))))
% 7.30/1.78  | 
% 7.30/1.78  | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1 gives:
% 7.30/1.78  |   (27)  ic(all_12_1) = all_20_0 & iext(uri_rdf_rest, all_12_0, uri_rdf_nil) =
% 7.30/1.78  |         all_20_1 & ( ~ (all_20_1 = 0) | (all_20_0 = 0 &  ! [v0: $i] : (v0 =
% 7.30/1.78  |               uri_ex_u |  ~ (icext(all_12_1, v0) = 0) |  ~ $i(v0)) &  ! [v0:
% 7.30/1.78  |               int] : (v0 = 0 |  ~ (icext(all_12_1, uri_ex_u) = v0))))
% 7.30/1.78  | 
% 7.30/1.78  | ALPHA: (27) implies:
% 7.30/1.78  |   (28)  iext(uri_rdf_rest, all_12_0, uri_rdf_nil) = all_20_1
% 7.30/1.78  |   (29)   ~ (all_20_1 = 0) | (all_20_0 = 0 &  ! [v0: $i] : (v0 = uri_ex_u |  ~
% 7.30/1.78  |             (icext(all_12_1, v0) = 0) |  ~ $i(v0)) &  ! [v0: int] : (v0 = 0 | 
% 7.30/1.78  |             ~ (icext(all_12_1, uri_ex_u) = v0)))
% 7.30/1.78  | 
% 7.30/1.78  | DELTA: instantiating (25) with fresh symbols all_22_0, all_22_1 gives:
% 7.30/1.78  |   (30)  ic(all_12_1) = all_22_0 & iext(uri_rdf_rest, all_12_0, uri_rdf_nil) =
% 7.30/1.78  |         all_22_1 & ( ~ (all_22_1 = 0) | (all_22_0 = 0 &  ! [v0: $i] : (v0 =
% 7.30/1.78  |               uri_ex_v |  ~ (icext(all_12_1, v0) = 0) |  ~ $i(v0)) &  ! [v0:
% 7.30/1.78  |               int] : (v0 = 0 |  ~ (icext(all_12_1, uri_ex_v) = v0))))
% 7.30/1.78  | 
% 7.30/1.78  | ALPHA: (30) implies:
% 7.30/1.78  |   (31)  iext(uri_rdf_rest, all_12_0, uri_rdf_nil) = all_22_1
% 7.30/1.78  |   (32)   ~ (all_22_1 = 0) | (all_22_0 = 0 &  ! [v0: $i] : (v0 = uri_ex_v |  ~
% 7.30/1.78  |             (icext(all_12_1, v0) = 0) |  ~ $i(v0)) &  ! [v0: int] : (v0 = 0 | 
% 7.30/1.78  |             ~ (icext(all_12_1, uri_ex_v) = v0)))
% 7.30/1.78  | 
% 7.30/1.78  | GROUND_INST: instantiating (9) with 0, all_22_1, uri_rdf_nil, all_12_0,
% 7.30/1.78  |              uri_rdf_rest, simplifying with (22), (31) gives:
% 7.30/1.78  |   (33)  all_22_1 = 0
% 7.30/1.78  | 
% 7.30/1.78  | GROUND_INST: instantiating (9) with all_20_1, all_22_1, uri_rdf_nil, all_12_0,
% 7.30/1.78  |              uri_rdf_rest, simplifying with (28), (31) gives:
% 7.30/1.78  |   (34)  all_22_1 = all_20_1
% 7.30/1.78  | 
% 7.30/1.78  | COMBINE_EQS: (33), (34) imply:
% 7.30/1.78  |   (35)  all_20_1 = 0
% 7.30/1.78  | 
% 7.30/1.78  | BETA: splitting (29) gives:
% 7.30/1.78  | 
% 7.30/1.78  | Case 1:
% 7.30/1.78  | | 
% 7.30/1.78  | |   (36)   ~ (all_20_1 = 0)
% 7.30/1.78  | | 
% 7.30/1.78  | | REDUCE: (35), (36) imply:
% 7.30/1.78  | |   (37)  $false
% 7.30/1.79  | | 
% 7.30/1.79  | | CLOSE: (37) is inconsistent.
% 7.30/1.79  | | 
% 7.30/1.79  | Case 2:
% 7.30/1.79  | | 
% 7.30/1.79  | |   (38)  all_20_0 = 0 &  ! [v0: $i] : (v0 = uri_ex_u |  ~ (icext(all_12_1,
% 7.30/1.79  | |               v0) = 0) |  ~ $i(v0)) &  ! [v0: int] : (v0 = 0 |  ~
% 7.30/1.79  | |           (icext(all_12_1, uri_ex_u) = v0))
% 7.30/1.79  | | 
% 7.30/1.79  | | ALPHA: (38) implies:
% 7.30/1.79  | |   (39)   ! [v0: $i] : (v0 = uri_ex_u |  ~ (icext(all_12_1, v0) = 0) |  ~
% 7.30/1.79  | |           $i(v0))
% 7.30/1.79  | | 
% 7.30/1.79  | | BETA: splitting (32) gives:
% 7.30/1.79  | | 
% 7.30/1.79  | | Case 1:
% 7.30/1.79  | | | 
% 7.30/1.79  | | |   (40)   ~ (all_22_1 = 0)
% 7.30/1.79  | | | 
% 7.30/1.79  | | | REDUCE: (33), (40) imply:
% 7.30/1.79  | | |   (41)  $false
% 7.30/1.79  | | | 
% 7.30/1.79  | | | CLOSE: (41) is inconsistent.
% 7.30/1.79  | | | 
% 7.30/1.79  | | Case 2:
% 7.30/1.79  | | | 
% 7.30/1.79  | | |   (42)  all_22_0 = 0 &  ! [v0: $i] : (v0 = uri_ex_v |  ~ (icext(all_12_1,
% 7.30/1.79  | | |               v0) = 0) |  ~ $i(v0)) &  ! [v0: int] : (v0 = 0 |  ~
% 7.30/1.79  | | |           (icext(all_12_1, uri_ex_v) = v0))
% 7.30/1.79  | | | 
% 7.30/1.79  | | | ALPHA: (42) implies:
% 7.30/1.79  | | |   (43)   ! [v0: $i] : (v0 = uri_ex_v |  ~ (icext(all_12_1, v0) = 0) |  ~
% 7.30/1.79  | | |           $i(v0))
% 7.30/1.79  | | | 
% 7.30/1.79  | | | GROUND_INST: instantiating (43) with uri_ex_w, simplifying with (5), (24)
% 7.30/1.79  | | |              gives:
% 7.30/1.79  | | |   (44)  uri_ex_v = uri_ex_w
% 7.30/1.79  | | | 
% 7.30/1.79  | | | GROUND_INST: instantiating (39) with uri_ex_w, simplifying with (5), (24)
% 7.30/1.79  | | |              gives:
% 7.30/1.79  | | |   (45)  uri_ex_u = uri_ex_w
% 7.30/1.79  | | | 
% 7.30/1.79  | | | REDUCE: (12), (44) imply:
% 7.30/1.79  | | |   (46)  iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_8_0
% 7.30/1.79  | | | 
% 7.30/1.79  | | | REDUCE: (11), (45) imply:
% 7.30/1.79  | | |   (47)  iext(uri_owl_sameAs, uri_ex_w, uri_ex_w) = all_8_1
% 7.30/1.79  | | | 
% 7.30/1.79  | | | GROUND_INST: instantiating (9) with all_8_1, all_8_0, uri_ex_w, uri_ex_w,
% 7.30/1.79  | | |              uri_owl_sameAs, simplifying with (46), (47) gives:
% 7.30/1.79  | | |   (48)  all_8_0 = all_8_1
% 7.30/1.79  | | | 
% 7.30/1.79  | | | BETA: splitting (13) gives:
% 7.30/1.79  | | | 
% 7.30/1.79  | | | Case 1:
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | |   (49)   ~ (all_8_0 = 0)
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | REDUCE: (48), (49) imply:
% 7.30/1.79  | | | |   (50)   ~ (all_8_1 = 0)
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | GROUND_INST: instantiating (3) with uri_ex_w, all_8_1, simplifying with
% 7.30/1.79  | | | |              (5), (47) gives:
% 7.30/1.79  | | | |   (51)  all_8_1 = 0
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | REDUCE: (50), (51) imply:
% 7.30/1.79  | | | |   (52)  $false
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | CLOSE: (52) is inconsistent.
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | Case 2:
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | |   (53)  all_8_0 = 0
% 7.30/1.79  | | | |   (54)   ~ (all_8_1 = 0)
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | COMBINE_EQS: (48), (53) imply:
% 7.30/1.79  | | | |   (55)  all_8_1 = 0
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | REDUCE: (54), (55) imply:
% 7.30/1.79  | | | |   (56)  $false
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | | CLOSE: (56) is inconsistent.
% 7.30/1.79  | | | | 
% 7.30/1.79  | | | End of split
% 7.30/1.79  | | | 
% 7.30/1.79  | | End of split
% 7.30/1.79  | | 
% 7.30/1.79  | End of split
% 7.30/1.79  | 
% 7.30/1.79  End of proof
% 7.30/1.79  % SZS output end Proof for theBenchmark
% 7.30/1.79  
% 7.30/1.79  1274ms
%------------------------------------------------------------------------------