TSTP Solution File: SWB024+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWB024+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 : n017.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 20:11:50 EDT 2023
% Result : Theorem 5.03s 1.56s
% Output : Proof 7.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWB024+2 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n017.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 : Sun Aug 27 05:47:56 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.
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.03/1.06 Prover 4: Preprocessing ...
% 2.03/1.06 Prover 1: Preprocessing ...
% 2.69/1.11 Prover 2: Preprocessing ...
% 2.69/1.11 Prover 6: Preprocessing ...
% 2.69/1.11 Prover 3: Preprocessing ...
% 2.69/1.11 Prover 5: Preprocessing ...
% 2.69/1.11 Prover 0: Preprocessing ...
% 3.59/1.30 Prover 5: Proving ...
% 3.59/1.30 Prover 2: Proving ...
% 4.35/1.36 Prover 6: Proving ...
% 4.35/1.37 Prover 1: Constructing countermodel ...
% 4.35/1.38 Prover 3: Constructing countermodel ...
% 5.03/1.45 Prover 0: Proving ...
% 5.03/1.46 Prover 4: Constructing countermodel ...
% 5.03/1.56 Prover 3: proved (907ms)
% 5.03/1.56
% 5.03/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.56
% 5.03/1.56 Prover 6: stopped
% 5.03/1.56 Prover 2: stopped
% 5.03/1.56 Prover 5: stopped
% 5.03/1.57 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.03/1.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.03/1.57 Prover 0: stopped
% 5.03/1.57 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.03/1.57 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.03/1.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.87/1.59 Prover 8: Preprocessing ...
% 5.87/1.60 Prover 11: Preprocessing ...
% 5.87/1.60 Prover 7: Preprocessing ...
% 5.87/1.60 Prover 13: Preprocessing ...
% 5.87/1.63 Prover 10: Preprocessing ...
% 5.87/1.64 Prover 7: Constructing countermodel ...
% 5.87/1.65 Prover 13: Constructing countermodel ...
% 5.87/1.67 Prover 10: Constructing countermodel ...
% 7.18/1.70 Prover 1: Found proof (size 49)
% 7.18/1.70 Prover 1: proved (1054ms)
% 7.18/1.70 Prover 13: stopped
% 7.18/1.70 Prover 4: stopped
% 7.18/1.70 Prover 7: stopped
% 7.18/1.70 Prover 10: stopped
% 7.30/1.71 Prover 8: Warning: ignoring some quantifiers
% 7.34/1.71 Prover 8: Constructing countermodel ...
% 7.34/1.72 Prover 8: stopped
% 7.34/1.72 Prover 11: Constructing countermodel ...
% 7.34/1.73 Prover 11: stopped
% 7.34/1.73
% 7.34/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.34/1.73
% 7.34/1.74 % SZS output start Proof for theBenchmark
% 7.34/1.74 Assumptions after simplification:
% 7.34/1.74 ---------------------------------
% 7.34/1.74
% 7.34/1.74 (owl_char_transitive)
% 7.34/1.77 $i(uri_owl_TransitiveProperty) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 7.34/1.77 (icext(uri_owl_TransitiveProperty, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 7.34/1.77 [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & iext(v0, v3, v4) = 0
% 7.34/1.77 & iext(v0, v2, v4) = v5 & iext(v0, v2, v3) = 0 & $i(v4) & $i(v3) & $i(v2))
% 7.34/1.77 | ? [v2: int] : ( ~ (v2 = 0) & ip(v0) = v2)) & ! [v0: $i] : ( ~
% 7.34/1.77 (icext(uri_owl_TransitiveProperty, v0) = 0) | ~ $i(v0) | (ip(v0) = 0 & !
% 7.34/1.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 7.34/1.77 (iext(v0, v1, v3) = v4) | ~ (iext(v0, v1, v2) = 0) | ~ $i(v3) | ~
% 7.34/1.77 $i(v2) | ~ $i(v1) | ? [v5: int] : ( ~ (v5 = 0) & iext(v0, v2, v3) =
% 7.34/1.77 v5))))
% 7.34/1.77
% 7.34/1.77 (owl_rdfsext_subclassof)
% 7.34/1.78 $i(uri_rdfs_subClassOf) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 7.34/1.78 ~ (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 7.34/1.78 [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & icext(v1, v3) = v4 & icext(v0, v3)
% 7.34/1.78 = 0 & $i(v3)) | ? [v3: any] : ? [v4: any] : (ic(v1) = v4 & ic(v0) = v3 &
% 7.34/1.78 ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 7.34/1.78 (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) =
% 7.34/1.78 0 & ic(v0) = 0 & ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~ $i(v2) |
% 7.34/1.78 icext(v1, v2) = 0)))
% 7.34/1.78
% 7.34/1.78 (owl_restrict_mincard_001)
% 7.34/1.78 $i(uri_owl_onProperty) & $i(uri_xsd_nonNegativeInteger) & $i(dat_str_1) &
% 7.34/1.78 $i(uri_owl_minCardinality) & ? [v0: $i] : (literal_typed(dat_str_1,
% 7.34/1.78 uri_xsd_nonNegativeInteger) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (
% 7.34/1.78 ~ (iext(uri_owl_onProperty, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3:
% 7.34/1.78 int] : ( ~ (v3 = 0) & iext(uri_owl_minCardinality, v1, v0) = v3) | ( !
% 7.34/1.78 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (icext(v1, v3) = v4) | ~ $i(v3)
% 7.34/1.78 | ! [v5: $i] : ( ~ (iext(v2, v3, v5) = 0) | ~ $i(v5))) & ! [v3: $i]
% 7.34/1.78 : ( ~ (icext(v1, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (iext(v2, v3, v4)
% 7.34/1.78 = 0 & $i(v4))))))
% 7.34/1.78
% 7.34/1.78 (rdfs_cext_def)
% 7.34/1.79 $i(uri_rdf_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 7.34/1.79 (iext(uri_rdf_type, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 7.34/1.79 ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 7.34/1.79 (iext(uri_rdf_type, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | icext(v1, v0) =
% 7.34/1.79 0)
% 7.34/1.79
% 7.34/1.79 (testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties)
% 7.34/1.79 $i(uri_ex_alice) & $i(uri_ex_bob) & $i(uri_ex_hasAncestor) & ! [v0: $i] : ( ~
% 7.34/1.79 (iext(uri_ex_hasAncestor, uri_ex_bob, v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 7.34/1.79 ( ~ (v1 = 0) & iext(uri_ex_hasAncestor, uri_ex_alice, v0) = v1))
% 7.34/1.79
% 7.34/1.79 (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties)
% 7.34/1.79 $i(uri_owl_Restriction) & $i(uri_ex_Person) & $i(uri_ex_alice) &
% 7.34/1.79 $i(uri_ex_bob) & $i(uri_ex_hasAncestor) & $i(uri_owl_TransitiveProperty) &
% 7.34/1.79 $i(uri_rdfs_subClassOf) & $i(uri_owl_onProperty) &
% 7.34/1.79 $i(uri_xsd_nonNegativeInteger) & $i(dat_str_1) & $i(uri_owl_minCardinality) &
% 7.34/1.79 $i(uri_rdf_type) & ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 7.34/1.79 ? [v4: any] : (literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = v1 &
% 7.34/1.79 iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = v4 & iext(uri_rdf_type,
% 7.34/1.79 uri_ex_alice, uri_ex_Person) = v2 & iext(uri_rdf_type, uri_ex_bob,
% 7.34/1.79 uri_ex_Person) = v3 & iext(uri_rdf_type, uri_ex_hasAncestor,
% 7.34/1.79 uri_owl_TransitiveProperty) = v0 & $i(v1) & ? [v5: $i] : (v4 = 0 & v3 = 0
% 7.34/1.79 & v2 = 0 & v0 = 0 & iext(uri_rdfs_subClassOf, uri_ex_Person, v5) = 0 &
% 7.34/1.79 iext(uri_owl_onProperty, v5, uri_ex_hasAncestor) = 0 &
% 7.34/1.79 iext(uri_owl_minCardinality, v5, v1) = 0 & iext(uri_rdf_type, v5,
% 7.34/1.79 uri_owl_Restriction) = 0 & $i(v5)))
% 7.34/1.79
% 7.34/1.79 (function-axioms)
% 7.34/1.79 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.34/1.79 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4,
% 7.34/1.79 v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 7.34/1.79 (v1 = v0 | ~ (literal_typed(v3, v2) = v1) | ~ (literal_typed(v3, v2) = v0))
% 7.34/1.79 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.34/1.79 [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) & !
% 7.34/1.79 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 7.34/1.79 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 7.34/1.79 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ic(v2) = v1) | ~
% 7.34/1.79 (ic(v2) = v0))
% 7.34/1.79
% 7.34/1.79 Those formulas are unsatisfiable:
% 7.34/1.79 ---------------------------------
% 7.34/1.79
% 7.34/1.79 Begin of proof
% 7.34/1.80 |
% 7.34/1.80 | ALPHA: (rdfs_cext_def) implies:
% 7.34/1.80 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | ~
% 7.34/1.80 | $i(v1) | ~ $i(v0) | icext(v1, v0) = 0)
% 7.34/1.80 |
% 7.34/1.80 | ALPHA: (owl_restrict_mincard_001) implies:
% 7.34/1.80 | (2) ? [v0: $i] : (literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) =
% 7.34/1.80 | v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 7.34/1.80 | (iext(uri_owl_onProperty, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ?
% 7.34/1.80 | [v3: int] : ( ~ (v3 = 0) & iext(uri_owl_minCardinality, v1, v0) =
% 7.34/1.80 | v3) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (icext(v1, v3) =
% 7.34/1.80 | v4) | ~ $i(v3) | ! [v5: $i] : ( ~ (iext(v2, v3, v5) = 0) |
% 7.34/1.80 | ~ $i(v5))) & ! [v3: $i] : ( ~ (icext(v1, v3) = 0) | ~
% 7.34/1.80 | $i(v3) | ? [v4: $i] : (iext(v2, v3, v4) = 0 & $i(v4))))))
% 7.34/1.80 |
% 7.34/1.80 | ALPHA: (owl_rdfsext_subclassof) implies:
% 7.34/1.80 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_rdfs_subClassOf, v0, v1) = 0)
% 7.34/1.80 | | ~ $i(v1) | ~ $i(v0) | (ic(v1) = 0 & ic(v0) = 0 & ! [v2: $i] : (
% 7.34/1.80 | ~ (icext(v0, v2) = 0) | ~ $i(v2) | icext(v1, v2) = 0)))
% 7.34/1.80 |
% 7.34/1.80 | ALPHA: (owl_char_transitive) implies:
% 7.34/1.80 | (4) ! [v0: $i] : ( ~ (icext(uri_owl_TransitiveProperty, v0) = 0) | ~
% 7.34/1.80 | $i(v0) | (ip(v0) = 0 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 7.34/1.80 | [v4: int] : (v4 = 0 | ~ (iext(v0, v1, v3) = v4) | ~ (iext(v0, v1,
% 7.34/1.80 | v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: int] :
% 7.34/1.80 | ( ~ (v5 = 0) & iext(v0, v2, v3) = v5))))
% 7.34/1.80 |
% 7.34/1.80 | ALPHA: (testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties)
% 7.34/1.80 | implies:
% 7.34/1.80 | (5) $i(uri_owl_TransitiveProperty)
% 7.34/1.80 | (6) $i(uri_ex_Person)
% 7.80/1.80 | (7) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] : ? [v4: any]
% 7.80/1.80 | : (literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = v1 &
% 7.80/1.80 | iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = v4 &
% 7.80/1.80 | iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) = v2 &
% 7.80/1.80 | iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) = v3 &
% 7.80/1.80 | iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) =
% 7.80/1.80 | v0 & $i(v1) & ? [v5: $i] : (v4 = 0 & v3 = 0 & v2 = 0 & v0 = 0 &
% 7.80/1.80 | iext(uri_rdfs_subClassOf, uri_ex_Person, v5) = 0 &
% 7.80/1.80 | iext(uri_owl_onProperty, v5, uri_ex_hasAncestor) = 0 &
% 7.80/1.80 | iext(uri_owl_minCardinality, v5, v1) = 0 & iext(uri_rdf_type, v5,
% 7.80/1.80 | uri_owl_Restriction) = 0 & $i(v5)))
% 7.80/1.80 |
% 7.80/1.80 | ALPHA: (testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties)
% 7.80/1.80 | implies:
% 7.80/1.81 | (8) $i(uri_ex_hasAncestor)
% 7.80/1.81 | (9) $i(uri_ex_bob)
% 7.80/1.81 | (10) $i(uri_ex_alice)
% 7.80/1.81 | (11) ! [v0: $i] : ( ~ (iext(uri_ex_hasAncestor, uri_ex_bob, v0) = 0) | ~
% 7.80/1.81 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & iext(uri_ex_hasAncestor,
% 7.80/1.81 | uri_ex_alice, v0) = v1))
% 7.80/1.81 |
% 7.80/1.81 | ALPHA: (function-axioms) implies:
% 7.80/1.81 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 7.80/1.81 | (literal_typed(v3, v2) = v1) | ~ (literal_typed(v3, v2) = v0))
% 7.80/1.81 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.80/1.81 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) |
% 7.80/1.81 | ~ (iext(v4, v3, v2) = v0))
% 7.80/1.81 |
% 7.80/1.81 | DELTA: instantiating (7) with fresh symbols all_8_0, all_8_1, all_8_2,
% 7.80/1.81 | all_8_3, all_8_4 gives:
% 7.80/1.81 | (14) literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = all_8_3 &
% 7.80/1.81 | iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = all_8_0 &
% 7.80/1.81 | iext(uri_rdf_type, uri_ex_alice, uri_ex_Person) = all_8_2 &
% 7.80/1.81 | iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) = all_8_1 &
% 7.80/1.81 | iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) =
% 7.80/1.81 | all_8_4 & $i(all_8_3) & ? [v0: $i] : (all_8_0 = 0 & all_8_1 = 0 &
% 7.80/1.81 | all_8_2 = 0 & all_8_4 = 0 & iext(uri_rdfs_subClassOf, uri_ex_Person,
% 7.80/1.81 | v0) = 0 & iext(uri_owl_onProperty, v0, uri_ex_hasAncestor) = 0 &
% 7.80/1.81 | iext(uri_owl_minCardinality, v0, all_8_3) = 0 & iext(uri_rdf_type,
% 7.80/1.81 | v0, uri_owl_Restriction) = 0 & $i(v0))
% 7.80/1.81 |
% 7.80/1.81 | ALPHA: (14) implies:
% 7.80/1.81 | (15) iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) =
% 7.80/1.81 | all_8_4
% 7.80/1.81 | (16) iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) = all_8_1
% 7.80/1.81 | (17) iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = all_8_0
% 7.80/1.81 | (18) literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = all_8_3
% 7.80/1.81 | (19) ? [v0: $i] : (all_8_0 = 0 & all_8_1 = 0 & all_8_2 = 0 & all_8_4 = 0 &
% 7.80/1.81 | iext(uri_rdfs_subClassOf, uri_ex_Person, v0) = 0 &
% 7.80/1.81 | iext(uri_owl_onProperty, v0, uri_ex_hasAncestor) = 0 &
% 7.80/1.81 | iext(uri_owl_minCardinality, v0, all_8_3) = 0 & iext(uri_rdf_type,
% 7.80/1.81 | v0, uri_owl_Restriction) = 0 & $i(v0))
% 7.80/1.81 |
% 7.80/1.81 | DELTA: instantiating (2) with fresh symbol all_10_0 gives:
% 7.80/1.81 | (20) literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = all_10_0 &
% 7.80/1.81 | $i(all_10_0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 7.80/1.81 | (iext(uri_owl_onProperty, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 7.80/1.81 | [v2: int] : ( ~ (v2 = 0) & iext(uri_owl_minCardinality, v0,
% 7.80/1.81 | all_10_0) = v2) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 7.80/1.81 | (icext(v0, v2) = v3) | ~ $i(v2) | ! [v4: $i] : ( ~ (iext(v1,
% 7.80/1.81 | v2, v4) = 0) | ~ $i(v4))) & ! [v2: $i] : ( ~ (icext(v0,
% 7.80/1.81 | v2) = 0) | ~ $i(v2) | ? [v3: $i] : (iext(v1, v2, v3) = 0 &
% 7.80/1.81 | $i(v3)))))
% 7.80/1.81 |
% 7.80/1.81 | ALPHA: (20) implies:
% 7.80/1.81 | (21) literal_typed(dat_str_1, uri_xsd_nonNegativeInteger) = all_10_0
% 7.80/1.82 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_onProperty, v0, v1) = 0)
% 7.80/1.82 | | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 7.80/1.82 | iext(uri_owl_minCardinality, v0, all_10_0) = v2) | ( ! [v2: $i] :
% 7.80/1.82 | ! [v3: int] : (v3 = 0 | ~ (icext(v0, v2) = v3) | ~ $i(v2) | !
% 7.80/1.82 | [v4: $i] : ( ~ (iext(v1, v2, v4) = 0) | ~ $i(v4))) & ! [v2:
% 7.80/1.82 | $i] : ( ~ (icext(v0, v2) = 0) | ~ $i(v2) | ? [v3: $i] :
% 7.80/1.82 | (iext(v1, v2, v3) = 0 & $i(v3)))))
% 7.80/1.82 |
% 7.80/1.82 | DELTA: instantiating (19) with fresh symbol all_13_0 gives:
% 7.80/1.82 | (23) all_8_0 = 0 & all_8_1 = 0 & all_8_2 = 0 & all_8_4 = 0 &
% 7.80/1.82 | iext(uri_rdfs_subClassOf, uri_ex_Person, all_13_0) = 0 &
% 7.80/1.82 | iext(uri_owl_onProperty, all_13_0, uri_ex_hasAncestor) = 0 &
% 7.80/1.82 | iext(uri_owl_minCardinality, all_13_0, all_8_3) = 0 &
% 7.80/1.82 | iext(uri_rdf_type, all_13_0, uri_owl_Restriction) = 0 & $i(all_13_0)
% 7.80/1.82 |
% 7.80/1.82 | ALPHA: (23) implies:
% 7.80/1.82 | (24) all_8_4 = 0
% 7.80/1.82 | (25) all_8_1 = 0
% 7.80/1.82 | (26) all_8_0 = 0
% 7.80/1.82 | (27) $i(all_13_0)
% 7.80/1.82 | (28) iext(uri_owl_minCardinality, all_13_0, all_8_3) = 0
% 7.80/1.82 | (29) iext(uri_owl_onProperty, all_13_0, uri_ex_hasAncestor) = 0
% 7.80/1.82 | (30) iext(uri_rdfs_subClassOf, uri_ex_Person, all_13_0) = 0
% 7.80/1.82 |
% 7.80/1.82 | REDUCE: (17), (26) imply:
% 7.80/1.82 | (31) iext(uri_ex_hasAncestor, uri_ex_alice, uri_ex_bob) = 0
% 7.80/1.82 |
% 7.80/1.82 | REDUCE: (16), (25) imply:
% 7.80/1.82 | (32) iext(uri_rdf_type, uri_ex_bob, uri_ex_Person) = 0
% 7.80/1.82 |
% 7.80/1.82 | REDUCE: (15), (24) imply:
% 7.80/1.82 | (33) iext(uri_rdf_type, uri_ex_hasAncestor, uri_owl_TransitiveProperty) = 0
% 7.80/1.82 |
% 7.80/1.82 | GROUND_INST: instantiating (12) with all_8_3, all_10_0,
% 7.80/1.82 | uri_xsd_nonNegativeInteger, dat_str_1, simplifying with (18),
% 7.80/1.82 | (21) gives:
% 7.80/1.82 | (34) all_10_0 = all_8_3
% 7.80/1.82 |
% 7.80/1.82 | GROUND_INST: instantiating (1) with uri_ex_hasAncestor,
% 7.80/1.82 | uri_owl_TransitiveProperty, simplifying with (5), (8), (33)
% 7.80/1.82 | gives:
% 7.80/1.82 | (35) icext(uri_owl_TransitiveProperty, uri_ex_hasAncestor) = 0
% 7.80/1.82 |
% 7.80/1.82 | GROUND_INST: instantiating (1) with uri_ex_bob, uri_ex_Person, simplifying
% 7.80/1.82 | with (6), (9), (32) gives:
% 7.80/1.82 | (36) icext(uri_ex_Person, uri_ex_bob) = 0
% 7.80/1.82 |
% 7.80/1.82 | GROUND_INST: instantiating (22) with all_13_0, uri_ex_hasAncestor, simplifying
% 7.80/1.82 | with (8), (27), (29) gives:
% 7.80/1.82 | (37) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_owl_minCardinality, all_13_0,
% 7.80/1.82 | all_10_0) = v0) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 7.80/1.82 | (icext(all_13_0, v0) = v1) | ~ $i(v0) | ! [v2: $i] : ( ~
% 7.80/1.82 | (iext(uri_ex_hasAncestor, v0, v2) = 0) | ~ $i(v2))) & ! [v0:
% 7.80/1.82 | $i] : ( ~ (icext(all_13_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 7.80/1.82 | (iext(uri_ex_hasAncestor, v0, v1) = 0 & $i(v1))))
% 7.80/1.82 |
% 7.80/1.82 | GROUND_INST: instantiating (3) with uri_ex_Person, all_13_0, simplifying with
% 7.80/1.82 | (6), (27), (30) gives:
% 7.80/1.82 | (38) ic(all_13_0) = 0 & ic(uri_ex_Person) = 0 & ! [v0: $i] : ( ~
% 7.80/1.82 | (icext(uri_ex_Person, v0) = 0) | ~ $i(v0) | icext(all_13_0, v0) =
% 7.80/1.82 | 0)
% 7.80/1.82 |
% 7.80/1.82 | ALPHA: (38) implies:
% 7.80/1.83 | (39) ! [v0: $i] : ( ~ (icext(uri_ex_Person, v0) = 0) | ~ $i(v0) |
% 7.80/1.83 | icext(all_13_0, v0) = 0)
% 7.80/1.83 |
% 7.80/1.83 | BETA: splitting (37) gives:
% 7.80/1.83 |
% 7.80/1.83 | Case 1:
% 7.80/1.83 | |
% 7.80/1.83 | | (40) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_owl_minCardinality, all_13_0,
% 7.80/1.83 | | all_10_0) = v0)
% 7.80/1.83 | |
% 7.80/1.83 | | DELTA: instantiating (40) with fresh symbol all_29_0 gives:
% 7.80/1.83 | | (41) ~ (all_29_0 = 0) & iext(uri_owl_minCardinality, all_13_0, all_10_0)
% 7.80/1.83 | | = all_29_0
% 7.80/1.83 | |
% 7.80/1.83 | | ALPHA: (41) implies:
% 7.80/1.83 | | (42) ~ (all_29_0 = 0)
% 7.80/1.83 | | (43) iext(uri_owl_minCardinality, all_13_0, all_10_0) = all_29_0
% 7.80/1.83 | |
% 7.80/1.83 | | REDUCE: (34), (43) imply:
% 7.80/1.83 | | (44) iext(uri_owl_minCardinality, all_13_0, all_8_3) = all_29_0
% 7.80/1.83 | |
% 7.80/1.83 | | GROUND_INST: instantiating (13) with 0, all_29_0, all_8_3, all_13_0,
% 7.80/1.83 | | uri_owl_minCardinality, simplifying with (28), (44) gives:
% 7.80/1.83 | | (45) all_29_0 = 0
% 7.80/1.83 | |
% 7.80/1.83 | | REDUCE: (42), (45) imply:
% 7.80/1.83 | | (46) $false
% 7.80/1.83 | |
% 7.80/1.83 | | CLOSE: (46) is inconsistent.
% 7.80/1.83 | |
% 7.80/1.83 | Case 2:
% 7.80/1.83 | |
% 7.80/1.83 | | (47) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (icext(all_13_0, v0) = v1)
% 7.80/1.83 | | | ~ $i(v0) | ! [v2: $i] : ( ~ (iext(uri_ex_hasAncestor, v0, v2)
% 7.80/1.83 | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (icext(all_13_0, v0) =
% 7.80/1.83 | | 0) | ~ $i(v0) | ? [v1: $i] : (iext(uri_ex_hasAncestor, v0, v1)
% 7.80/1.83 | | = 0 & $i(v1)))
% 7.80/1.83 | |
% 7.80/1.83 | | ALPHA: (47) implies:
% 7.80/1.83 | | (48) ! [v0: $i] : ( ~ (icext(all_13_0, v0) = 0) | ~ $i(v0) | ? [v1:
% 7.80/1.83 | | $i] : (iext(uri_ex_hasAncestor, v0, v1) = 0 & $i(v1)))
% 7.80/1.83 | |
% 7.80/1.83 | | GROUND_INST: instantiating (4) with uri_ex_hasAncestor, simplifying with
% 7.80/1.83 | | (8), (35) gives:
% 7.80/1.83 | | (49) ip(uri_ex_hasAncestor) = 0 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 7.80/1.83 | | : ! [v3: int] : (v3 = 0 | ~ (iext(uri_ex_hasAncestor, v0, v2) =
% 7.80/1.83 | | v3) | ~ (iext(uri_ex_hasAncestor, v0, v1) = 0) | ~ $i(v2) | ~
% 7.80/1.83 | | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 7.80/1.83 | | iext(uri_ex_hasAncestor, v1, v2) = v4))
% 7.80/1.83 | |
% 7.80/1.83 | | ALPHA: (49) implies:
% 7.80/1.83 | | (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 7.80/1.83 | | ~ (iext(uri_ex_hasAncestor, v0, v2) = v3) | ~
% 7.80/1.83 | | (iext(uri_ex_hasAncestor, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 7.80/1.83 | | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & iext(uri_ex_hasAncestor,
% 7.80/1.83 | | v1, v2) = v4))
% 7.80/1.83 | |
% 7.80/1.83 | | GROUND_INST: instantiating (39) with uri_ex_bob, simplifying with (9), (36)
% 7.80/1.83 | | gives:
% 7.80/1.83 | | (51) icext(all_13_0, uri_ex_bob) = 0
% 7.80/1.83 | |
% 7.80/1.83 | | GROUND_INST: instantiating (48) with uri_ex_bob, simplifying with (9), (51)
% 7.80/1.83 | | gives:
% 7.80/1.84 | | (52) ? [v0: $i] : (iext(uri_ex_hasAncestor, uri_ex_bob, v0) = 0 &
% 7.80/1.84 | | $i(v0))
% 7.80/1.84 | |
% 7.80/1.84 | | DELTA: instantiating (52) with fresh symbol all_43_0 gives:
% 7.80/1.84 | | (53) iext(uri_ex_hasAncestor, uri_ex_bob, all_43_0) = 0 & $i(all_43_0)
% 7.80/1.84 | |
% 7.80/1.84 | | ALPHA: (53) implies:
% 7.80/1.84 | | (54) $i(all_43_0)
% 7.80/1.84 | | (55) iext(uri_ex_hasAncestor, uri_ex_bob, all_43_0) = 0
% 7.80/1.84 | |
% 7.80/1.84 | | GROUND_INST: instantiating (11) with all_43_0, simplifying with (54), (55)
% 7.80/1.84 | | gives:
% 7.80/1.84 | | (56) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_ex_hasAncestor, uri_ex_alice,
% 7.80/1.84 | | all_43_0) = v0)
% 7.80/1.84 | |
% 7.80/1.84 | | DELTA: instantiating (56) with fresh symbol all_50_0 gives:
% 7.80/1.84 | | (57) ~ (all_50_0 = 0) & iext(uri_ex_hasAncestor, uri_ex_alice, all_43_0)
% 7.80/1.84 | | = all_50_0
% 7.80/1.84 | |
% 7.80/1.84 | | ALPHA: (57) implies:
% 7.80/1.84 | | (58) ~ (all_50_0 = 0)
% 7.80/1.84 | | (59) iext(uri_ex_hasAncestor, uri_ex_alice, all_43_0) = all_50_0
% 7.80/1.84 | |
% 7.80/1.84 | | GROUND_INST: instantiating (50) with uri_ex_alice, uri_ex_bob, all_43_0,
% 7.80/1.84 | | all_50_0, simplifying with (9), (10), (31), (54), (59) gives:
% 7.80/1.84 | | (60) all_50_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 7.80/1.84 | | iext(uri_ex_hasAncestor, uri_ex_bob, all_43_0) = v0)
% 7.80/1.84 | |
% 7.80/1.84 | | BETA: splitting (60) gives:
% 7.80/1.84 | |
% 7.80/1.84 | | Case 1:
% 7.80/1.84 | | |
% 7.80/1.84 | | | (61) all_50_0 = 0
% 7.80/1.84 | | |
% 7.80/1.84 | | | REDUCE: (58), (61) imply:
% 7.80/1.84 | | | (62) $false
% 7.80/1.84 | | |
% 7.80/1.84 | | | CLOSE: (62) is inconsistent.
% 7.80/1.84 | | |
% 7.80/1.84 | | Case 2:
% 7.80/1.84 | | |
% 7.80/1.84 | | | (63) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_ex_hasAncestor, uri_ex_bob,
% 7.80/1.84 | | | all_43_0) = v0)
% 7.80/1.84 | | |
% 7.80/1.84 | | | DELTA: instantiating (63) with fresh symbol all_59_0 gives:
% 7.80/1.84 | | | (64) ~ (all_59_0 = 0) & iext(uri_ex_hasAncestor, uri_ex_bob, all_43_0)
% 7.80/1.84 | | | = all_59_0
% 7.80/1.84 | | |
% 7.80/1.84 | | | ALPHA: (64) implies:
% 7.80/1.84 | | | (65) ~ (all_59_0 = 0)
% 7.80/1.84 | | | (66) iext(uri_ex_hasAncestor, uri_ex_bob, all_43_0) = all_59_0
% 7.80/1.84 | | |
% 7.80/1.84 | | | GROUND_INST: instantiating (13) with 0, all_59_0, all_43_0, uri_ex_bob,
% 7.80/1.84 | | | uri_ex_hasAncestor, simplifying with (55), (66) gives:
% 7.80/1.84 | | | (67) all_59_0 = 0
% 7.80/1.84 | | |
% 7.80/1.84 | | | REDUCE: (65), (67) imply:
% 7.80/1.84 | | | (68) $false
% 7.80/1.84 | | |
% 7.80/1.84 | | | CLOSE: (68) is inconsistent.
% 7.80/1.84 | | |
% 7.80/1.84 | | End of split
% 7.80/1.84 | |
% 7.80/1.84 | End of split
% 7.80/1.84 |
% 7.80/1.84 End of proof
% 7.80/1.84 % SZS output end Proof for theBenchmark
% 7.80/1.84
% 7.80/1.84 1215ms
%------------------------------------------------------------------------------