TSTP Solution File: SWB028+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWB028+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 : n025.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 20:11:53 EDT 2023
% Result : Theorem 6.91s 1.70s
% Output : Proof 8.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB028+2 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n025.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 06:44:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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 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 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
% 2.63/1.08 Prover 4: Preprocessing ...
% 2.63/1.08 Prover 1: Preprocessing ...
% 2.84/1.13 Prover 6: Preprocessing ...
% 2.84/1.14 Prover 5: Preprocessing ...
% 2.84/1.14 Prover 0: Preprocessing ...
% 2.84/1.14 Prover 2: Preprocessing ...
% 2.84/1.14 Prover 3: Preprocessing ...
% 4.10/1.38 Prover 2: Constructing countermodel ...
% 4.78/1.40 Prover 5: Proving ...
% 5.54/1.52 Prover 3: Constructing countermodel ...
% 5.54/1.53 Prover 6: Proving ...
% 5.54/1.53 Prover 1: Constructing countermodel ...
% 5.54/1.57 Prover 4: Constructing countermodel ...
% 5.54/1.58 Prover 0: Proving ...
% 6.91/1.70 Prover 3: proved (1056ms)
% 6.91/1.70
% 6.91/1.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.91/1.70
% 6.91/1.70 Prover 0: stopped
% 6.91/1.70 Prover 5: stopped
% 6.91/1.70 Prover 2: stopped
% 6.91/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.91/1.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.91/1.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.91/1.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.91/1.71 Prover 6: stopped
% 6.91/1.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.91/1.74 Prover 7: Preprocessing ...
% 6.91/1.74 Prover 13: Preprocessing ...
% 6.91/1.74 Prover 8: Preprocessing ...
% 6.91/1.74 Prover 11: Preprocessing ...
% 6.91/1.75 Prover 10: Preprocessing ...
% 7.67/1.79 Prover 13: Constructing countermodel ...
% 7.82/1.82 Prover 7: Constructing countermodel ...
% 7.82/1.82 Prover 10: Constructing countermodel ...
% 7.82/1.83 Prover 1: Found proof (size 65)
% 7.82/1.83 Prover 1: proved (1187ms)
% 7.82/1.83 Prover 4: stopped
% 7.82/1.83 Prover 13: stopped
% 7.82/1.83 Prover 10: stopped
% 7.82/1.83 Prover 7: stopped
% 7.82/1.84 Prover 11: stopped
% 7.82/1.85 Prover 8: Warning: ignoring some quantifiers
% 7.82/1.85 Prover 8: Constructing countermodel ...
% 7.82/1.86 Prover 8: stopped
% 7.82/1.86
% 7.82/1.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.82/1.86
% 7.82/1.87 % SZS output start Proof for theBenchmark
% 7.82/1.87 Assumptions after simplification:
% 7.82/1.87 ---------------------------------
% 7.82/1.87
% 7.82/1.87 (owl_char_functional)
% 8.33/1.90 $i(uri_owl_FunctionalProperty) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.33/1.90 (icext(uri_owl_FunctionalProperty, v0) = v1) | ~ $i(v0) | ? [v2: $i] : ?
% 8.33/1.90 [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) & iext(v0, v2, v4) = 0 & iext(v0, v2,
% 8.33/1.90 v3) = 0 & $i(v4) & $i(v3) & $i(v2)) | ? [v2: int] : ( ~ (v2 = 0) &
% 8.33/1.90 ip(v0) = v2)) & ! [v0: $i] : ( ~ (icext(uri_owl_FunctionalProperty, v0) =
% 8.33/1.90 0) | ~ $i(v0) | (ip(v0) = 0 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 8.33/1.90 (v3 = v2 | ~ (iext(v0, v1, v3) = 0) | ~ (iext(v0, v1, v2) = 0) | ~
% 8.33/1.90 $i(v3) | ~ $i(v2) | ~ $i(v1))))
% 8.33/1.90
% 8.33/1.90 (owl_char_inversefunctional)
% 8.33/1.90 $i(uri_owl_InverseFunctionalProperty) & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 8.33/1.90 ~ (icext(uri_owl_InverseFunctionalProperty, v0) = v1) | ~ $i(v0) | ? [v2:
% 8.33/1.90 $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 = v2) & iext(v0, v3, v4) = 0 &
% 8.33/1.91 iext(v0, v2, v4) = 0 & $i(v4) & $i(v3) & $i(v2)) | ? [v2: int] : ( ~ (v2
% 8.33/1.91 = 0) & ip(v0) = v2)) & ! [v0: $i] : ( ~
% 8.33/1.91 (icext(uri_owl_InverseFunctionalProperty, v0) = 0) | ~ $i(v0) | (ip(v0) = 0
% 8.33/1.91 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~ (iext(v0, v2,
% 8.33/1.91 v3) = 0) | ~ (iext(v0, v1, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 8.33/1.91 $i(v1))))
% 8.33/1.91
% 8.33/1.91 (owl_class_inversefunctionalproperty_type)
% 8.33/1.91 ic(uri_owl_InverseFunctionalProperty) = 0 &
% 8.33/1.91 $i(uri_owl_InverseFunctionalProperty)
% 8.33/1.91
% 8.33/1.91 (owl_eqdis_equivalentclass)
% 8.33/1.91 $i(uri_owl_equivalentClass) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 8.33/1.91 0 | ~ (iext(uri_owl_equivalentClass, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 8.33/1.91 | ? [v3: $i] : ? [v4: any] : ? [v5: any] : (icext(v1, v3) = v5 &
% 8.33/1.91 icext(v0, v3) = v4 & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 =
% 8.33/1.91 0)) | ? [v3: any] : ? [v4: any] : (ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4
% 8.33/1.91 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.33/1.91 (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.33/1.91 (ic(v1) = 0 & ic(v0) = 0 & ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 8.33/1.91 (icext(v0, v2) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 8.33/1.91 icext(v1, v2) = v4)) & ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~
% 8.33/1.91 $i(v2) | icext(v1, v2) = 0)))
% 8.33/1.91
% 8.33/1.91 (owl_inv)
% 8.33/1.92 $i(uri_owl_inverseOf) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 8.33/1.92 ~ (iext(uri_owl_inverseOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 8.33/1.92 $i] : ? [v4: $i] : ? [v5: any] : ? [v6: any] : (iext(v1, v4, v3) = v6 &
% 8.33/1.92 iext(v0, v3, v4) = v5 & $i(v4) & $i(v3) & ( ~ (v6 = 0) | ~ (v5 = 0)) &
% 8.33/1.92 (v6 = 0 | v5 = 0)) | ? [v3: any] : ? [v4: any] : (ip(v1) = v4 & ip(v0) =
% 8.33/1.92 v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.33/1.92 (iext(uri_owl_inverseOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ip(v1) = 0
% 8.33/1.92 & ip(v0) = 0 & ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 8.33/1.92 (iext(v0, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5
% 8.33/1.92 = 0) & iext(v1, v3, v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 8.33/1.92 (iext(v0, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | iext(v1, v3, v2) = 0)))
% 8.33/1.92
% 8.33/1.92 (owl_prop_equivalentclass_ext)
% 8.33/1.92 $i(uri_owl_equivalentClass) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.33/1.92 (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.33/1.92 (ic(v1) = 0 & ic(v0) = 0))
% 8.33/1.92
% 8.33/1.92 (owl_prop_inverseof_ext)
% 8.33/1.92 $i(uri_owl_inverseOf) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.33/1.92 (iext(uri_owl_inverseOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ip(v1) = 0
% 8.33/1.92 & ip(v0) = 0))
% 8.33/1.92
% 8.33/1.92 (owl_rdfsext_subclassof)
% 8.33/1.92 $i(uri_rdfs_subClassOf) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 |
% 8.33/1.92 ~ (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 8.33/1.92 [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & icext(v1, v3) = v4 & icext(v0, v3)
% 8.33/1.92 = 0 & $i(v3)) | ? [v3: any] : ? [v4: any] : (ic(v1) = v4 & ic(v0) = v3 &
% 8.33/1.92 ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.33/1.92 (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) =
% 8.33/1.92 0 & ic(v0) = 0 & ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~ $i(v2) |
% 8.33/1.92 icext(v1, v2) = 0)))
% 8.33/1.92
% 8.33/1.92 (owl_restrict_somevaluesfrom)
% 8.33/1.92 $i(uri_owl_onProperty) & $i(uri_owl_someValuesFrom) & ! [v0: $i] : ! [v1:
% 8.33/1.92 $i] : ! [v2: $i] : ( ~ (iext(uri_owl_onProperty, v0, v1) = 0) | ~
% 8.33/1.92 (iext(uri_owl_someValuesFrom, v0, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 8.33/1.92 $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (icext(v0, v3) = v4) |
% 8.33/1.92 ~ $i(v3) | ! [v5: $i] : ( ~ (icext(v2, v5) = 0) | ~ $i(v5) | ? [v6:
% 8.33/1.92 int] : ( ~ (v6 = 0) & iext(v1, v3, v5) = v6))) & ! [v3: $i] : ( ~
% 8.33/1.92 (icext(v0, v3) = 0) | ~ $i(v3) | ? [v4: $i] : (icext(v2, v4) = 0 &
% 8.33/1.92 iext(v1, v3, v4) = 0 & $i(v4)))))
% 8.33/1.92
% 8.33/1.92 (testcase_conclusion_fullish_028_Inferred_Property_Characteristics_III)
% 8.33/1.92 $i(uri_ex_InversesOfFunctionalProperties) & $i(uri_rdfs_subClassOf) &
% 8.33/1.92 $i(uri_owl_InverseFunctionalProperty) & ? [v0: int] : ( ~ (v0 = 0) &
% 8.33/1.92 iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties,
% 8.33/1.92 uri_owl_InverseFunctionalProperty) = v0)
% 8.33/1.92
% 8.33/1.92 (testcase_premise_fullish_028_Inferred_Property_Characteristics_III)
% 8.33/1.92 $i(uri_owl_Restriction) & $i(uri_rdf_type) &
% 8.33/1.92 $i(uri_ex_InversesOfFunctionalProperties) & $i(uri_owl_onProperty) &
% 8.33/1.92 $i(uri_owl_someValuesFrom) & $i(uri_owl_FunctionalProperty) &
% 8.33/1.92 $i(uri_owl_equivalentClass) & $i(uri_owl_inverseOf) & ? [v0: $i] :
% 8.33/1.92 (iext(uri_rdf_type, v0, uri_owl_Restriction) = 0 & iext(uri_owl_onProperty,
% 8.33/1.92 v0, uri_owl_inverseOf) = 0 & iext(uri_owl_someValuesFrom, v0,
% 8.33/1.92 uri_owl_FunctionalProperty) = 0 & iext(uri_owl_equivalentClass,
% 8.33/1.92 uri_ex_InversesOfFunctionalProperties, v0) = 0 & $i(v0))
% 8.33/1.92
% 8.33/1.92 (function-axioms)
% 8.33/1.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.33/1.93 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4,
% 8.33/1.93 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 8.33/1.93 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~
% 8.33/1.93 (icext(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.33/1.93 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2)
% 8.33/1.93 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.33/1.93 $i] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0))
% 8.33/1.93
% 8.33/1.93 Those formulas are unsatisfiable:
% 8.33/1.93 ---------------------------------
% 8.33/1.93
% 8.33/1.93 Begin of proof
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_class_inversefunctionalproperty_type) implies:
% 8.33/1.93 | (1) ic(uri_owl_InverseFunctionalProperty) = 0
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_prop_inverseof_ext) implies:
% 8.33/1.93 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_inverseOf, v0, v1) = 0) |
% 8.33/1.93 | ~ $i(v1) | ~ $i(v0) | (ip(v1) = 0 & ip(v0) = 0))
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_prop_equivalentclass_ext) implies:
% 8.33/1.93 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_equivalentClass, v0, v1)
% 8.33/1.93 | = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) = 0 & ic(v0) = 0))
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_char_functional) implies:
% 8.33/1.93 | (4) ! [v0: $i] : ( ~ (icext(uri_owl_FunctionalProperty, v0) = 0) | ~
% 8.33/1.93 | $i(v0) | (ip(v0) = 0 & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3
% 8.33/1.93 | = v2 | ~ (iext(v0, v1, v3) = 0) | ~ (iext(v0, v1, v2) = 0) | ~
% 8.33/1.93 | $i(v3) | ~ $i(v2) | ~ $i(v1))))
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_char_inversefunctional) implies:
% 8.33/1.93 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.33/1.93 | (icext(uri_owl_InverseFunctionalProperty, v0) = v1) | ~ $i(v0) | ?
% 8.33/1.93 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 = v2) & iext(v0, v3,
% 8.33/1.93 | v4) = 0 & iext(v0, v2, v4) = 0 & $i(v4) & $i(v3) & $i(v2)) | ?
% 8.33/1.93 | [v2: int] : ( ~ (v2 = 0) & ip(v0) = v2))
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_rdfsext_subclassof) implies:
% 8.33/1.93 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.33/1.93 | (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 8.33/1.93 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & icext(v1, v3) = v4 &
% 8.33/1.93 | icext(v0, v3) = 0 & $i(v3)) | ? [v3: any] : ? [v4: any] : (ic(v1)
% 8.33/1.93 | = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 8.33/1.93 |
% 8.33/1.93 | ALPHA: (owl_eqdis_equivalentclass) implies:
% 8.33/1.94 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_equivalentClass, v0, v1)
% 8.33/1.94 | = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) = 0 & ic(v0) = 0 & ! [v2:
% 8.33/1.94 | $i] : ! [v3: int] : (v3 = 0 | ~ (icext(v0, v2) = v3) | ~
% 8.33/1.94 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & icext(v1, v2) = v4)) & !
% 8.33/1.94 | [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~ $i(v2) | icext(v1, v2) =
% 8.33/1.94 | 0)))
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (owl_restrict_somevaluesfrom) implies:
% 8.33/1.94 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (iext(uri_owl_onProperty,
% 8.33/1.94 | v0, v1) = 0) | ~ (iext(uri_owl_someValuesFrom, v0, v2) = 0) | ~
% 8.33/1.94 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 =
% 8.33/1.94 | 0 | ~ (icext(v0, v3) = v4) | ~ $i(v3) | ! [v5: $i] : ( ~
% 8.33/1.94 | (icext(v2, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 8.33/1.94 | iext(v1, v3, v5) = v6))) & ! [v3: $i] : ( ~ (icext(v0, v3) =
% 8.33/1.94 | 0) | ~ $i(v3) | ? [v4: $i] : (icext(v2, v4) = 0 & iext(v1,
% 8.33/1.94 | v3, v4) = 0 & $i(v4)))))
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (owl_inv) implies:
% 8.33/1.94 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_inverseOf, v0, v1) = 0) |
% 8.33/1.94 | ~ $i(v1) | ~ $i(v0) | (ip(v1) = 0 & ip(v0) = 0 & ! [v2: $i] : !
% 8.33/1.94 | [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (iext(v0, v2, v3) = v4) | ~
% 8.33/1.94 | $i(v3) | ~ $i(v2) | ? [v5: int] : ( ~ (v5 = 0) & iext(v1, v3,
% 8.33/1.94 | v2) = v5)) & ! [v2: $i] : ! [v3: $i] : ( ~ (iext(v0, v2,
% 8.33/1.94 | v3) = 0) | ~ $i(v3) | ~ $i(v2) | iext(v1, v3, v2) = 0)))
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (testcase_premise_fullish_028_Inferred_Property_Characteristics_III)
% 8.33/1.94 | implies:
% 8.33/1.94 | (10) $i(uri_owl_inverseOf)
% 8.33/1.94 | (11) $i(uri_owl_FunctionalProperty)
% 8.33/1.94 | (12) ? [v0: $i] : (iext(uri_rdf_type, v0, uri_owl_Restriction) = 0 &
% 8.33/1.94 | iext(uri_owl_onProperty, v0, uri_owl_inverseOf) = 0 &
% 8.33/1.94 | iext(uri_owl_someValuesFrom, v0, uri_owl_FunctionalProperty) = 0 &
% 8.33/1.94 | iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties,
% 8.33/1.94 | v0) = 0 & $i(v0))
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (testcase_conclusion_fullish_028_Inferred_Property_Characteristics_III)
% 8.33/1.94 | implies:
% 8.33/1.94 | (13) $i(uri_owl_InverseFunctionalProperty)
% 8.33/1.94 | (14) $i(uri_ex_InversesOfFunctionalProperties)
% 8.33/1.94 | (15) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_rdfs_subClassOf,
% 8.33/1.94 | uri_ex_InversesOfFunctionalProperties,
% 8.33/1.94 | uri_owl_InverseFunctionalProperty) = v0)
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (function-axioms) implies:
% 8.33/1.94 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.33/1.94 | : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0))
% 8.33/1.94 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.33/1.94 | : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0))
% 8.33/1.94 |
% 8.33/1.94 | DELTA: instantiating (15) with fresh symbol all_12_0 gives:
% 8.33/1.94 | (18) ~ (all_12_0 = 0) & iext(uri_rdfs_subClassOf,
% 8.33/1.94 | uri_ex_InversesOfFunctionalProperties,
% 8.33/1.94 | uri_owl_InverseFunctionalProperty) = all_12_0
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (18) implies:
% 8.33/1.94 | (19) ~ (all_12_0 = 0)
% 8.33/1.94 | (20) iext(uri_rdfs_subClassOf, uri_ex_InversesOfFunctionalProperties,
% 8.33/1.94 | uri_owl_InverseFunctionalProperty) = all_12_0
% 8.33/1.94 |
% 8.33/1.94 | DELTA: instantiating (12) with fresh symbol all_14_0 gives:
% 8.33/1.94 | (21) iext(uri_rdf_type, all_14_0, uri_owl_Restriction) = 0 &
% 8.33/1.94 | iext(uri_owl_onProperty, all_14_0, uri_owl_inverseOf) = 0 &
% 8.33/1.94 | iext(uri_owl_someValuesFrom, all_14_0, uri_owl_FunctionalProperty) = 0
% 8.33/1.94 | & iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties,
% 8.33/1.94 | all_14_0) = 0 & $i(all_14_0)
% 8.33/1.94 |
% 8.33/1.94 | ALPHA: (21) implies:
% 8.33/1.94 | (22) $i(all_14_0)
% 8.33/1.95 | (23) iext(uri_owl_equivalentClass, uri_ex_InversesOfFunctionalProperties,
% 8.33/1.95 | all_14_0) = 0
% 8.33/1.95 | (24) iext(uri_owl_someValuesFrom, all_14_0, uri_owl_FunctionalProperty) = 0
% 8.33/1.95 | (25) iext(uri_owl_onProperty, all_14_0, uri_owl_inverseOf) = 0
% 8.33/1.95 |
% 8.33/1.95 | GROUND_INST: instantiating (7) with uri_ex_InversesOfFunctionalProperties,
% 8.33/1.95 | all_14_0, simplifying with (14), (22), (23) gives:
% 8.33/1.95 | (26) ic(all_14_0) = 0 & ic(uri_ex_InversesOfFunctionalProperties) = 0 & !
% 8.33/1.95 | [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.33/1.95 | (icext(uri_ex_InversesOfFunctionalProperties, v0) = v1) | ~ $i(v0)
% 8.33/1.95 | | ? [v2: int] : ( ~ (v2 = 0) & icext(all_14_0, v0) = v2)) & ! [v0:
% 8.33/1.95 | $i] : ( ~ (icext(uri_ex_InversesOfFunctionalProperties, v0) = 0) |
% 8.33/1.95 | ~ $i(v0) | icext(all_14_0, v0) = 0)
% 8.33/1.95 |
% 8.33/1.95 | ALPHA: (26) implies:
% 8.33/1.95 | (27) ! [v0: $i] : ( ~ (icext(uri_ex_InversesOfFunctionalProperties, v0) =
% 8.33/1.95 | 0) | ~ $i(v0) | icext(all_14_0, v0) = 0)
% 8.33/1.95 |
% 8.33/1.95 | GROUND_INST: instantiating (3) with uri_ex_InversesOfFunctionalProperties,
% 8.33/1.95 | all_14_0, simplifying with (14), (22), (23) gives:
% 8.33/1.95 | (28) ic(all_14_0) = 0 & ic(uri_ex_InversesOfFunctionalProperties) = 0
% 8.33/1.95 |
% 8.33/1.95 | ALPHA: (28) implies:
% 8.33/1.95 | (29) ic(uri_ex_InversesOfFunctionalProperties) = 0
% 8.33/1.95 |
% 8.33/1.95 | GROUND_INST: instantiating (6) with uri_ex_InversesOfFunctionalProperties,
% 8.33/1.95 | uri_owl_InverseFunctionalProperty, all_12_0, simplifying with
% 8.33/1.95 | (13), (14), (20) gives:
% 8.33/1.95 | (30) all_12_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.33/1.95 | icext(uri_ex_InversesOfFunctionalProperties, v0) = 0 &
% 8.33/1.95 | icext(uri_owl_InverseFunctionalProperty, v0) = v1 & $i(v0)) | ?
% 8.33/1.95 | [v0: any] : ? [v1: any] : (ic(uri_ex_InversesOfFunctionalProperties)
% 8.33/1.95 | = v0 & ic(uri_owl_InverseFunctionalProperty) = v1 & ( ~ (v1 = 0) |
% 8.33/1.95 | ~ (v0 = 0)))
% 8.33/1.95 |
% 8.33/1.95 | GROUND_INST: instantiating (8) with all_14_0, uri_owl_inverseOf,
% 8.33/1.95 | uri_owl_FunctionalProperty, simplifying with (10), (11), (22),
% 8.33/1.95 | (24), (25) gives:
% 8.33/1.95 | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (icext(all_14_0, v0) = v1) |
% 8.33/1.95 | ~ $i(v0) | ! [v2: $i] : ( ~ (icext(uri_owl_FunctionalProperty, v2)
% 8.33/1.95 | = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.33/1.95 | iext(uri_owl_inverseOf, v0, v2) = v3))) & ! [v0: $i] : ( ~
% 8.33/1.95 | (icext(all_14_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 8.33/1.95 | (icext(uri_owl_FunctionalProperty, v1) = 0 & iext(uri_owl_inverseOf,
% 8.33/1.95 | v0, v1) = 0 & $i(v1)))
% 8.33/1.95 |
% 8.33/1.95 | ALPHA: (31) implies:
% 8.33/1.95 | (32) ! [v0: $i] : ( ~ (icext(all_14_0, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 8.33/1.95 | : (icext(uri_owl_FunctionalProperty, v1) = 0 &
% 8.33/1.95 | iext(uri_owl_inverseOf, v0, v1) = 0 & $i(v1)))
% 8.33/1.95 |
% 8.33/1.95 | BETA: splitting (30) gives:
% 8.33/1.95 |
% 8.33/1.95 | Case 1:
% 8.33/1.95 | |
% 8.33/1.95 | | (33) all_12_0 = 0
% 8.33/1.95 | |
% 8.33/1.95 | | REDUCE: (19), (33) imply:
% 8.33/1.95 | | (34) $false
% 8.33/1.95 | |
% 8.33/1.95 | | CLOSE: (34) is inconsistent.
% 8.33/1.95 | |
% 8.33/1.95 | Case 2:
% 8.33/1.95 | |
% 8.33/1.96 | | (35) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.33/1.96 | | icext(uri_ex_InversesOfFunctionalProperties, v0) = 0 &
% 8.33/1.96 | | icext(uri_owl_InverseFunctionalProperty, v0) = v1 & $i(v0)) | ?
% 8.33/1.96 | | [v0: any] : ? [v1: any] :
% 8.33/1.96 | | (ic(uri_ex_InversesOfFunctionalProperties) = v0 &
% 8.33/1.96 | | ic(uri_owl_InverseFunctionalProperty) = v1 & ( ~ (v1 = 0) | ~ (v0
% 8.33/1.96 | | = 0)))
% 8.33/1.96 | |
% 8.33/1.96 | | BETA: splitting (35) gives:
% 8.33/1.96 | |
% 8.33/1.96 | | Case 1:
% 8.33/1.96 | | |
% 8.33/1.96 | | | (36) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 8.33/1.96 | | | icext(uri_ex_InversesOfFunctionalProperties, v0) = 0 &
% 8.33/1.96 | | | icext(uri_owl_InverseFunctionalProperty, v0) = v1 & $i(v0))
% 8.33/1.96 | | |
% 8.33/1.96 | | | DELTA: instantiating (36) with fresh symbols all_31_0, all_31_1 gives:
% 8.33/1.96 | | | (37) ~ (all_31_0 = 0) & icext(uri_ex_InversesOfFunctionalProperties,
% 8.33/1.96 | | | all_31_1) = 0 & icext(uri_owl_InverseFunctionalProperty,
% 8.33/1.96 | | | all_31_1) = all_31_0 & $i(all_31_1)
% 8.33/1.96 | | |
% 8.33/1.96 | | | ALPHA: (37) implies:
% 8.33/1.96 | | | (38) ~ (all_31_0 = 0)
% 8.33/1.96 | | | (39) $i(all_31_1)
% 8.33/1.96 | | | (40) icext(uri_owl_InverseFunctionalProperty, all_31_1) = all_31_0
% 8.33/1.96 | | | (41) icext(uri_ex_InversesOfFunctionalProperties, all_31_1) = 0
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (5) with all_31_1, all_31_0, simplifying with
% 8.33/1.96 | | | (39), (40) gives:
% 8.33/1.96 | | | (42) all_31_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 =
% 8.33/1.96 | | | v0) & iext(all_31_1, v1, v2) = 0 & iext(all_31_1, v0, v2) = 0
% 8.33/1.96 | | | & $i(v2) & $i(v1) & $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) &
% 8.33/1.96 | | | ip(all_31_1) = v0)
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (27) with all_31_1, simplifying with (39), (41)
% 8.33/1.96 | | | gives:
% 8.33/1.96 | | | (43) icext(all_14_0, all_31_1) = 0
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (32) with all_31_1, simplifying with (39), (43)
% 8.33/1.96 | | | gives:
% 8.33/1.96 | | | (44) ? [v0: $i] : (icext(uri_owl_FunctionalProperty, v0) = 0 &
% 8.33/1.96 | | | iext(uri_owl_inverseOf, all_31_1, v0) = 0 & $i(v0))
% 8.33/1.96 | | |
% 8.33/1.96 | | | DELTA: instantiating (44) with fresh symbol all_44_0 gives:
% 8.33/1.96 | | | (45) icext(uri_owl_FunctionalProperty, all_44_0) = 0 &
% 8.33/1.96 | | | iext(uri_owl_inverseOf, all_31_1, all_44_0) = 0 & $i(all_44_0)
% 8.33/1.96 | | |
% 8.33/1.96 | | | ALPHA: (45) implies:
% 8.33/1.96 | | | (46) $i(all_44_0)
% 8.33/1.96 | | | (47) iext(uri_owl_inverseOf, all_31_1, all_44_0) = 0
% 8.33/1.96 | | | (48) icext(uri_owl_FunctionalProperty, all_44_0) = 0
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (9) with all_31_1, all_44_0, simplifying with
% 8.33/1.96 | | | (39), (46), (47) gives:
% 8.33/1.96 | | | (49) ip(all_44_0) = 0 & ip(all_31_1) = 0 & ! [v0: $i] : ! [v1: $i] :
% 8.33/1.96 | | | ! [v2: int] : (v2 = 0 | ~ (iext(all_31_1, v0, v1) = v2) | ~
% 8.33/1.96 | | | $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.33/1.96 | | | iext(all_44_0, v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : (
% 8.33/1.96 | | | ~ (iext(all_31_1, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.33/1.96 | | | iext(all_44_0, v1, v0) = 0)
% 8.33/1.96 | | |
% 8.33/1.96 | | | ALPHA: (49) implies:
% 8.33/1.96 | | | (50) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(all_31_1, v0, v1) = 0) | ~
% 8.33/1.96 | | | $i(v1) | ~ $i(v0) | iext(all_44_0, v1, v0) = 0)
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (2) with all_31_1, all_44_0, simplifying with
% 8.33/1.96 | | | (39), (46), (47) gives:
% 8.33/1.96 | | | (51) ip(all_44_0) = 0 & ip(all_31_1) = 0
% 8.33/1.96 | | |
% 8.33/1.96 | | | ALPHA: (51) implies:
% 8.33/1.96 | | | (52) ip(all_31_1) = 0
% 8.33/1.96 | | |
% 8.33/1.96 | | | GROUND_INST: instantiating (4) with all_44_0, simplifying with (46), (48)
% 8.33/1.96 | | | gives:
% 8.33/1.97 | | | (53) ip(all_44_0) = 0 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 =
% 8.33/1.97 | | | v1 | ~ (iext(all_44_0, v0, v2) = 0) | ~ (iext(all_44_0, v0,
% 8.33/1.97 | | | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 8.33/1.97 | | |
% 8.33/1.97 | | | ALPHA: (53) implies:
% 8.33/1.97 | | | (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 8.33/1.97 | | | (iext(all_44_0, v0, v2) = 0) | ~ (iext(all_44_0, v0, v1) = 0) |
% 8.33/1.97 | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0))
% 8.33/1.97 | | |
% 8.33/1.97 | | | BETA: splitting (42) gives:
% 8.33/1.97 | | |
% 8.33/1.97 | | | Case 1:
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | (55) all_31_0 = 0
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | REDUCE: (38), (55) imply:
% 8.33/1.97 | | | | (56) $false
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | CLOSE: (56) is inconsistent.
% 8.33/1.97 | | | |
% 8.33/1.97 | | | Case 2:
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 8.33/1.97 | | | | iext(all_31_1, v1, v2) = 0 & iext(all_31_1, v0, v2) = 0 &
% 8.33/1.97 | | | | $i(v2) & $i(v1) & $i(v0)) | ? [v0: int] : ( ~ (v0 = 0) &
% 8.33/1.97 | | | | ip(all_31_1) = v0)
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | BETA: splitting (57) gives:
% 8.33/1.97 | | | |
% 8.33/1.97 | | | | Case 1:
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 8.33/1.97 | | | | | iext(all_31_1, v1, v2) = 0 & iext(all_31_1, v0, v2) = 0 &
% 8.33/1.97 | | | | | $i(v2) & $i(v1) & $i(v0))
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | DELTA: instantiating (58) with fresh symbols all_61_0, all_61_1,
% 8.33/1.97 | | | | | all_61_2 gives:
% 8.33/1.97 | | | | | (59) ~ (all_61_1 = all_61_2) & iext(all_31_1, all_61_1, all_61_0)
% 8.33/1.97 | | | | | = 0 & iext(all_31_1, all_61_2, all_61_0) = 0 & $i(all_61_0) &
% 8.33/1.97 | | | | | $i(all_61_1) & $i(all_61_2)
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | ALPHA: (59) implies:
% 8.33/1.97 | | | | | (60) ~ (all_61_1 = all_61_2)
% 8.33/1.97 | | | | | (61) $i(all_61_2)
% 8.33/1.97 | | | | | (62) $i(all_61_1)
% 8.33/1.97 | | | | | (63) $i(all_61_0)
% 8.33/1.97 | | | | | (64) iext(all_31_1, all_61_2, all_61_0) = 0
% 8.33/1.97 | | | | | (65) iext(all_31_1, all_61_1, all_61_0) = 0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | GROUND_INST: instantiating (50) with all_61_2, all_61_0, simplifying
% 8.33/1.97 | | | | | with (61), (63), (64) gives:
% 8.33/1.97 | | | | | (66) iext(all_44_0, all_61_0, all_61_2) = 0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | GROUND_INST: instantiating (50) with all_61_1, all_61_0, simplifying
% 8.33/1.97 | | | | | with (62), (63), (65) gives:
% 8.33/1.97 | | | | | (67) iext(all_44_0, all_61_0, all_61_1) = 0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | GROUND_INST: instantiating (54) with all_61_0, all_61_2, all_61_1,
% 8.33/1.97 | | | | | simplifying with (61), (62), (63), (66), (67) gives:
% 8.33/1.97 | | | | | (68) all_61_1 = all_61_2
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | REDUCE: (60), (68) imply:
% 8.33/1.97 | | | | | (69) $false
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | CLOSE: (69) is inconsistent.
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | Case 2:
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | (70) ? [v0: int] : ( ~ (v0 = 0) & ip(all_31_1) = v0)
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | DELTA: instantiating (70) with fresh symbol all_61_0 gives:
% 8.33/1.97 | | | | | (71) ~ (all_61_0 = 0) & ip(all_31_1) = all_61_0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | ALPHA: (71) implies:
% 8.33/1.97 | | | | | (72) ~ (all_61_0 = 0)
% 8.33/1.97 | | | | | (73) ip(all_31_1) = all_61_0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | GROUND_INST: instantiating (17) with 0, all_61_0, all_31_1,
% 8.33/1.97 | | | | | simplifying with (52), (73) gives:
% 8.33/1.97 | | | | | (74) all_61_0 = 0
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | REDUCE: (72), (74) imply:
% 8.33/1.97 | | | | | (75) $false
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | | CLOSE: (75) is inconsistent.
% 8.33/1.97 | | | | |
% 8.33/1.97 | | | | End of split
% 8.33/1.97 | | | |
% 8.33/1.97 | | | End of split
% 8.33/1.97 | | |
% 8.33/1.97 | | Case 2:
% 8.33/1.97 | | |
% 8.33/1.97 | | | (76) ? [v0: any] : ? [v1: any] :
% 8.33/1.97 | | | (ic(uri_ex_InversesOfFunctionalProperties) = v0 &
% 8.33/1.97 | | | ic(uri_owl_InverseFunctionalProperty) = v1 & ( ~ (v1 = 0) | ~
% 8.33/1.97 | | | (v0 = 0)))
% 8.33/1.97 | | |
% 8.33/1.97 | | | DELTA: instantiating (76) with fresh symbols all_31_0, all_31_1 gives:
% 8.33/1.97 | | | (77) ic(uri_ex_InversesOfFunctionalProperties) = all_31_1 &
% 8.33/1.97 | | | ic(uri_owl_InverseFunctionalProperty) = all_31_0 & ( ~ (all_31_0 =
% 8.33/1.97 | | | 0) | ~ (all_31_1 = 0))
% 8.33/1.97 | | |
% 8.33/1.97 | | | ALPHA: (77) implies:
% 8.33/1.98 | | | (78) ic(uri_owl_InverseFunctionalProperty) = all_31_0
% 8.33/1.98 | | | (79) ic(uri_ex_InversesOfFunctionalProperties) = all_31_1
% 8.33/1.98 | | | (80) ~ (all_31_0 = 0) | ~ (all_31_1 = 0)
% 8.33/1.98 | | |
% 8.33/1.98 | | | GROUND_INST: instantiating (16) with 0, all_31_0,
% 8.33/1.98 | | | uri_owl_InverseFunctionalProperty, simplifying with (1), (78)
% 8.33/1.98 | | | gives:
% 8.33/1.98 | | | (81) all_31_0 = 0
% 8.33/1.98 | | |
% 8.33/1.98 | | | GROUND_INST: instantiating (16) with 0, all_31_1,
% 8.33/1.98 | | | uri_ex_InversesOfFunctionalProperties, simplifying with (29),
% 8.33/1.98 | | | (79) gives:
% 8.33/1.98 | | | (82) all_31_1 = 0
% 8.33/1.98 | | |
% 8.33/1.98 | | | BETA: splitting (80) gives:
% 8.33/1.98 | | |
% 8.33/1.98 | | | Case 1:
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | (83) ~ (all_31_0 = 0)
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | REDUCE: (81), (83) imply:
% 8.33/1.98 | | | | (84) $false
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | CLOSE: (84) is inconsistent.
% 8.33/1.98 | | | |
% 8.33/1.98 | | | Case 2:
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | (85) ~ (all_31_1 = 0)
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | REDUCE: (82), (85) imply:
% 8.33/1.98 | | | | (86) $false
% 8.33/1.98 | | | |
% 8.33/1.98 | | | | CLOSE: (86) is inconsistent.
% 8.33/1.98 | | | |
% 8.33/1.98 | | | End of split
% 8.33/1.98 | | |
% 8.33/1.98 | | End of split
% 8.33/1.98 | |
% 8.33/1.98 | End of split
% 8.33/1.98 |
% 8.33/1.98 End of proof
% 8.33/1.98 % SZS output end Proof for theBenchmark
% 8.33/1.98
% 8.33/1.98 1358ms
%------------------------------------------------------------------------------