TSTP Solution File: SWB016+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWB016+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 : n024.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 20:11:44 EDT 2023
% Result : Theorem 6.51s 1.76s
% Output : Proof 8.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWB016+2 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n024.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 06:34:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.52/0.68 ________ _____
% 0.52/0.68 ___ __ \_________(_)________________________________
% 0.52/0.68 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.68 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.68 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.68
% 0.52/0.68 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.68 (2023-06-19)
% 0.52/0.68
% 0.52/0.68 (c) Philipp Rümmer, 2009-2023
% 0.52/0.68 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.68 Amanda Stjerna.
% 0.52/0.68 Free software under BSD-3-Clause.
% 0.52/0.68
% 0.52/0.68 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.68
% 0.52/0.68 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.69 Running up to 7 provers in parallel.
% 0.76/0.71 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.71 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.71 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.71 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.71 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.71 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.71 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.34/1.09 Prover 1: Preprocessing ...
% 2.34/1.09 Prover 4: Preprocessing ...
% 2.60/1.14 Prover 2: Preprocessing ...
% 2.60/1.14 Prover 5: Preprocessing ...
% 2.60/1.14 Prover 3: Preprocessing ...
% 2.60/1.14 Prover 0: Preprocessing ...
% 2.60/1.14 Prover 6: Preprocessing ...
% 4.18/1.38 Prover 5: Constructing countermodel ...
% 4.18/1.39 Prover 2: Constructing countermodel ...
% 4.75/1.47 Prover 3: Constructing countermodel ...
% 4.75/1.49 Prover 1: Constructing countermodel ...
% 4.75/1.51 Prover 6: Proving ...
% 4.75/1.52 Prover 0: Proving ...
% 4.75/1.52 Prover 4: Constructing countermodel ...
% 6.15/1.67 Prover 3: gave up
% 6.15/1.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.51/1.73 Prover 7: Preprocessing ...
% 6.51/1.76 Prover 0: proved (1055ms)
% 6.51/1.76
% 6.51/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.51/1.76
% 6.51/1.76 Prover 5: stopped
% 6.51/1.76 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.51/1.76 Prover 2: stopped
% 6.51/1.76 Prover 6: stopped
% 6.51/1.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.51/1.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.51/1.77 Prover 8: Preprocessing ...
% 6.51/1.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.51/1.79 Prover 13: Preprocessing ...
% 6.51/1.80 Prover 7: Constructing countermodel ...
% 6.51/1.80 Prover 11: Preprocessing ...
% 6.51/1.80 Prover 10: Preprocessing ...
% 6.51/1.80 Prover 1: gave up
% 6.51/1.81 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.22/1.85 Prover 16: Preprocessing ...
% 7.22/1.86 Prover 4: Found proof (size 55)
% 7.22/1.86 Prover 4: proved (1156ms)
% 7.22/1.86 Prover 7: stopped
% 7.22/1.86 Prover 11: stopped
% 7.22/1.87 Prover 10: Constructing countermodel ...
% 7.22/1.87 Prover 16: stopped
% 7.22/1.87 Prover 13: Constructing countermodel ...
% 7.22/1.87 Prover 10: stopped
% 7.22/1.88 Prover 13: stopped
% 7.22/1.89 Prover 8: Warning: ignoring some quantifiers
% 7.22/1.89 Prover 8: Constructing countermodel ...
% 7.22/1.90 Prover 8: stopped
% 7.22/1.90
% 7.22/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/1.90
% 7.22/1.91 % SZS output start Proof for theBenchmark
% 7.86/1.91 Assumptions after simplification:
% 7.86/1.91 ---------------------------------
% 7.86/1.91
% 7.86/1.91 (owl_eqdis_equivalentclass)
% 7.86/1.96 $i(uri_owl_equivalentClass) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 7.86/1.96 [v3: int] : (v3 = 0 | ~ (icext(v1, v2) = v3) | ~
% 7.86/1.96 (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.86/1.96 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & icext(v0, v2) = v4)) & ! [v0: $i] :
% 7.86/1.96 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (icext(v0, v2) = v3) |
% 7.86/1.96 ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.86/1.96 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & icext(v1, v2) = v4)) & ! [v0: $i] :
% 7.86/1.96 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (iext(uri_owl_equivalentClass, v0,
% 7.86/1.96 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 7.86/1.96 [v5: $i] : ? [v6: any] : ? [v7: any] : ($i(v5) & ((ic(v1) = v4 & ic(v0) =
% 7.86/1.96 v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (icext(v1, v5) = v7 & icext(v0,
% 7.86/1.96 v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)) & (v7 = 0 | v6 = 0))))) & !
% 7.86/1.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (icext(v1, v2) = 0) | ~
% 7.86/1.96 (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 7.86/1.96 $i(v0) | icext(v0, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 7.86/1.96 (icext(v0, v2) = 0) | ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~
% 7.86/1.96 $i(v2) | ~ $i(v1) | ~ $i(v0) | icext(v1, v2) = 0) & ! [v0: $i] : ! [v1:
% 7.86/1.96 $i] : ( ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v1) | ~
% 7.86/1.96 $i(v0) | (ic(v1) = 0 & ic(v0) = 0))
% 7.86/1.96
% 7.86/1.96 (owl_prop_equivalentclass_type)
% 7.86/1.96 ip(uri_owl_equivalentClass) = 0 & $i(uri_owl_equivalentClass)
% 7.86/1.96
% 7.86/1.96 (owl_rdfsext_subclassof)
% 7.86/1.97 $i(uri_rdfs_subClassOf) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 7.86/1.97 int] : (v3 = 0 | ~ (icext(v1, v2) = v3) | ~ (iext(uri_rdfs_subClassOf, v0,
% 7.86/1.97 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 7.86/1.97 0) & icext(v0, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] :
% 7.86/1.97 (v2 = 0 | ~ (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 7.86/1.97 | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7: int] :
% 7.86/1.97 ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & icext(v1, v5) = v7 & icext(v0, v5) = 0) |
% 7.86/1.97 (ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & ! [v0:
% 7.86/1.97 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~
% 8.14/1.97 (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 8.14/1.97 | icext(v1, v2) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.14/1.97 (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) =
% 8.14/1.97 0 & ic(v0) = 0))
% 8.14/1.97
% 8.14/1.97 (owl_rdfsext_subpropertyof)
% 8.14/1.97 $i(uri_rdfs_subPropertyOf) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 8.14/1.97 $i] : ! [v4: int] : (v4 = 0 | ~ (iext(v1, v2, v3) = v4) | ~
% 8.14/1.97 (iext(uri_rdfs_subPropertyOf, v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 8.14/1.97 $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & iext(v0, v2, v3) = v5)) &
% 8.14/1.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (iext(v0, v2, v3)
% 8.14/1.97 = 0) | ~ (iext(uri_rdfs_subPropertyOf, v0, v1) = 0) | ~ $i(v3) | ~
% 8.14/1.97 $i(v2) | ~ $i(v1) | ~ $i(v0) | iext(v1, v2, v3) = 0) & ! [v0: $i] : !
% 8.14/1.97 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (iext(uri_rdfs_subPropertyOf, v0, v1) =
% 8.14/1.97 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 8.14/1.97 ? [v6: $i] : ? [v7: int] : ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 & ~
% 8.14/1.97 (v8 = 0) & iext(v1, v5, v6) = v8 & iext(v0, v5, v6) = 0) | (ip(v1) =
% 8.14/1.97 v4 & ip(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))))) & ! [v0: $i] : !
% 8.14/1.97 [v1: $i] : ( ~ (iext(uri_rdfs_subPropertyOf, v0, v1) = 0) | ~ $i(v1) | ~
% 8.14/1.97 $i(v0) | (ip(v1) = 0 & ip(v0) = 0))
% 8.14/1.97
% 8.14/1.97 (rdf_type_ip)
% 8.14/1.97 $i(uri_rdf_Property) & $i(uri_rdf_type) & ! [v0: $i] : ! [v1: int] : (v1 = 0
% 8.14/1.97 | ~ (ip(v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 8.14/1.97 iext(uri_rdf_type, v0, uri_rdf_Property) = v2)) & ! [v0: $i] : ! [v1:
% 8.14/1.97 int] : (v1 = 0 | ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = v1) | ~
% 8.14/1.97 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ip(v0) = v2)) & ! [v0: $i] : ( ~
% 8.14/1.97 (ip(v0) = 0) | ~ $i(v0) | iext(uri_rdf_type, v0, uri_rdf_Property) = 0) &
% 8.14/1.97 ! [v0: $i] : ( ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = 0) | ~ $i(v0) |
% 8.14/1.97 ip(v0) = 0)
% 8.14/1.97
% 8.14/1.97 (rdfs_cext_def)
% 8.14/1.98 $i(uri_rdf_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.14/1.98 (icext(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 8.14/1.98 iext(uri_rdf_type, v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 8.14/1.98 int] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ~ $i(v1) | ~
% 8.14/1.98 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0: $i] :
% 8.14/1.98 ! [v1: $i] : ( ~ (icext(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 8.14/1.98 iext(uri_rdf_type, v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 8.14/1.98 (iext(uri_rdf_type, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | icext(v1, v0) =
% 8.14/1.98 0)
% 8.14/1.98
% 8.14/1.98 (rdfs_domain_domain)
% 8.14/1.98 iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) = 0 &
% 8.14/1.98 $i(uri_rdfs_domain) & $i(uri_rdf_Property)
% 8.14/1.98
% 8.14/1.98 (rdfs_domain_main)
% 8.14/1.98 $i(uri_rdfs_domain) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 8.14/1.98 ! [v4: int] : (v4 = 0 | ~ (icext(v1, v2) = v4) | ~ (iext(v0, v2, v3) = 0) |
% 8.14/1.98 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 8.14/1.98 iext(uri_rdfs_domain, v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 8.14/1.98 $i] : ! [v3: $i] : ( ~ (iext(v0, v2, v3) = 0) | ~ (iext(uri_rdfs_domain,
% 8.14/1.98 v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | icext(v1,
% 8.14/1.98 v2) = 0)
% 8.14/1.98
% 8.14/1.98 (rdfs_subclassof_domain)
% 8.14/1.98 iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class) = 0 &
% 8.14/1.98 $i(uri_rdfs_Class) & $i(uri_rdfs_subClassOf) & $i(uri_rdfs_domain)
% 8.14/1.98
% 8.14/1.98 (testcase_conclusion_fullish_016_Reflective_Tautologies_II)
% 8.14/1.98 $i(uri_rdfs_subPropertyOf) & $i(uri_owl_equivalentClass) &
% 8.14/1.98 $i(uri_rdfs_subClassOf) & ? [v0: int] : ( ~ (v0 = 0) &
% 8.14/1.98 iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass, uri_rdfs_subClassOf) =
% 8.14/1.98 v0)
% 8.14/1.98
% 8.14/1.98 (function-axioms)
% 8.14/1.98 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 8.14/1.98 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4,
% 8.14/1.98 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 8.14/1.98 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~
% 8.14/1.98 (icext(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.14/1.98 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2)
% 8.14/1.98 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 8.14/1.98 $i] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0))
% 8.14/1.98
% 8.14/1.98 Further assumptions not needed in the proof:
% 8.14/1.98 --------------------------------------------
% 8.14/1.98 owl_prop_equivalentclass_ext
% 8.14/1.98
% 8.14/1.98 Those formulas are unsatisfiable:
% 8.14/1.98 ---------------------------------
% 8.14/1.98
% 8.14/1.98 Begin of proof
% 8.14/1.98 |
% 8.14/1.98 | ALPHA: (rdf_type_ip) implies:
% 8.14/1.98 | (1) ! [v0: $i] : ( ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = 0) | ~
% 8.14/1.98 | $i(v0) | ip(v0) = 0)
% 8.14/1.98 |
% 8.14/1.98 | ALPHA: (rdfs_cext_def) implies:
% 8.14/1.98 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (icext(v1, v0) = 0) | ~ $i(v1) | ~
% 8.14/1.99 | $i(v0) | iext(uri_rdf_type, v0, v1) = 0)
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (rdfs_domain_main) implies:
% 8.14/1.99 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (iext(v0,
% 8.14/1.99 | v2, v3) = 0) | ~ (iext(uri_rdfs_domain, v0, v1) = 0) | ~ $i(v3)
% 8.14/1.99 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | icext(v1, v2) = 0)
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (rdfs_domain_domain) implies:
% 8.14/1.99 | (4) $i(uri_rdf_Property)
% 8.14/1.99 | (5) iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) = 0
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (rdfs_subclassof_domain) implies:
% 8.14/1.99 | (6) $i(uri_rdfs_domain)
% 8.14/1.99 | (7) $i(uri_rdfs_Class)
% 8.14/1.99 | (8) iext(uri_rdfs_domain, uri_rdfs_subClassOf, uri_rdfs_Class) = 0
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (owl_prop_equivalentclass_type) implies:
% 8.14/1.99 | (9) ip(uri_owl_equivalentClass) = 0
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (owl_rdfsext_subclassof) implies:
% 8.14/1.99 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.14/1.99 | (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 8.14/1.99 | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: int] : ? [v7:
% 8.14/1.99 | int] : ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & icext(v1, v5) = v7 &
% 8.14/1.99 | icext(v0, v5) = 0) | (ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0)
% 8.14/1.99 | | ~ (v3 = 0))))))
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (owl_rdfsext_subpropertyof) implies:
% 8.14/1.99 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 8.14/1.99 | (iext(uri_rdfs_subPropertyOf, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 8.14/1.99 | | ? [v3: any] : ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 8.14/1.99 | int] : ? [v8: int] : ($i(v6) & $i(v5) & ((v7 = 0 & ~ (v8 = 0) &
% 8.14/1.99 | iext(v1, v5, v6) = v8 & iext(v0, v5, v6) = 0) | (ip(v1) = v4 &
% 8.14/1.99 | ip(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))))
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (owl_eqdis_equivalentclass) implies:
% 8.14/1.99 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_owl_equivalentClass, v0, v1)
% 8.14/1.99 | = 0) | ~ $i(v1) | ~ $i(v0) | (ic(v1) = 0 & ic(v0) = 0))
% 8.14/1.99 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (icext(v0, v2) = 0) | ~
% 8.14/1.99 | (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 8.14/1.99 | | ~ $i(v0) | icext(v1, v2) = 0)
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (testcase_conclusion_fullish_016_Reflective_Tautologies_II) implies:
% 8.14/1.99 | (14) $i(uri_rdfs_subClassOf)
% 8.14/1.99 | (15) $i(uri_owl_equivalentClass)
% 8.14/1.99 | (16) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_rdfs_subPropertyOf,
% 8.14/1.99 | uri_owl_equivalentClass, uri_rdfs_subClassOf) = v0)
% 8.14/1.99 |
% 8.14/1.99 | ALPHA: (function-axioms) implies:
% 8.14/1.99 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.14/1.99 | : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0))
% 8.14/1.99 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.14/1.99 | : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0))
% 8.14/2.00 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 8.14/2.00 | : ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2)
% 8.14/2.00 | = v0))
% 8.14/2.00 |
% 8.14/2.00 | DELTA: instantiating (16) with fresh symbol all_11_0 gives:
% 8.14/2.00 | (20) ~ (all_11_0 = 0) & iext(uri_rdfs_subPropertyOf,
% 8.14/2.00 | uri_owl_equivalentClass, uri_rdfs_subClassOf) = all_11_0
% 8.14/2.00 |
% 8.14/2.00 | ALPHA: (20) implies:
% 8.14/2.00 | (21) ~ (all_11_0 = 0)
% 8.14/2.00 | (22) iext(uri_rdfs_subPropertyOf, uri_owl_equivalentClass,
% 8.14/2.00 | uri_rdfs_subClassOf) = all_11_0
% 8.14/2.00 |
% 8.14/2.00 | GROUND_INST: instantiating (3) with uri_rdfs_domain, uri_rdf_Property,
% 8.14/2.00 | uri_rdfs_subClassOf, uri_rdfs_Class, simplifying with (4), (5),
% 8.14/2.00 | (6), (7), (8), (14) gives:
% 8.14/2.00 | (23) icext(uri_rdf_Property, uri_rdfs_subClassOf) = 0
% 8.14/2.00 |
% 8.14/2.00 | GROUND_INST: instantiating (11) with uri_owl_equivalentClass,
% 8.14/2.00 | uri_rdfs_subClassOf, all_11_0, simplifying with (14), (15), (22)
% 8.14/2.00 | gives:
% 8.14/2.00 | (24) all_11_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i]
% 8.14/2.00 | : ? [v4: int] : ? [v5: int] : ($i(v3) & $i(v2) & ((v4 = 0 & ~ (v5 =
% 8.14/2.00 | 0) & iext(uri_owl_equivalentClass, v2, v3) = 0 &
% 8.14/2.00 | iext(uri_rdfs_subClassOf, v2, v3) = v5) |
% 8.14/2.00 | (ip(uri_owl_equivalentClass) = v0 & ip(uri_rdfs_subClassOf) = v1 &
% 8.14/2.00 | ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 8.14/2.00 |
% 8.14/2.00 | BETA: splitting (24) gives:
% 8.14/2.00 |
% 8.14/2.00 | Case 1:
% 8.14/2.00 | |
% 8.14/2.00 | | (25) all_11_0 = 0
% 8.14/2.00 | |
% 8.14/2.00 | | REDUCE: (21), (25) imply:
% 8.14/2.00 | | (26) $false
% 8.14/2.00 | |
% 8.14/2.00 | | CLOSE: (26) is inconsistent.
% 8.14/2.00 | |
% 8.14/2.00 | Case 2:
% 8.14/2.00 | |
% 8.14/2.00 | | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 8.14/2.00 | | int] : ? [v5: int] : ($i(v3) & $i(v2) & ((v4 = 0 & ~ (v5 = 0) &
% 8.14/2.00 | | iext(uri_owl_equivalentClass, v2, v3) = 0 &
% 8.14/2.00 | | iext(uri_rdfs_subClassOf, v2, v3) = v5) |
% 8.14/2.00 | | (ip(uri_owl_equivalentClass) = v0 & ip(uri_rdfs_subClassOf) = v1
% 8.14/2.00 | | & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 8.14/2.00 | |
% 8.14/2.00 | | DELTA: instantiating (27) with fresh symbols all_23_0, all_23_1, all_23_2,
% 8.14/2.00 | | all_23_3, all_23_4, all_23_5 gives:
% 8.14/2.01 | | (28) $i(all_23_2) & $i(all_23_3) & ((all_23_1 = 0 & ~ (all_23_0 = 0) &
% 8.14/2.01 | | iext(uri_owl_equivalentClass, all_23_3, all_23_2) = 0 &
% 8.14/2.01 | | iext(uri_rdfs_subClassOf, all_23_3, all_23_2) = all_23_0) |
% 8.14/2.01 | | (ip(uri_owl_equivalentClass) = all_23_5 & ip(uri_rdfs_subClassOf)
% 8.14/2.01 | | = all_23_4 & ( ~ (all_23_4 = 0) | ~ (all_23_5 = 0))))
% 8.14/2.01 | |
% 8.14/2.01 | | ALPHA: (28) implies:
% 8.14/2.01 | | (29) $i(all_23_3)
% 8.14/2.01 | | (30) $i(all_23_2)
% 8.14/2.01 | | (31) (all_23_1 = 0 & ~ (all_23_0 = 0) & iext(uri_owl_equivalentClass,
% 8.14/2.01 | | all_23_3, all_23_2) = 0 & iext(uri_rdfs_subClassOf, all_23_3,
% 8.14/2.01 | | all_23_2) = all_23_0) | (ip(uri_owl_equivalentClass) = all_23_5
% 8.14/2.01 | | & ip(uri_rdfs_subClassOf) = all_23_4 & ( ~ (all_23_4 = 0) | ~
% 8.14/2.01 | | (all_23_5 = 0)))
% 8.14/2.01 | |
% 8.14/2.01 | | GROUND_INST: instantiating (2) with uri_rdfs_subClassOf, uri_rdf_Property,
% 8.14/2.01 | | simplifying with (4), (14), (23) gives:
% 8.14/2.01 | | (32) iext(uri_rdf_type, uri_rdfs_subClassOf, uri_rdf_Property) = 0
% 8.14/2.01 | |
% 8.14/2.01 | | GROUND_INST: instantiating (1) with uri_rdfs_subClassOf, simplifying with
% 8.14/2.01 | | (14), (32) gives:
% 8.14/2.01 | | (33) ip(uri_rdfs_subClassOf) = 0
% 8.14/2.01 | |
% 8.14/2.01 | | BETA: splitting (31) gives:
% 8.14/2.01 | |
% 8.14/2.01 | | Case 1:
% 8.14/2.01 | | |
% 8.14/2.01 | | | (34) all_23_1 = 0 & ~ (all_23_0 = 0) & iext(uri_owl_equivalentClass,
% 8.14/2.01 | | | all_23_3, all_23_2) = 0 & iext(uri_rdfs_subClassOf, all_23_3,
% 8.14/2.01 | | | all_23_2) = all_23_0
% 8.14/2.01 | | |
% 8.14/2.01 | | | ALPHA: (34) implies:
% 8.14/2.01 | | | (35) ~ (all_23_0 = 0)
% 8.14/2.01 | | | (36) iext(uri_rdfs_subClassOf, all_23_3, all_23_2) = all_23_0
% 8.14/2.01 | | | (37) iext(uri_owl_equivalentClass, all_23_3, all_23_2) = 0
% 8.14/2.01 | | |
% 8.14/2.01 | | | GROUND_INST: instantiating (10) with all_23_3, all_23_2, all_23_0,
% 8.14/2.01 | | | simplifying with (29), (30), (36) gives:
% 8.14/2.01 | | | (38) all_23_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 8.14/2.01 | | | int] : ? [v4: int] : ($i(v2) & ((v3 = 0 & ~ (v4 = 0) &
% 8.14/2.01 | | | icext(all_23_2, v2) = v4 & icext(all_23_3, v2) = 0) |
% 8.14/2.01 | | | (ic(all_23_2) = v1 & ic(all_23_3) = v0 & ( ~ (v1 = 0) | ~ (v0
% 8.14/2.01 | | | = 0)))))
% 8.14/2.01 | | |
% 8.14/2.01 | | | GROUND_INST: instantiating (12) with all_23_3, all_23_2, simplifying with
% 8.14/2.01 | | | (29), (30), (37) gives:
% 8.14/2.01 | | | (39) ic(all_23_2) = 0 & ic(all_23_3) = 0
% 8.14/2.01 | | |
% 8.14/2.01 | | | ALPHA: (39) implies:
% 8.14/2.01 | | | (40) ic(all_23_3) = 0
% 8.14/2.01 | | | (41) ic(all_23_2) = 0
% 8.14/2.01 | | |
% 8.14/2.01 | | | BETA: splitting (38) gives:
% 8.14/2.01 | | |
% 8.14/2.01 | | | Case 1:
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | (42) all_23_0 = 0
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | REDUCE: (35), (42) imply:
% 8.14/2.01 | | | | (43) $false
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | CLOSE: (43) is inconsistent.
% 8.14/2.01 | | | |
% 8.14/2.01 | | | Case 2:
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | (44) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ?
% 8.14/2.01 | | | | [v4: int] : ($i(v2) & ((v3 = 0 & ~ (v4 = 0) & icext(all_23_2,
% 8.14/2.01 | | | | v2) = v4 & icext(all_23_3, v2) = 0) | (ic(all_23_2) = v1
% 8.14/2.01 | | | | & ic(all_23_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | DELTA: instantiating (44) with fresh symbols all_51_0, all_51_1,
% 8.14/2.01 | | | | all_51_2, all_51_3, all_51_4 gives:
% 8.14/2.01 | | | | (45) $i(all_51_2) & ((all_51_1 = 0 & ~ (all_51_0 = 0) &
% 8.14/2.01 | | | | icext(all_23_2, all_51_2) = all_51_0 & icext(all_23_3,
% 8.14/2.01 | | | | all_51_2) = 0) | (ic(all_23_2) = all_51_3 & ic(all_23_3) =
% 8.14/2.01 | | | | all_51_4 & ( ~ (all_51_3 = 0) | ~ (all_51_4 = 0))))
% 8.14/2.01 | | | |
% 8.14/2.01 | | | | ALPHA: (45) implies:
% 8.14/2.01 | | | | (46) $i(all_51_2)
% 8.14/2.02 | | | | (47) (all_51_1 = 0 & ~ (all_51_0 = 0) & icext(all_23_2, all_51_2) =
% 8.14/2.02 | | | | all_51_0 & icext(all_23_3, all_51_2) = 0) | (ic(all_23_2) =
% 8.14/2.02 | | | | all_51_3 & ic(all_23_3) = all_51_4 & ( ~ (all_51_3 = 0) | ~
% 8.14/2.02 | | | | (all_51_4 = 0)))
% 8.14/2.02 | | | |
% 8.14/2.02 | | | | BETA: splitting (47) gives:
% 8.14/2.02 | | | |
% 8.14/2.02 | | | | Case 1:
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | (48) all_51_1 = 0 & ~ (all_51_0 = 0) & icext(all_23_2, all_51_2) =
% 8.14/2.02 | | | | | all_51_0 & icext(all_23_3, all_51_2) = 0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | ALPHA: (48) implies:
% 8.14/2.02 | | | | | (49) ~ (all_51_0 = 0)
% 8.14/2.02 | | | | | (50) icext(all_23_3, all_51_2) = 0
% 8.14/2.02 | | | | | (51) icext(all_23_2, all_51_2) = all_51_0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | GROUND_INST: instantiating (13) with all_23_3, all_23_2, all_51_2,
% 8.14/2.02 | | | | | simplifying with (29), (30), (37), (46), (50) gives:
% 8.14/2.02 | | | | | (52) icext(all_23_2, all_51_2) = 0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | GROUND_INST: instantiating (19) with all_51_0, 0, all_51_2, all_23_2,
% 8.14/2.02 | | | | | simplifying with (51), (52) gives:
% 8.14/2.02 | | | | | (53) all_51_0 = 0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | REDUCE: (49), (53) imply:
% 8.14/2.02 | | | | | (54) $false
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | CLOSE: (54) is inconsistent.
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | Case 2:
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | (55) ic(all_23_2) = all_51_3 & ic(all_23_3) = all_51_4 & ( ~
% 8.14/2.02 | | | | | (all_51_3 = 0) | ~ (all_51_4 = 0))
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | ALPHA: (55) implies:
% 8.14/2.02 | | | | | (56) ic(all_23_3) = all_51_4
% 8.14/2.02 | | | | | (57) ic(all_23_2) = all_51_3
% 8.14/2.02 | | | | | (58) ~ (all_51_3 = 0) | ~ (all_51_4 = 0)
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | GROUND_INST: instantiating (18) with 0, all_51_4, all_23_3,
% 8.14/2.02 | | | | | simplifying with (40), (56) gives:
% 8.14/2.02 | | | | | (59) all_51_4 = 0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | GROUND_INST: instantiating (18) with 0, all_51_3, all_23_2,
% 8.14/2.02 | | | | | simplifying with (41), (57) gives:
% 8.14/2.02 | | | | | (60) all_51_3 = 0
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | BETA: splitting (58) gives:
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | | Case 1:
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | (61) ~ (all_51_3 = 0)
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | REDUCE: (60), (61) imply:
% 8.14/2.02 | | | | | | (62) $false
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | CLOSE: (62) is inconsistent.
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | Case 2:
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | (63) ~ (all_51_4 = 0)
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | REDUCE: (59), (63) imply:
% 8.14/2.02 | | | | | | (64) $false
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | | CLOSE: (64) is inconsistent.
% 8.14/2.02 | | | | | |
% 8.14/2.02 | | | | | End of split
% 8.14/2.02 | | | | |
% 8.14/2.02 | | | | End of split
% 8.14/2.02 | | | |
% 8.14/2.02 | | | End of split
% 8.14/2.02 | | |
% 8.14/2.02 | | Case 2:
% 8.14/2.02 | | |
% 8.14/2.02 | | | (65) ip(uri_owl_equivalentClass) = all_23_5 & ip(uri_rdfs_subClassOf) =
% 8.14/2.02 | | | all_23_4 & ( ~ (all_23_4 = 0) | ~ (all_23_5 = 0))
% 8.14/2.02 | | |
% 8.14/2.02 | | | ALPHA: (65) implies:
% 8.14/2.02 | | | (66) ip(uri_rdfs_subClassOf) = all_23_4
% 8.14/2.02 | | | (67) ip(uri_owl_equivalentClass) = all_23_5
% 8.14/2.02 | | | (68) ~ (all_23_4 = 0) | ~ (all_23_5 = 0)
% 8.14/2.02 | | |
% 8.14/2.02 | | | GROUND_INST: instantiating (17) with 0, all_23_4, uri_rdfs_subClassOf,
% 8.14/2.02 | | | simplifying with (33), (66) gives:
% 8.14/2.02 | | | (69) all_23_4 = 0
% 8.14/2.02 | | |
% 8.14/2.02 | | | GROUND_INST: instantiating (17) with 0, all_23_5, uri_owl_equivalentClass,
% 8.14/2.02 | | | simplifying with (9), (67) gives:
% 8.14/2.02 | | | (70) all_23_5 = 0
% 8.14/2.02 | | |
% 8.14/2.02 | | | BETA: splitting (68) gives:
% 8.14/2.02 | | |
% 8.14/2.02 | | | Case 1:
% 8.14/2.02 | | | |
% 8.14/2.02 | | | | (71) ~ (all_23_4 = 0)
% 8.14/2.02 | | | |
% 8.14/2.02 | | | | REDUCE: (69), (71) imply:
% 8.14/2.02 | | | | (72) $false
% 8.14/2.02 | | | |
% 8.14/2.02 | | | | CLOSE: (72) is inconsistent.
% 8.14/2.02 | | | |
% 8.14/2.03 | | | Case 2:
% 8.14/2.03 | | | |
% 8.14/2.03 | | | | (73) ~ (all_23_5 = 0)
% 8.14/2.03 | | | |
% 8.14/2.03 | | | | REDUCE: (70), (73) imply:
% 8.14/2.03 | | | | (74) $false
% 8.14/2.03 | | | |
% 8.14/2.03 | | | | CLOSE: (74) is inconsistent.
% 8.14/2.03 | | | |
% 8.14/2.03 | | | End of split
% 8.14/2.03 | | |
% 8.14/2.03 | | End of split
% 8.14/2.03 | |
% 8.14/2.03 | End of split
% 8.14/2.03 |
% 8.14/2.03 End of proof
% 8.14/2.03 % SZS output end Proof for theBenchmark
% 8.14/2.03
% 8.14/2.03 1342ms
%------------------------------------------------------------------------------