TSTP Solution File: SWB009+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWB009+3 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n029.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 20:11:38 EDT 2023
% Result : Theorem 36.99s 5.64s
% Output : Proof 47.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWB009+3 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.34 % Computer : n029.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sun Aug 27 07:49:11 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.23/1.38 Prover 4: Preprocessing ...
% 4.23/1.38 Prover 1: Preprocessing ...
% 4.23/1.41 Prover 6: Preprocessing ...
% 4.23/1.41 Prover 0: Preprocessing ...
% 4.23/1.41 Prover 5: Preprocessing ...
% 4.23/1.41 Prover 2: Preprocessing ...
% 4.23/1.41 Prover 3: Preprocessing ...
% 10.35/2.15 Prover 5: Proving ...
% 10.72/2.20 Prover 2: Proving ...
% 12.59/2.43 Prover 3: Constructing countermodel ...
% 12.59/2.46 Prover 6: Proving ...
% 12.97/2.47 Prover 1: Constructing countermodel ...
% 23.25/3.85 Prover 4: Constructing countermodel ...
% 27.43/4.44 Prover 0: Proving ...
% 36.99/5.63 Prover 3: proved (5022ms)
% 36.99/5.63
% 36.99/5.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.99/5.64
% 36.99/5.64 Prover 6: stopped
% 36.99/5.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 36.99/5.66 Prover 5: stopped
% 36.99/5.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 36.99/5.67 Prover 2: stopped
% 37.30/5.68 Prover 0: stopped
% 37.30/5.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 37.30/5.69 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 37.30/5.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 37.96/5.79 Prover 7: Preprocessing ...
% 38.37/5.82 Prover 8: Preprocessing ...
% 38.59/5.85 Prover 13: Preprocessing ...
% 38.59/5.87 Prover 11: Preprocessing ...
% 38.59/5.87 Prover 10: Preprocessing ...
% 38.59/5.93 Prover 7: Warning: ignoring some quantifiers
% 38.59/5.97 Prover 10: Warning: ignoring some quantifiers
% 38.59/5.98 Prover 7: Constructing countermodel ...
% 38.59/6.00 Prover 10: Constructing countermodel ...
% 38.59/6.01 Prover 13: Warning: ignoring some quantifiers
% 38.59/6.02 Prover 13: Constructing countermodel ...
% 40.64/6.13 Prover 8: Warning: ignoring some quantifiers
% 40.64/6.15 Prover 8: Constructing countermodel ...
% 43.53/6.51 Prover 1: Found proof (size 27)
% 43.53/6.51 Prover 1: proved (5900ms)
% 43.53/6.51 Prover 13: stopped
% 43.53/6.51 Prover 7: stopped
% 43.53/6.51 Prover 4: stopped
% 43.53/6.51 Prover 10: stopped
% 43.53/6.51 Prover 8: stopped
% 46.41/7.25 Prover 11: Constructing countermodel ...
% 46.66/7.28 Prover 11: stopped
% 46.66/7.28
% 46.66/7.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.66/7.28
% 46.66/7.29 % SZS output start Proof for theBenchmark
% 46.66/7.30 Assumptions after simplification:
% 46.66/7.30 ---------------------------------
% 46.66/7.30
% 46.66/7.30 (owl_restrict_somevaluesfrom)
% 46.66/7.34 $i(uri_owl_someValuesFrom) & $i(uri_owl_onProperty) & ! [v0: $i] : ! [v1:
% 46.66/7.35 $i] : ! [v2: $i] : ( ~ (iext(uri_owl_someValuesFrom, v0, v2) = 0) | ~
% 46.66/7.35 (iext(uri_owl_onProperty, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 46.66/7.35 ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (icext(v0, v3) = v4) | ~ $i(v3)
% 46.66/7.35 | ! [v5: $i] : ( ~ (icext(v2, v5) = 0) | ~ $i(v5) | ? [v6: int] : ( ~
% 46.66/7.35 (v6 = 0) & iext(v1, v3, v5) = v6))) & ! [v3: $i] : ( ~ (icext(v0,
% 46.66/7.35 v3) = 0) | ~ $i(v3) | ? [v4: $i] : (iext(v1, v3, v4) = 0 &
% 46.66/7.35 icext(v2, v4) = 0 & $i(v4)))))
% 46.66/7.35
% 46.66/7.35 (rdfs_cext_def)
% 46.66/7.35 $i(uri_rdf_type) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.66/7.35 (iext(uri_rdf_type, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 46.66/7.35 ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 46.66/7.35 (iext(uri_rdf_type, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | icext(v1, v0) =
% 46.66/7.35 0)
% 46.66/7.35
% 46.66/7.35 (testcase_conclusion_fullish_009_Existential_Restriction_Entailments)
% 46.66/7.35 $i(uri_ex_c) & $i(uri_ex_s) & $i(uri_ex_p) & $i(uri_rdf_type) & ! [v0: $i] :
% 46.66/7.35 ( ~ (iext(uri_ex_p, uri_ex_s, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 46.66/7.35 0) & iext(uri_rdf_type, v0, uri_ex_c) = v1))
% 46.66/7.35
% 46.66/7.35 (testcase_premise_fullish_009_Existential_Restriction_Entailments)
% 46.66/7.36 $i(uri_owl_Class) & $i(uri_owl_ObjectProperty) & $i(uri_ex_c) & $i(uri_ex_s) &
% 46.66/7.36 $i(uri_ex_p) & $i(uri_owl_someValuesFrom) & $i(uri_owl_onProperty) &
% 46.66/7.36 $i(uri_owl_Restriction) & $i(uri_rdf_type) & ? [v0: any] : ? [v1: any] :
% 46.66/7.36 (iext(uri_rdf_type, uri_ex_c, uri_owl_Class) = v1 & iext(uri_rdf_type,
% 46.66/7.36 uri_ex_p, uri_owl_ObjectProperty) = v0 & ? [v2: $i] : (v1 = 0 & v0 = 0 &
% 46.66/7.36 iext(uri_owl_someValuesFrom, v2, uri_ex_c) = 0 & iext(uri_owl_onProperty,
% 46.66/7.36 v2, uri_ex_p) = 0 & iext(uri_rdf_type, v2, uri_owl_Restriction) = 0 &
% 46.66/7.36 iext(uri_rdf_type, uri_ex_s, v2) = 0 & $i(v2)))
% 46.66/7.36
% 46.66/7.36 (function-axioms)
% 46.66/7.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 46.66/7.37 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4,
% 46.66/7.37 v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 46.66/7.37 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~
% 46.66/7.37 (icext(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.66/7.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ioxp(v2) = v1) | ~
% 46.66/7.37 (ioxp(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 46.66/7.37 ! [v2: $i] : (v1 = v0 | ~ (ix(v2) = v1) | ~ (ix(v2) = v0)) & ! [v0:
% 46.66/7.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 46.66/7.37 ~ (iodp(v2) = v1) | ~ (iodp(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 46.66/7.37 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ip(v2) = v1) | ~
% 46.66/7.37 (ip(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 46.66/7.37 ! [v2: $i] : (v1 = v0 | ~ (ioap(v2) = v1) | ~ (ioap(v2) = v0)) & ! [v0:
% 46.66/7.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 46.66/7.37 ~ (idc(v2) = v1) | ~ (idc(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 46.66/7.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (lv(v2) = v1) | ~ (lv(v2)
% 46.66/7.37 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 46.66/7.37 $i] : (v1 = v0 | ~ (ir(v2) = v1) | ~ (ir(v2) = v0)) & ! [v0:
% 46.66/7.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 46.66/7.37 ~ (ic(v2) = v1) | ~ (ic(v2) = v0))
% 46.66/7.37
% 46.66/7.37 Further assumptions not needed in the proof:
% 46.66/7.37 --------------------------------------------
% 46.66/7.37 owl_bool_complementof_class, owl_bool_intersectionof_class_000,
% 46.66/7.37 owl_bool_intersectionof_class_001, owl_bool_intersectionof_class_002,
% 46.66/7.37 owl_bool_intersectionof_class_003, owl_bool_unionof_class_000,
% 46.66/7.37 owl_bool_unionof_class_001, owl_bool_unionof_class_002,
% 46.66/7.37 owl_bool_unionof_class_003, owl_class_nothing_ext, owl_class_nothing_type,
% 46.66/7.37 owl_class_thing_ext, owl_class_thing_type, owl_parts_ic_cond_inst,
% 46.66/7.37 owl_parts_ic_cond_set, owl_parts_ic_def, owl_parts_idc_cond_inst,
% 46.66/7.37 owl_parts_idc_cond_set, owl_parts_idc_def, owl_parts_ioap_cond_inst,
% 46.66/7.37 owl_parts_ioap_cond_set, owl_parts_ioap_def, owl_parts_iodp_cond_inst,
% 46.66/7.37 owl_parts_iodp_cond_set, owl_parts_iodp_def, owl_parts_ioxp_cond_inst,
% 46.66/7.37 owl_parts_ioxp_cond_set, owl_parts_ioxp_def, owl_parts_ip_cond_inst,
% 46.66/7.37 owl_parts_ip_cond_set, owl_parts_ip_def, owl_parts_ir_cond_set,
% 46.66/7.37 owl_parts_ir_def, owl_parts_ix_cond_set, owl_parts_ix_def,
% 46.66/7.37 owl_parts_lv_cond_set, owl_parts_lv_def, owl_prop_allvaluesfrom_ext,
% 46.66/7.37 owl_prop_allvaluesfrom_type, owl_prop_complementof_ext,
% 46.66/7.37 owl_prop_complementof_type, owl_prop_hasvalue_ext, owl_prop_hasvalue_type,
% 46.66/7.37 owl_prop_intersectionof_ext, owl_prop_intersectionof_type,
% 46.66/7.37 owl_prop_onproperty_ext, owl_prop_onproperty_type, owl_prop_somevaluesfrom_ext,
% 46.66/7.37 owl_prop_somevaluesfrom_type, owl_prop_unionof_ext, owl_prop_unionof_type,
% 46.66/7.37 owl_rdfsext_domain, owl_rdfsext_range, owl_rdfsext_subclassof,
% 46.66/7.37 owl_rdfsext_subpropertyof, owl_restrict_allvaluesfrom, owl_restrict_hasvalue,
% 46.66/7.37 rdf_collection_first_type, rdf_collection_nil_type, rdf_collection_rest_type,
% 46.66/7.37 rdf_container_n_type_001, rdf_container_n_type_002, rdf_container_n_type_003,
% 46.66/7.37 rdf_reification_object_type, rdf_reification_predicate_type,
% 46.66/7.37 rdf_reification_subject_type, rdf_type_ip, rdf_type_type, rdf_value_type,
% 46.66/7.37 rdfs_annotation_comment_domain, rdfs_annotation_comment_range,
% 46.66/7.37 rdfs_annotation_isdefinedby_domain, rdfs_annotation_isdefinedby_range,
% 46.66/7.37 rdfs_annotation_isdefinedby_sub, rdfs_annotation_label_domain,
% 46.66/7.37 rdfs_annotation_label_range, rdfs_annotation_seealso_domain,
% 46.66/7.37 rdfs_annotation_seealso_range, rdfs_class_instsub_resource,
% 46.66/7.37 rdfs_collection_first_domain, rdfs_collection_first_range,
% 46.66/7.37 rdfs_collection_rest_domain, rdfs_collection_rest_range, rdfs_container_alt_sub,
% 46.66/7.37 rdfs_container_bag_sub,
% 46.66/7.37 rdfs_container_containermembershipproperty_instsub_member,
% 46.66/7.37 rdfs_container_containermembershipproperty_sub, rdfs_container_member_domain,
% 46.66/7.37 rdfs_container_member_range, rdfs_container_n_domain_001,
% 46.66/7.37 rdfs_container_n_domain_002, rdfs_container_n_domain_003,
% 46.66/7.37 rdfs_container_n_range_001, rdfs_container_n_range_002,
% 46.66/7.37 rdfs_container_n_range_003, rdfs_container_n_type_001,
% 46.66/7.37 rdfs_container_n_type_002, rdfs_container_n_type_003, rdfs_container_seq_sub,
% 46.66/7.37 rdfs_dat_xmlliteral_sub, rdfs_dat_xmlliteral_type,
% 46.66/7.37 rdfs_datatype_instsub_literal, rdfs_datatype_sub, rdfs_domain_domain,
% 46.66/7.37 rdfs_domain_main, rdfs_domain_range, rdfs_ic_def, rdfs_ir_def, rdfs_lv_def,
% 46.66/7.37 rdfs_property_type, rdfs_range_domain, rdfs_range_main, rdfs_range_range,
% 46.66/7.37 rdfs_reification_object_domain, rdfs_reification_object_range,
% 46.66/7.37 rdfs_reification_predicate_domain, rdfs_reification_predicate_range,
% 46.66/7.37 rdfs_reification_subject_domain, rdfs_reification_subject_range,
% 46.66/7.37 rdfs_subclassof_domain, rdfs_subclassof_main, rdfs_subclassof_range,
% 46.66/7.37 rdfs_subclassof_reflex, rdfs_subclassof_trans, rdfs_subpropertyof_domain,
% 46.66/7.37 rdfs_subpropertyof_main, rdfs_subpropertyof_range, rdfs_subpropertyof_reflex,
% 46.66/7.37 rdfs_subpropertyof_trans, rdfs_type_domain, rdfs_type_range, rdfs_value_domain,
% 46.66/7.37 rdfs_value_range, simple_iext_property, simple_ir, simple_lv
% 46.66/7.37
% 46.66/7.37 Those formulas are unsatisfiable:
% 46.66/7.37 ---------------------------------
% 46.66/7.37
% 46.66/7.37 Begin of proof
% 46.66/7.37 |
% 46.66/7.37 | ALPHA: (owl_restrict_somevaluesfrom) implies:
% 46.66/7.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 46.66/7.38 | (iext(uri_owl_someValuesFrom, v0, v2) = 0) | ~
% 46.66/7.38 | (iext(uri_owl_onProperty, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 46.66/7.38 | $i(v0) | ( ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (icext(v0, v3) =
% 46.66/7.38 | v4) | ~ $i(v3) | ! [v5: $i] : ( ~ (icext(v2, v5) = 0) | ~
% 46.66/7.38 | $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & iext(v1, v3, v5) = v6)))
% 46.66/7.38 | & ! [v3: $i] : ( ~ (icext(v0, v3) = 0) | ~ $i(v3) | ? [v4: $i] :
% 46.66/7.38 | (iext(v1, v3, v4) = 0 & icext(v2, v4) = 0 & $i(v4)))))
% 46.66/7.38 |
% 46.66/7.38 | ALPHA: (rdfs_cext_def) implies:
% 46.66/7.38 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | ~
% 46.66/7.38 | $i(v1) | ~ $i(v0) | icext(v1, v0) = 0)
% 46.66/7.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 46.66/7.38 | (iext(uri_rdf_type, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 46.66/7.38 | int] : ( ~ (v3 = 0) & icext(v1, v0) = v3))
% 46.66/7.38 |
% 46.66/7.38 | ALPHA: (testcase_premise_fullish_009_Existential_Restriction_Entailments)
% 46.66/7.38 | implies:
% 46.66/7.38 | (4) ? [v0: any] : ? [v1: any] : (iext(uri_rdf_type, uri_ex_c,
% 46.66/7.38 | uri_owl_Class) = v1 & iext(uri_rdf_type, uri_ex_p,
% 46.66/7.38 | uri_owl_ObjectProperty) = v0 & ? [v2: $i] : (v1 = 0 & v0 = 0 &
% 46.66/7.38 | iext(uri_owl_someValuesFrom, v2, uri_ex_c) = 0 &
% 46.66/7.38 | iext(uri_owl_onProperty, v2, uri_ex_p) = 0 & iext(uri_rdf_type, v2,
% 46.66/7.38 | uri_owl_Restriction) = 0 & iext(uri_rdf_type, uri_ex_s, v2) = 0 &
% 46.66/7.38 | $i(v2)))
% 46.66/7.38 |
% 46.66/7.38 | ALPHA: (testcase_conclusion_fullish_009_Existential_Restriction_Entailments)
% 46.66/7.38 | implies:
% 46.66/7.39 | (5) $i(uri_ex_p)
% 46.66/7.39 | (6) $i(uri_ex_s)
% 46.66/7.39 | (7) $i(uri_ex_c)
% 46.66/7.39 | (8) ! [v0: $i] : ( ~ (iext(uri_ex_p, uri_ex_s, v0) = 0) | ~ $i(v0) | ?
% 46.66/7.39 | [v1: int] : ( ~ (v1 = 0) & iext(uri_rdf_type, v0, uri_ex_c) = v1))
% 46.66/7.39 |
% 46.66/7.39 | ALPHA: (function-axioms) implies:
% 46.66/7.39 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 46.66/7.39 | ! [v3: $i] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) =
% 46.66/7.39 | v0))
% 46.66/7.39 |
% 46.66/7.39 | DELTA: instantiating (4) with fresh symbols all_74_0, all_74_1 gives:
% 46.66/7.39 | (10) iext(uri_rdf_type, uri_ex_c, uri_owl_Class) = all_74_0 &
% 46.66/7.39 | iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) = all_74_1 & ?
% 46.66/7.39 | [v0: $i] : (all_74_0 = 0 & all_74_1 = 0 & iext(uri_owl_someValuesFrom,
% 46.66/7.39 | v0, uri_ex_c) = 0 & iext(uri_owl_onProperty, v0, uri_ex_p) = 0 &
% 46.66/7.39 | iext(uri_rdf_type, v0, uri_owl_Restriction) = 0 & iext(uri_rdf_type,
% 46.66/7.39 | uri_ex_s, v0) = 0 & $i(v0))
% 46.66/7.39 |
% 46.66/7.39 | ALPHA: (10) implies:
% 46.66/7.39 | (11) ? [v0: $i] : (all_74_0 = 0 & all_74_1 = 0 &
% 46.66/7.39 | iext(uri_owl_someValuesFrom, v0, uri_ex_c) = 0 &
% 46.66/7.39 | iext(uri_owl_onProperty, v0, uri_ex_p) = 0 & iext(uri_rdf_type, v0,
% 46.66/7.39 | uri_owl_Restriction) = 0 & iext(uri_rdf_type, uri_ex_s, v0) = 0 &
% 46.66/7.39 | $i(v0))
% 46.66/7.39 |
% 46.66/7.39 | DELTA: instantiating (11) with fresh symbol all_76_0 gives:
% 46.66/7.39 | (12) all_74_0 = 0 & all_74_1 = 0 & iext(uri_owl_someValuesFrom, all_76_0,
% 46.66/7.39 | uri_ex_c) = 0 & iext(uri_owl_onProperty, all_76_0, uri_ex_p) = 0 &
% 46.66/7.39 | iext(uri_rdf_type, all_76_0, uri_owl_Restriction) = 0 &
% 46.66/7.39 | iext(uri_rdf_type, uri_ex_s, all_76_0) = 0 & $i(all_76_0)
% 46.66/7.39 |
% 46.66/7.40 | ALPHA: (12) implies:
% 46.66/7.40 | (13) $i(all_76_0)
% 46.66/7.40 | (14) iext(uri_rdf_type, uri_ex_s, all_76_0) = 0
% 46.66/7.40 | (15) iext(uri_owl_onProperty, all_76_0, uri_ex_p) = 0
% 46.66/7.40 | (16) iext(uri_owl_someValuesFrom, all_76_0, uri_ex_c) = 0
% 46.66/7.40 |
% 46.66/7.40 | GROUND_INST: instantiating (2) with uri_ex_s, all_76_0, simplifying with (6),
% 46.66/7.40 | (13), (14) gives:
% 46.66/7.40 | (17) icext(all_76_0, uri_ex_s) = 0
% 46.66/7.40 |
% 46.66/7.40 | GROUND_INST: instantiating (1) with all_76_0, uri_ex_p, uri_ex_c, simplifying
% 46.66/7.40 | with (5), (7), (13), (15), (16) gives:
% 46.66/7.40 | (18) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (icext(all_76_0, v0) = v1) |
% 46.66/7.40 | ~ $i(v0) | ! [v2: $i] : ( ~ (icext(uri_ex_c, v2) = 0) | ~ $i(v2)
% 46.66/7.40 | | ? [v3: int] : ( ~ (v3 = 0) & iext(uri_ex_p, v0, v2) = v3))) &
% 46.66/7.40 | ! [v0: $i] : ( ~ (icext(all_76_0, v0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 46.66/7.40 | (iext(uri_ex_p, v0, v1) = 0 & icext(uri_ex_c, v1) = 0 & $i(v1)))
% 46.66/7.40 |
% 46.66/7.40 | ALPHA: (18) implies:
% 46.66/7.40 | (19) ! [v0: $i] : ( ~ (icext(all_76_0, v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 46.66/7.40 | : (iext(uri_ex_p, v0, v1) = 0 & icext(uri_ex_c, v1) = 0 & $i(v1)))
% 46.66/7.40 |
% 46.66/7.40 | GROUND_INST: instantiating (19) with uri_ex_s, simplifying with (6), (17)
% 46.66/7.40 | gives:
% 46.66/7.40 | (20) ? [v0: $i] : (iext(uri_ex_p, uri_ex_s, v0) = 0 & icext(uri_ex_c, v0)
% 46.66/7.40 | = 0 & $i(v0))
% 46.66/7.40 |
% 46.66/7.40 | DELTA: instantiating (20) with fresh symbol all_182_0 gives:
% 46.66/7.40 | (21) iext(uri_ex_p, uri_ex_s, all_182_0) = 0 & icext(uri_ex_c, all_182_0) =
% 46.66/7.40 | 0 & $i(all_182_0)
% 46.66/7.40 |
% 46.66/7.40 | ALPHA: (21) implies:
% 46.66/7.41 | (22) $i(all_182_0)
% 46.66/7.41 | (23) icext(uri_ex_c, all_182_0) = 0
% 46.66/7.41 | (24) iext(uri_ex_p, uri_ex_s, all_182_0) = 0
% 46.66/7.41 |
% 46.66/7.41 | GROUND_INST: instantiating (8) with all_182_0, simplifying with (22), (24)
% 46.66/7.41 | gives:
% 46.66/7.41 | (25) ? [v0: int] : ( ~ (v0 = 0) & iext(uri_rdf_type, all_182_0, uri_ex_c)
% 46.66/7.41 | = v0)
% 46.66/7.41 |
% 46.66/7.41 | DELTA: instantiating (25) with fresh symbol all_194_0 gives:
% 46.66/7.41 | (26) ~ (all_194_0 = 0) & iext(uri_rdf_type, all_182_0, uri_ex_c) =
% 46.66/7.41 | all_194_0
% 46.66/7.41 |
% 46.66/7.41 | ALPHA: (26) implies:
% 46.66/7.41 | (27) ~ (all_194_0 = 0)
% 46.66/7.41 | (28) iext(uri_rdf_type, all_182_0, uri_ex_c) = all_194_0
% 46.66/7.41 |
% 46.66/7.41 | GROUND_INST: instantiating (3) with all_182_0, uri_ex_c, all_194_0,
% 46.66/7.41 | simplifying with (7), (22), (28) gives:
% 46.66/7.41 | (29) all_194_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & icext(uri_ex_c,
% 46.66/7.41 | all_182_0) = v0)
% 46.66/7.41 |
% 46.66/7.41 | BETA: splitting (29) gives:
% 46.66/7.41 |
% 46.66/7.41 | Case 1:
% 46.66/7.41 | |
% 46.66/7.41 | | (30) all_194_0 = 0
% 46.66/7.41 | |
% 46.66/7.41 | | REDUCE: (27), (30) imply:
% 46.66/7.41 | | (31) $false
% 46.66/7.41 | |
% 46.66/7.41 | | CLOSE: (31) is inconsistent.
% 46.66/7.41 | |
% 46.66/7.41 | Case 2:
% 46.66/7.41 | |
% 47.34/7.41 | | (32) ? [v0: int] : ( ~ (v0 = 0) & icext(uri_ex_c, all_182_0) = v0)
% 47.34/7.41 | |
% 47.34/7.41 | | DELTA: instantiating (32) with fresh symbol all_206_0 gives:
% 47.34/7.41 | | (33) ~ (all_206_0 = 0) & icext(uri_ex_c, all_182_0) = all_206_0
% 47.34/7.41 | |
% 47.34/7.41 | | ALPHA: (33) implies:
% 47.34/7.41 | | (34) ~ (all_206_0 = 0)
% 47.34/7.41 | | (35) icext(uri_ex_c, all_182_0) = all_206_0
% 47.34/7.41 | |
% 47.34/7.41 | | GROUND_INST: instantiating (9) with 0, all_206_0, all_182_0, uri_ex_c,
% 47.34/7.41 | | simplifying with (23), (35) gives:
% 47.34/7.41 | | (36) all_206_0 = 0
% 47.34/7.41 | |
% 47.34/7.41 | | REDUCE: (34), (36) imply:
% 47.34/7.41 | | (37) $false
% 47.34/7.41 | |
% 47.34/7.41 | | CLOSE: (37) is inconsistent.
% 47.34/7.41 | |
% 47.34/7.41 | End of split
% 47.34/7.41 |
% 47.34/7.41 End of proof
% 47.34/7.41 % SZS output end Proof for theBenchmark
% 47.34/7.41
% 47.34/7.41 6825ms
%------------------------------------------------------------------------------