TSTP Solution File: SWB012+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWB012+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 : 600s
% DateTime : Tue Jul 19 18:59:37 EDT 2022
% Result : Theorem 2.98s 1.39s
% Output : Proof 4.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWB012+2 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 1 05:35:00 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.58/0.62 ____ _
% 0.58/0.62 ___ / __ \_____(_)___ ________ __________
% 0.58/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.62
% 0.58/0.62 A Theorem Prover for First-Order Logic
% 0.58/0.62 (ePrincess v.1.0)
% 0.58/0.62
% 0.58/0.62 (c) Philipp Rümmer, 2009-2015
% 0.58/0.62 (c) Peter Backeman, 2014-2015
% 0.58/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.62 Bug reports to peter@backeman.se
% 0.58/0.62
% 0.58/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.62
% 0.58/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.97 Prover 0: Preprocessing ...
% 1.90/1.16 Prover 0: Constructing countermodel ...
% 2.98/1.39 Prover 0: proved (719ms)
% 2.98/1.39
% 2.98/1.39 No countermodel exists, formula is valid
% 2.98/1.39 % SZS status Theorem for theBenchmark
% 2.98/1.39
% 2.98/1.39 Generating proof ... found it (size 13)
% 4.01/1.65
% 4.01/1.65 % SZS output start Proof for theBenchmark
% 4.01/1.65 Assumed formulas after preprocessing and simplification:
% 4.01/1.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (literal_plain(dat_str_alice) = v0 & iext(uri_ex_name, uri_ex_alice, v0) & iext(uri_owl_onProperty, v4, uri_rdfs_domain) & iext(uri_owl_hasValue, v4, uri_foaf_Person) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, v1) & iext(uri_rdf_rest, v3, uri_rdf_nil) & iext(uri_rdf_rest, v2, v3) & iext(uri_rdf_rest, v1, v2) & iext(uri_rdf_first, v3, v4) & iext(uri_rdf_first, v2, uri_owl_FunctionalProperty) & iext(uri_rdf_first, v1, uri_owl_DatatypeProperty) & iext(uri_rdf_type, v4, uri_owl_Restriction) & iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ icext(v11, v12) | ~ icext(v9, v12) | ~ icext(v7, v12) | ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | icext(v5, v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ icext(v5, v12) | ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | icext(v11, v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ icext(v5, v12) | ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | icext(v9, v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ icext(v5, v12) | ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | icext(v7, v12)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ ic(v11) | ~ ic(v9) | ~ ic(v7) | ~ ic(v5) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | iext(uri_owl_intersectionOf, v5, v6) | ? [v12] : (( ~ icext(v11, v12) | ~ icext(v9, v12) | ~ icext(v7, v12) | ~ icext(v5, v12)) & (icext(v5, v12) | (icext(v11, v12) & icext(v9, v12) & icext(v7, v12))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | ic(v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | ic(v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | ic(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ iext(uri_owl_intersectionOf, v5, v6) | ~ iext(uri_rdf_rest, v10, uri_rdf_nil) | ~ iext(uri_rdf_rest, v8, v10) | ~ iext(uri_rdf_rest, v6, v8) | ~ iext(uri_rdf_first, v10, v11) | ~ iext(uri_rdf_first, v8, v9) | ~ iext(uri_rdf_first, v6, v7) | ic(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ icext(v5, v8) | ~ iext(uri_owl_onProperty, v5, v6) | ~ iext(uri_owl_hasValue, v5, v7) | iext(v6, v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ iext(v6, v8, v7) | ~ iext(uri_owl_onProperty, v5, v6) | ~ iext(uri_owl_hasValue, v5, v7) | icext(v5, v8)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ iext(v5, v7, v8) | ~ iext(uri_rdfs_domain, v5, v6) | icext(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (literal_plain(v7) = v6) | ~ (literal_plain(v7) = v5)) & ! [v5] : ! [v6] : ( ~ icext(v6, v5) | iext(uri_rdf_type, v5, v6)) & ! [v5] : ! [v6] : ( ~ iext(uri_rdf_type, v5, v6) | icext(v6, v5)) & ( ~ iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) | ~ iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)))
% 4.34/1.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 4.34/1.70 | (1) literal_plain(dat_str_alice) = all_0_4_4 & iext(uri_ex_name, uri_ex_alice, all_0_4_4) & iext(uri_owl_onProperty, all_0_0_0, uri_rdfs_domain) & iext(uri_owl_hasValue, all_0_0_0, uri_foaf_Person) & iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, all_0_3_3) & iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil) & iext(uri_rdf_rest, all_0_2_2, all_0_1_1) & iext(uri_rdf_rest, all_0_3_3, all_0_2_2) & iext(uri_rdf_first, all_0_1_1, all_0_0_0) & iext(uri_rdf_first, all_0_2_2, uri_owl_FunctionalProperty) & iext(uri_rdf_first, all_0_3_3, uri_owl_DatatypeProperty) & iext(uri_rdf_type, all_0_0_0, uri_owl_Restriction) & iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class) & iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v6, v7) | ~ icext(v4, v7) | ~ icext(v2, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v0, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v6, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v4, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v2, v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ ic(v6) | ~ ic(v4) | ~ ic(v2) | ~ ic(v0) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_intersectionOf, v0, v1) | ? [v7] : (( ~ icext(v6, v7) | ~ icext(v4, v7) | ~ icext(v2, v7) | ~ icext(v0, v7)) & (icext(v0, v7) | (icext(v6, v7) & icext(v4, v7) & icext(v2, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ icext(v0, v3) | ~ iext(uri_owl_onProperty, v0, v1) | ~ iext(uri_owl_hasValue, v0, v2) | iext(v1, v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v1, v3, v2) | ~ iext(uri_owl_onProperty, v0, v1) | ~ iext(uri_owl_hasValue, v0, v2) | icext(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_rdfs_domain, v0, v1) | icext(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (literal_plain(v2) = v1) | ~ (literal_plain(v2) = v0)) & ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1)) & ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0)) & ( ~ iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) | ~ iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty))
% 4.34/1.71 |
% 4.34/1.71 | Applying alpha-rule on (1) yields:
% 4.34/1.72 | (2) iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil)
% 4.34/1.72 | (3) iext(uri_owl_hasValue, all_0_0_0, uri_foaf_Person)
% 4.34/1.72 | (4) ~ iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person) | ~ iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)
% 4.34/1.72 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v2))
% 4.34/1.72 | (6) iext(uri_rdf_first, all_0_1_1, all_0_0_0)
% 4.34/1.72 | (7) iext(uri_rdf_rest, all_0_2_2, all_0_1_1)
% 4.34/1.72 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v0))
% 4.34/1.72 | (9) iext(uri_rdf_first, all_0_2_2, uri_owl_FunctionalProperty)
% 4.34/1.72 | (10) iext(uri_rdf_first, all_0_3_3, uri_owl_DatatypeProperty)
% 4.34/1.72 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ icext(v0, v3) | ~ iext(uri_owl_onProperty, v0, v1) | ~ iext(uri_owl_hasValue, v0, v2) | iext(v1, v3, v2))
% 4.34/1.72 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v6, v7) | ~ icext(v4, v7) | ~ icext(v2, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v0, v7))
% 4.34/1.72 | (13) iext(uri_owl_onProperty, all_0_0_0, uri_rdfs_domain)
% 4.34/1.72 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v2, v7))
% 4.34/1.72 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v1, v3, v2) | ~ iext(uri_owl_onProperty, v0, v1) | ~ iext(uri_owl_hasValue, v0, v2) | icext(v0, v3))
% 4.34/1.72 | (16) iext(uri_rdf_type, uri_foaf_Person, uri_owl_Class)
% 4.34/1.72 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ ic(v6) | ~ ic(v4) | ~ ic(v2) | ~ ic(v0) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_intersectionOf, v0, v1) | ? [v7] : (( ~ icext(v6, v7) | ~ icext(v4, v7) | ~ icext(v2, v7) | ~ icext(v0, v7)) & (icext(v0, v7) | (icext(v6, v7) & icext(v4, v7) & icext(v2, v7)))))
% 4.34/1.72 | (18) iext(uri_rdf_rest, all_0_3_3, all_0_2_2)
% 4.34/1.72 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v4))
% 4.34/1.72 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v4, v7))
% 4.34/1.73 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ icext(v0, v7) | ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | icext(v6, v7))
% 4.34/1.73 | (22) iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute)
% 4.34/1.73 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_rdfs_domain, v0, v1) | icext(v1, v2))
% 4.34/1.73 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_intersectionOf, v0, v1) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_rest, v3, v5) | ~ iext(uri_rdf_rest, v1, v3) | ~ iext(uri_rdf_first, v5, v6) | ~ iext(uri_rdf_first, v3, v4) | ~ iext(uri_rdf_first, v1, v2) | ic(v6))
% 4.34/1.73 | (25) iext(uri_rdf_type, all_0_0_0, uri_owl_Restriction)
% 4.34/1.73 | (26) iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, all_0_3_3)
% 4.34/1.73 | (27) ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0))
% 4.34/1.73 | (28) ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1))
% 4.34/1.73 | (29) iext(uri_ex_name, uri_ex_alice, all_0_4_4)
% 4.34/1.73 | (30) literal_plain(dat_str_alice) = all_0_4_4
% 4.34/1.73 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (literal_plain(v2) = v1) | ~ (literal_plain(v2) = v0))
% 4.34/1.73 |
% 4.34/1.73 | Instantiating formula (27) with uri_ex_PersonAttribute, uri_ex_name and discharging atoms iext(uri_rdf_type, uri_ex_name, uri_ex_PersonAttribute), yields:
% 4.34/1.73 | (32) icext(uri_ex_PersonAttribute, uri_ex_name)
% 4.34/1.73 |
% 4.34/1.73 | Instantiating formula (21) with uri_ex_name, all_0_0_0, all_0_1_1, uri_owl_FunctionalProperty, all_0_2_2, uri_owl_DatatypeProperty, all_0_3_3, uri_ex_PersonAttribute and discharging atoms icext(uri_ex_PersonAttribute, uri_ex_name), iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, all_0_3_3), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_rest, all_0_3_3, all_0_2_2), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_owl_FunctionalProperty), iext(uri_rdf_first, all_0_3_3, uri_owl_DatatypeProperty), yields:
% 4.34/1.73 | (33) icext(all_0_0_0, uri_ex_name)
% 4.34/1.73 |
% 4.34/1.73 | Instantiating formula (20) with uri_ex_name, all_0_0_0, all_0_1_1, uri_owl_FunctionalProperty, all_0_2_2, uri_owl_DatatypeProperty, all_0_3_3, uri_ex_PersonAttribute and discharging atoms icext(uri_ex_PersonAttribute, uri_ex_name), iext(uri_owl_intersectionOf, uri_ex_PersonAttribute, all_0_3_3), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_rest, all_0_3_3, all_0_2_2), iext(uri_rdf_first, all_0_1_1, all_0_0_0), iext(uri_rdf_first, all_0_2_2, uri_owl_FunctionalProperty), iext(uri_rdf_first, all_0_3_3, uri_owl_DatatypeProperty), yields:
% 4.34/1.73 | (34) icext(uri_owl_FunctionalProperty, uri_ex_name)
% 4.34/1.73 |
% 4.34/1.73 | Instantiating formula (11) with uri_ex_name, uri_foaf_Person, uri_rdfs_domain, all_0_0_0 and discharging atoms icext(all_0_0_0, uri_ex_name), iext(uri_owl_onProperty, all_0_0_0, uri_rdfs_domain), iext(uri_owl_hasValue, all_0_0_0, uri_foaf_Person), yields:
% 4.34/1.73 | (35) iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person)
% 4.34/1.73 |
% 4.34/1.73 | Instantiating formula (28) with uri_owl_FunctionalProperty, uri_ex_name and discharging atoms icext(uri_owl_FunctionalProperty, uri_ex_name), yields:
% 4.34/1.73 | (36) iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)
% 4.34/1.73 |
% 4.34/1.73 +-Applying beta-rule and splitting (4), into two cases.
% 4.34/1.73 |-Branch one:
% 4.34/1.73 | (37) ~ iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)
% 4.34/1.74 |
% 4.34/1.74 | Instantiating formula (23) with all_0_4_4, uri_ex_alice, uri_foaf_Person, uri_ex_name and discharging atoms iext(uri_ex_name, uri_ex_alice, all_0_4_4), iext(uri_rdfs_domain, uri_ex_name, uri_foaf_Person), yields:
% 4.34/1.74 | (38) icext(uri_foaf_Person, uri_ex_alice)
% 4.34/1.74 |
% 4.34/1.74 | Instantiating formula (28) with uri_foaf_Person, uri_ex_alice and discharging atoms icext(uri_foaf_Person, uri_ex_alice), ~ iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person), yields:
% 4.34/1.74 | (39) $false
% 4.34/1.74 |
% 4.34/1.74 |-The branch is then unsatisfiable
% 4.34/1.74 |-Branch two:
% 4.34/1.74 | (40) iext(uri_rdf_type, uri_ex_alice, uri_foaf_Person)
% 4.34/1.74 | (41) ~ iext(uri_rdf_type, uri_ex_name, uri_owl_FunctionalProperty)
% 4.34/1.74 |
% 4.34/1.74 | Using (36) and (41) yields:
% 4.34/1.74 | (39) $false
% 4.34/1.74 |
% 4.34/1.74 |-The branch is then unsatisfiable
% 4.34/1.74 % SZS output end Proof for theBenchmark
% 4.34/1.74
% 4.34/1.74 1111ms
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