%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWB004+2 : TPTP v8.1.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n023.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 18:59:34 EDT 2022 % Result : Theorem 19.57s 6.31s % Output : Proof 22.14s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWB004+2 : TPTP v8.1.0. Released v5.2.0. % 0.12/0.14 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.35 % Computer : n023.cluster.edu % 0.15/0.35 % Model : x86_64 x86_64 % 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.35 % Memory : 8042.1875MB % 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.35 % CPULimit : 300 % 0.15/0.35 % WCLimit : 600 % 0.15/0.35 % DateTime : Wed Jun 1 11:58:26 EDT 2022 % 0.15/0.36 % CPUTime : % 0.57/0.61 ____ _ % 0.57/0.61 ___ / __ \_____(_)___ ________ __________ % 0.57/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.57/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.57/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.57/0.61 % 0.57/0.61 A Theorem Prover for First-Order Logic % 0.57/0.61 (ePrincess v.1.0) % 0.57/0.61 % 0.57/0.61 (c) Philipp Rümmer, 2009-2015 % 0.57/0.61 (c) Peter Backeman, 2014-2015 % 0.57/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.57/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.57/0.61 Bug reports to peter@backeman.se % 0.57/0.61 % 0.57/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.57/0.61 % 0.57/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.49/0.96 Prover 0: Preprocessing ... % 1.85/1.08 Prover 0: Warning: ignoring some quantifiers % 1.85/1.10 Prover 0: Constructing countermodel ... % 17.90/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 17.90/5.99 Prover 1: Preprocessing ... % 18.60/6.14 Prover 1: Constructing countermodel ... % 19.50/6.30 Prover 1: proved (349ms) % 19.50/6.31 Prover 0: stopped % 19.50/6.31 % 19.57/6.31 No countermodel exists, formula is valid % 19.57/6.31 % SZS status Theorem for theBenchmark % 19.57/6.31 % 19.57/6.31 Generating proof ... found it (size 237) % 21.76/6.87 % 21.76/6.87 % SZS output start Proof for theBenchmark % 21.76/6.87 Assumed formulas after preprocessing and simplification: % 21.76/6.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (ic(uri_owl_Thing) = 0 & ic(uri_rdfs_Datatype) = 0 & ic(uri_rdfs_Class) = 0 & ic(uri_owl_Class) = 0 & iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = v3 & iext(uri_rdfs_subClassOf, uri_rdfs_Datatype, uri_owl_Class) = v4 & iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = v2 & iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = v0 & iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = v1 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (iext(v9, v8, v7) = v6) | ~ (iext(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (iext(uri_owl_equivalentClass, v5, v6) = 0) | ~ (icext(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & icext(v6, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (icext(v8, v7) = v6) | ~ (icext(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (iext(uri_owl_equivalentClass, v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((ic(v6) = v9 & ic(v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))) | (icext(v6, v8) = v10 & icext(v5, v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)) & (v10 = 0 | v9 = 0)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (iext(uri_rdfs_subClassOf, v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & icext(v6, v8) = v10 & icext(v5, v8) = 0) | (ic(v6) = v9 & ic(v5) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0))))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (iext(uri_rdf_type, v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & icext(v6, v5) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (idc(v7) = v6) | ~ (idc(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (ic(v7) = v6) | ~ (ic(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (ir(v7) = v6) | ~ (ir(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (iext(uri_owl_equivalentClass, v5, v6) = 0) | ~ (icext(v5, v7) = 0) | icext(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (iext(uri_rdfs_subClassOf, v5, v6) = 0) | ~ (icext(v5, v7) = 0) | icext(v6, v7) = 0) & ! [v5] : ! [v6] : (v6 = 0 | ~ (icext(uri_owl_Thing, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & ir(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (icext(uri_rdfs_Datatype, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & idc(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (icext(uri_rdfs_Class, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & ic(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (icext(uri_owl_Class, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & ic(v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (ir(v5) = v6)) & ! [v5] : ! [v6] : ( ~ (iext(uri_owl_equivalentClass, v5, v6) = 0) | (ic(v6) = 0 & ic(v5) = 0)) & ! [v5] : ! [v6] : ( ~ (iext(uri_rdfs_subClassOf, v5, v6) = 0) | (ic(v6) = 0 & ic(v5) = 0)) & ! [v5] : ! [v6] : ( ~ (iext(uri_rdf_type, v5, v6) = 0) | icext(v6, v5) = 0) & ! [v5] : ( ~ (idc(v5) = 0) | ic(v5) = 0) & ! [v5] : ( ~ (icext(uri_owl_Thing, v5) = 0) | ir(v5) = 0) & ! [v5] : ( ~ (icext(uri_rdfs_Datatype, v5) = 0) | idc(v5) = 0) & ! [v5] : ( ~ (icext(uri_rdfs_Class, v5) = 0) | ic(v5) = 0) & ! [v5] : ( ~ (icext(uri_owl_Class, v5) = 0) | ic(v5) = 0) & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 22.14/6.91 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 22.14/6.91 | (1) ic(uri_owl_Thing) = 0 & ic(uri_rdfs_Datatype) = 0 & ic(uri_rdfs_Class) = 0 & ic(uri_owl_Class) = 0 & iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = all_0_1_1 & iext(uri_rdfs_subClassOf, uri_rdfs_Datatype, uri_owl_Class) = all_0_0_0 & iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_2_2 & iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4 & iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_3_3 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ (icext(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & icext(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_owl_equivalentClass, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (icext(v1, v3) = v5 & icext(v0, v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & icext(v1, v3) = v5 & icext(v0, v3) = 0) | (ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (idc(v2) = v1) | ~ (idc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ir(v2) = v1) | ~ (ir(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ (icext(v0, v2) = 0) | icext(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ (icext(v0, v2) = 0) | icext(v1, v2) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Thing, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Datatype, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & idc(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Class, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ic(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Class, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ic(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ir(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | (ic(v1) = 0 & ic(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (iext(uri_rdfs_subClassOf, v0, v1) = 0) | (ic(v1) = 0 & ic(v0) = 0)) & ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0) & ! [v0] : ( ~ (idc(v0) = 0) | ic(v0) = 0) & ! [v0] : ( ~ (icext(uri_owl_Thing, v0) = 0) | ir(v0) = 0) & ! [v0] : ( ~ (icext(uri_rdfs_Datatype, v0) = 0) | idc(v0) = 0) & ! [v0] : ( ~ (icext(uri_rdfs_Class, v0) = 0) | ic(v0) = 0) & ! [v0] : ( ~ (icext(uri_owl_Class, v0) = 0) | ic(v0) = 0) & ( ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0)) % 22.14/6.91 | % 22.14/6.91 | Applying alpha-rule on (1) yields: % 22.14/6.92 | (2) ! [v0] : ( ~ (idc(v0) = 0) | ic(v0) = 0) % 22.14/6.92 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(uri_rdfs_subClassOf, v0, v1) = 0) | ~ (icext(v0, v2) = 0) | icext(v1, v2) = 0) % 22.14/6.92 | (4) ! [v0] : ( ~ (icext(uri_owl_Thing, v0) = 0) | ir(v0) = 0) % 22.14/6.92 | (5) ~ (all_0_0_0 = 0) | ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) % 22.14/6.92 | (6) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Class, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ic(v0) = v2)) % 22.14/6.92 | (7) ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0) % 22.14/6.92 | (8) ! [v0] : ( ~ (icext(uri_owl_Class, v0) = 0) | ic(v0) = 0) % 22.14/6.92 | (9) ic(uri_owl_Thing) = 0 % 22.14/6.92 | (10) ! [v0] : ! [v1] : ( ~ (iext(uri_rdfs_subClassOf, v0, v1) = 0) | (ic(v1) = 0 & ic(v0) = 0)) % 22.14/6.92 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) % 22.14/6.92 | (12) ic(uri_rdfs_Datatype) = 0 % 22.14/6.92 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ir(v2) = v1) | ~ (ir(v2) = v0)) % 22.14/6.92 | (14) ic(uri_rdfs_Class) = 0 % 22.14/6.92 | (15) iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = all_0_1_1 % 22.14/6.92 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (idc(v2) = v1) | ~ (idc(v2) = v0)) % 22.14/6.92 | (17) ic(uri_owl_Class) = 0 % 22.14/6.92 | (18) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Datatype, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & idc(v0) = v2)) % 22.14/6.92 | (19) ! [v0] : ! [v1] : ( ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | (ic(v1) = 0 & ic(v0) = 0)) % 22.14/6.92 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_owl_equivalentClass, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (icext(v1, v3) = v5 & icext(v0, v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))) % 22.14/6.92 | (21) iext(uri_rdfs_subClassOf, uri_rdfs_Datatype, uri_owl_Class) = all_0_0_0 % 22.14/6.92 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ (icext(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & icext(v1, v2) = v4)) % 22.14/6.92 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(uri_owl_equivalentClass, v0, v1) = 0) | ~ (icext(v0, v2) = 0) | icext(v1, v2) = 0) % 22.14/6.92 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0)) % 22.14/6.92 | (25) iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_3_3 % 22.14/6.92 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ic(v2) = v1) | ~ (ic(v2) = v0)) % 22.14/6.92 | (27) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdfs_subClassOf, v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v4 = 0 & ~ (v5 = 0) & icext(v1, v3) = v5 & icext(v0, v3) = 0) | (ic(v1) = v4 & ic(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) % 22.14/6.92 | (28) ! [v0] : ( ~ (icext(uri_rdfs_Datatype, v0) = 0) | idc(v0) = 0) % 22.14/6.92 | (29) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4 % 22.14/6.92 | (30) ! [v0] : ! [v1] : (v1 = 0 | ~ (ir(v0) = v1)) % 22.14/6.92 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Class, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ic(v0) = v2)) % 22.14/6.92 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) % 22.14/6.92 | (33) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Thing, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2)) % 22.14/6.92 | (34) iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_2_2 % 22.14/6.92 | (35) ! [v0] : ( ~ (icext(uri_rdfs_Class, v0) = 0) | ic(v0) = 0) % 22.14/6.92 | % 22.14/6.92 | Instantiating formula (24) with uri_rdf_type, uri_owl_Class, uri_owl_Thing, all_0_4_4, all_0_2_2 and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4, yields: % 22.14/6.92 | (36) all_0_2_2 = all_0_4_4 | ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2) % 22.14/6.92 | % 22.14/6.92 | Instantiating formula (24) with uri_rdf_type, uri_owl_Class, uri_owl_Class, all_0_3_3, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_3_3, yields: % 22.14/6.92 | (37) all_0_3_3 = all_0_4_4 | ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_4_4) % 22.14/6.92 | % 22.14/6.92 | Instantiating formula (20) with all_0_1_1, uri_rdfs_Class, uri_owl_Class and discharging atoms iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = all_0_1_1, yields: % 22.14/6.92 | (38) all_0_1_1 = 0 | ? [v0] : ? [v1] : ? [v2] : ((ic(uri_rdfs_Class) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (icext(uri_rdfs_Class, v0) = v2 & icext(uri_owl_Class, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))) % 22.14/6.92 | % 22.14/6.92 | Instantiating formula (27) with all_0_0_0, uri_owl_Class, uri_rdfs_Datatype and discharging atoms iext(uri_rdfs_subClassOf, uri_rdfs_Datatype, uri_owl_Class) = all_0_0_0, yields: % 22.14/6.92 | (39) all_0_0_0 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_rdfs_Datatype, v0) = 0 & icext(uri_owl_Class, v0) = v2) | (ic(uri_rdfs_Datatype) = v0 & ic(uri_owl_Class) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (27) with all_0_2_2, uri_owl_Thing, uri_owl_Class and discharging atoms iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_2_2, yields: % 22.14/6.93 | (40) all_0_2_2 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (11) with all_0_2_2, uri_owl_Thing, uri_owl_Class yields: % 22.14/6.93 | (41) all_0_2_2 = 0 | ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2) | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (7) with uri_owl_Thing, uri_owl_Class yields: % 22.14/6.93 | (42) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0) | icext(uri_owl_Thing, uri_owl_Class) = 0 % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (27) with all_0_4_4, uri_owl_Thing, uri_owl_Class yields: % 22.14/6.93 | (43) all_0_4_4 = 0 | ~ (iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_4_4) | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (11) with all_0_4_4, uri_owl_Thing, uri_owl_Class and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4, yields: % 22.14/6.93 | (44) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (7) with uri_owl_Class, uri_owl_Class yields: % 22.14/6.93 | (45) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0) | icext(uri_owl_Class, uri_owl_Class) = 0 % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (11) with all_0_3_3, uri_owl_Class, uri_owl_Class and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_3_3, yields: % 22.14/6.93 | (46) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Class, uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (45), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (47) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0) % 22.14/6.93 | % 22.14/6.93 | Using (25) and (47) yields: % 22.14/6.93 | (48) ~ (all_0_3_3 = 0) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (46), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (49) all_0_3_3 = 0 % 22.14/6.93 | % 22.14/6.93 | Equations (49) can reduce 48 to: % 22.14/6.93 | (50) $false % 22.14/6.93 | % 22.14/6.93 |-The branch is then unsatisfiable % 22.14/6.93 |-Branch two: % 22.14/6.93 | (48) ~ (all_0_3_3 = 0) % 22.14/6.93 | (52) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Class, uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 | Instantiating (52) with all_18_0_5 yields: % 22.14/6.93 | (53) ~ (all_18_0_5 = 0) & icext(uri_owl_Class, uri_owl_Class) = all_18_0_5 % 22.14/6.93 | % 22.14/6.93 | Applying alpha-rule on (53) yields: % 22.14/6.93 | (54) ~ (all_18_0_5 = 0) % 22.14/6.93 | (55) icext(uri_owl_Class, uri_owl_Class) = all_18_0_5 % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (31) with all_18_0_5, uri_owl_Class and discharging atoms icext(uri_owl_Class, uri_owl_Class) = all_18_0_5, yields: % 22.14/6.93 | (56) all_18_0_5 = 0 | ? [v0] : ( ~ (v0 = 0) & ic(uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (56), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (57) all_18_0_5 = 0 % 22.14/6.93 | % 22.14/6.93 | Equations (57) can reduce 54 to: % 22.14/6.93 | (50) $false % 22.14/6.93 | % 22.14/6.93 |-The branch is then unsatisfiable % 22.14/6.93 |-Branch two: % 22.14/6.93 | (54) ~ (all_18_0_5 = 0) % 22.14/6.93 | (60) ? [v0] : ( ~ (v0 = 0) & ic(uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 | Instantiating (60) with all_31_0_6 yields: % 22.14/6.93 | (61) ~ (all_31_0_6 = 0) & ic(uri_owl_Class) = all_31_0_6 % 22.14/6.93 | % 22.14/6.93 | Applying alpha-rule on (61) yields: % 22.14/6.93 | (62) ~ (all_31_0_6 = 0) % 22.14/6.93 | (63) ic(uri_owl_Class) = all_31_0_6 % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (26) with uri_owl_Class, all_31_0_6, 0 and discharging atoms ic(uri_owl_Class) = all_31_0_6, ic(uri_owl_Class) = 0, yields: % 22.14/6.93 | (64) all_31_0_6 = 0 % 22.14/6.93 | % 22.14/6.93 | Equations (64) can reduce 62 to: % 22.14/6.93 | (50) $false % 22.14/6.93 | % 22.14/6.93 |-The branch is then unsatisfiable % 22.14/6.93 |-Branch two: % 22.14/6.93 | (66) iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0 % 22.14/6.93 | (67) icext(uri_owl_Class, uri_owl_Class) = 0 % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (46), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (49) all_0_3_3 = 0 % 22.14/6.93 | % 22.14/6.93 | From (49) and (25) follows: % 22.14/6.93 | (66) iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0 % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (36), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (70) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2) % 22.14/6.93 | % 22.14/6.93 | Using (29) and (70) yields: % 22.14/6.93 | (71) ~ (all_0_2_2 = all_0_4_4) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (42), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (72) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0) % 22.14/6.93 | % 22.14/6.93 | Using (29) and (72) yields: % 22.14/6.93 | (73) ~ (all_0_4_4 = 0) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (44), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (74) all_0_4_4 = 0 % 22.14/6.93 | % 22.14/6.93 | Equations (74) can reduce 73 to: % 22.14/6.93 | (50) $false % 22.14/6.93 | % 22.14/6.93 |-The branch is then unsatisfiable % 22.14/6.93 |-Branch two: % 22.14/6.93 | (73) ~ (all_0_4_4 = 0) % 22.14/6.93 | (77) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 | Instantiating (77) with all_40_0_7 yields: % 22.14/6.93 | (78) ~ (all_40_0_7 = 0) & icext(uri_owl_Thing, uri_owl_Class) = all_40_0_7 % 22.14/6.93 | % 22.14/6.93 | Applying alpha-rule on (78) yields: % 22.14/6.93 | (79) ~ (all_40_0_7 = 0) % 22.14/6.93 | (80) icext(uri_owl_Thing, uri_owl_Class) = all_40_0_7 % 22.14/6.93 | % 22.14/6.93 | Instantiating formula (33) with all_40_0_7, uri_owl_Class and discharging atoms icext(uri_owl_Thing, uri_owl_Class) = all_40_0_7, yields: % 22.14/6.93 | (81) all_40_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_owl_Class) = v0) % 22.14/6.93 | % 22.14/6.93 +-Applying beta-rule and splitting (81), into two cases. % 22.14/6.93 |-Branch one: % 22.14/6.93 | (82) all_40_0_7 = 0 % 22.14/6.93 | % 22.14/6.94 | Equations (82) can reduce 79 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (79) ~ (all_40_0_7 = 0) % 22.14/6.94 | (85) ? [v0] : ( ~ (v0 = 0) & ir(uri_owl_Class) = v0) % 22.14/6.94 | % 22.14/6.94 | Instantiating (85) with all_56_0_8 yields: % 22.14/6.94 | (86) ~ (all_56_0_8 = 0) & ir(uri_owl_Class) = all_56_0_8 % 22.14/6.94 | % 22.14/6.94 | Applying alpha-rule on (86) yields: % 22.14/6.94 | (87) ~ (all_56_0_8 = 0) % 22.14/6.94 | (88) ir(uri_owl_Class) = all_56_0_8 % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (30) with all_56_0_8, uri_owl_Class and discharging atoms ir(uri_owl_Class) = all_56_0_8, yields: % 22.14/6.94 | (89) all_56_0_8 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (89) can reduce 87 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (91) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0 % 22.14/6.94 | (92) icext(uri_owl_Thing, uri_owl_Class) = 0 % 22.14/6.94 | % 22.14/6.94 +-Applying beta-rule and splitting (44), into two cases. % 22.14/6.94 |-Branch one: % 22.14/6.94 | (74) all_0_4_4 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (74) can reduce 71 to: % 22.14/6.94 | (94) ~ (all_0_2_2 = 0) % 22.14/6.94 | % 22.14/6.94 +-Applying beta-rule and splitting (40), into two cases. % 22.14/6.94 |-Branch one: % 22.14/6.94 | (95) all_0_2_2 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (95) can reduce 94 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (94) ~ (all_0_2_2 = 0) % 22.14/6.94 | (98) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.94 | % 22.14/6.94 | Instantiating (98) with all_44_0_9, all_44_1_10, all_44_2_11 yields: % 22.14/6.94 | (99) (all_44_1_10 = 0 & ~ (all_44_0_9 = 0) & icext(uri_owl_Thing, all_44_2_11) = all_44_0_9 & icext(uri_owl_Class, all_44_2_11) = 0) | (ic(uri_owl_Thing) = all_44_1_10 & ic(uri_owl_Class) = all_44_2_11 & ( ~ (all_44_1_10 = 0) | ~ (all_44_2_11 = 0))) % 22.14/6.94 | % 22.14/6.94 +-Applying beta-rule and splitting (99), into two cases. % 22.14/6.94 |-Branch one: % 22.14/6.94 | (100) all_44_1_10 = 0 & ~ (all_44_0_9 = 0) & icext(uri_owl_Thing, all_44_2_11) = all_44_0_9 & icext(uri_owl_Class, all_44_2_11) = 0 % 22.14/6.94 | % 22.14/6.94 | Applying alpha-rule on (100) yields: % 22.14/6.94 | (101) all_44_1_10 = 0 % 22.14/6.94 | (102) ~ (all_44_0_9 = 0) % 22.14/6.94 | (103) icext(uri_owl_Thing, all_44_2_11) = all_44_0_9 % 22.14/6.94 | (104) icext(uri_owl_Class, all_44_2_11) = 0 % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (33) with all_44_0_9, all_44_2_11 and discharging atoms icext(uri_owl_Thing, all_44_2_11) = all_44_0_9, yields: % 22.14/6.94 | (105) all_44_0_9 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(all_44_2_11) = v0) % 22.14/6.94 | % 22.14/6.94 +-Applying beta-rule and splitting (105), into two cases. % 22.14/6.94 |-Branch one: % 22.14/6.94 | (106) all_44_0_9 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (106) can reduce 102 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (102) ~ (all_44_0_9 = 0) % 22.14/6.94 | (109) ? [v0] : ( ~ (v0 = 0) & ir(all_44_2_11) = v0) % 22.14/6.94 | % 22.14/6.94 | Instantiating (109) with all_67_0_12 yields: % 22.14/6.94 | (110) ~ (all_67_0_12 = 0) & ir(all_44_2_11) = all_67_0_12 % 22.14/6.94 | % 22.14/6.94 | Applying alpha-rule on (110) yields: % 22.14/6.94 | (111) ~ (all_67_0_12 = 0) % 22.14/6.94 | (112) ir(all_44_2_11) = all_67_0_12 % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (30) with all_67_0_12, all_44_2_11 and discharging atoms ir(all_44_2_11) = all_67_0_12, yields: % 22.14/6.94 | (113) all_67_0_12 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (113) can reduce 111 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (115) ic(uri_owl_Thing) = all_44_1_10 & ic(uri_owl_Class) = all_44_2_11 & ( ~ (all_44_1_10 = 0) | ~ (all_44_2_11 = 0)) % 22.14/6.94 | % 22.14/6.94 | Applying alpha-rule on (115) yields: % 22.14/6.94 | (116) ic(uri_owl_Thing) = all_44_1_10 % 22.14/6.94 | (117) ic(uri_owl_Class) = all_44_2_11 % 22.14/6.94 | (118) ~ (all_44_1_10 = 0) | ~ (all_44_2_11 = 0) % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (26) with uri_owl_Thing, all_44_1_10, 0 and discharging atoms ic(uri_owl_Thing) = all_44_1_10, ic(uri_owl_Thing) = 0, yields: % 22.14/6.94 | (101) all_44_1_10 = 0 % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (26) with uri_owl_Class, all_44_2_11, 0 and discharging atoms ic(uri_owl_Class) = all_44_2_11, ic(uri_owl_Class) = 0, yields: % 22.14/6.94 | (120) all_44_2_11 = 0 % 22.14/6.94 | % 22.14/6.94 +-Applying beta-rule and splitting (118), into two cases. % 22.14/6.94 |-Branch one: % 22.14/6.94 | (121) ~ (all_44_1_10 = 0) % 22.14/6.94 | % 22.14/6.94 | Equations (101) can reduce 121 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (101) all_44_1_10 = 0 % 22.14/6.94 | (124) ~ (all_44_2_11 = 0) % 22.14/6.94 | % 22.14/6.94 | Equations (120) can reduce 124 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (73) ~ (all_0_4_4 = 0) % 22.14/6.94 | (77) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.94 | % 22.14/6.94 | Instantiating formula (24) with uri_rdf_type, uri_owl_Class, uri_owl_Thing, 0, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4, iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0, yields: % 22.14/6.94 | (74) all_0_4_4 = 0 % 22.14/6.94 | % 22.14/6.94 | Equations (74) can reduce 73 to: % 22.14/6.94 | (50) $false % 22.14/6.94 | % 22.14/6.94 |-The branch is then unsatisfiable % 22.14/6.94 |-Branch two: % 22.14/6.94 | (130) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2 % 22.14/6.94 | (131) all_0_2_2 = all_0_4_4 % 22.14/6.94 | % 22.14/6.94 | From (131) and (34) follows: % 22.14/6.94 | (132) iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_4_4 % 22.14/6.94 | % 22.14/6.94 | From (131) and (130) follows: % 22.14/6.95 | (29) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (42), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (72) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0) % 22.14/6.95 | % 22.14/6.95 | Using (29) and (72) yields: % 22.14/6.95 | (73) ~ (all_0_4_4 = 0) % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (40), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (95) all_0_2_2 = 0 % 22.14/6.95 | % 22.14/6.95 | Combining equations (95,131) yields a new equation: % 22.14/6.95 | (74) all_0_4_4 = 0 % 22.14/6.95 | % 22.14/6.95 | Equations (74) can reduce 73 to: % 22.14/6.95 | (50) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (94) ~ (all_0_2_2 = 0) % 22.14/6.95 | (98) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.95 | % 22.14/6.95 | Equations (131) can reduce 94 to: % 22.14/6.95 | (73) ~ (all_0_4_4 = 0) % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (44), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (74) all_0_4_4 = 0 % 22.14/6.95 | % 22.14/6.95 | Equations (74) can reduce 73 to: % 22.14/6.95 | (50) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (73) ~ (all_0_4_4 = 0) % 22.14/6.95 | (77) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.95 | % 22.14/6.95 | Instantiating (77) with all_40_0_17 yields: % 22.14/6.95 | (146) ~ (all_40_0_17 = 0) & icext(uri_owl_Thing, uri_owl_Class) = all_40_0_17 % 22.14/6.95 | % 22.14/6.95 | Applying alpha-rule on (146) yields: % 22.14/6.95 | (147) ~ (all_40_0_17 = 0) % 22.14/6.95 | (148) icext(uri_owl_Thing, uri_owl_Class) = all_40_0_17 % 22.14/6.95 | % 22.14/6.95 | Instantiating formula (33) with all_40_0_17, uri_owl_Class and discharging atoms icext(uri_owl_Thing, uri_owl_Class) = all_40_0_17, yields: % 22.14/6.95 | (149) all_40_0_17 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_owl_Class) = v0) % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (149), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (150) all_40_0_17 = 0 % 22.14/6.95 | % 22.14/6.95 | Equations (150) can reduce 147 to: % 22.14/6.95 | (50) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (147) ~ (all_40_0_17 = 0) % 22.14/6.95 | (85) ? [v0] : ( ~ (v0 = 0) & ir(uri_owl_Class) = v0) % 22.14/6.95 | % 22.14/6.95 | Instantiating (85) with all_73_0_21 yields: % 22.14/6.95 | (154) ~ (all_73_0_21 = 0) & ir(uri_owl_Class) = all_73_0_21 % 22.14/6.95 | % 22.14/6.95 | Applying alpha-rule on (154) yields: % 22.14/6.95 | (155) ~ (all_73_0_21 = 0) % 22.14/6.95 | (156) ir(uri_owl_Class) = all_73_0_21 % 22.14/6.95 | % 22.14/6.95 | Instantiating formula (30) with all_73_0_21, uri_owl_Class and discharging atoms ir(uri_owl_Class) = all_73_0_21, yields: % 22.14/6.95 | (157) all_73_0_21 = 0 % 22.14/6.95 | % 22.14/6.95 | Equations (157) can reduce 155 to: % 22.14/6.95 | (50) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (91) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0 % 22.14/6.95 | (92) icext(uri_owl_Thing, uri_owl_Class) = 0 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (41), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (70) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2) % 22.14/6.95 | % 22.14/6.95 | From (131) and (70) follows: % 22.14/6.95 | (162) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4) % 22.14/6.95 | % 22.14/6.95 | Using (29) and (162) yields: % 22.14/6.95 | (163) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (130) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_2_2 % 22.14/6.95 | (165) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.95 | % 22.14/6.95 | From (131) and (130) follows: % 22.14/6.95 | (29) iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (165), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (95) all_0_2_2 = 0 % 22.14/6.95 | % 22.14/6.95 | Combining equations (95,131) yields a new equation: % 22.14/6.95 | (74) all_0_4_4 = 0 % 22.14/6.95 | % 22.14/6.95 | Combining equations (74,131) yields a new equation: % 22.14/6.95 | (95) all_0_2_2 = 0 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (37), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (170) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_4_4) % 22.14/6.95 | % 22.14/6.95 | From (74) and (170) follows: % 22.14/6.95 | (47) ~ (iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0) % 22.14/6.95 | % 22.14/6.95 | Using (66) and (47) yields: % 22.14/6.95 | (163) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (173) iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_4_4 % 22.14/6.95 | (174) all_0_3_3 = all_0_4_4 % 22.14/6.95 | % 22.14/6.95 | Combining equations (49,174) yields a new equation: % 22.14/6.95 | (74) all_0_4_4 = 0 % 22.14/6.95 | % 22.14/6.95 | Combining equations (74,174) yields a new equation: % 22.14/6.95 | (49) all_0_3_3 = 0 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (38), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (177) all_0_1_1 = 0 % 22.14/6.95 | % 22.14/6.95 | From (177) and (15) follows: % 22.14/6.95 | (178) iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = 0 % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (5), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (179) ~ (all_0_0_0 = 0) % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (39), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (180) all_0_0_0 = 0 % 22.14/6.95 | % 22.14/6.95 | Equations (180) can reduce 179 to: % 22.14/6.95 | (50) $false % 22.14/6.95 | % 22.14/6.95 |-The branch is then unsatisfiable % 22.14/6.95 |-Branch two: % 22.14/6.95 | (179) ~ (all_0_0_0 = 0) % 22.14/6.95 | (183) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_rdfs_Datatype, v0) = 0 & icext(uri_owl_Class, v0) = v2) | (ic(uri_rdfs_Datatype) = v0 & ic(uri_owl_Class) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.95 | % 22.14/6.95 | Instantiating (183) with all_62_0_24, all_62_1_25, all_62_2_26 yields: % 22.14/6.95 | (184) (all_62_1_25 = 0 & ~ (all_62_0_24 = 0) & icext(uri_rdfs_Datatype, all_62_2_26) = 0 & icext(uri_owl_Class, all_62_2_26) = all_62_0_24) | (ic(uri_rdfs_Datatype) = all_62_2_26 & ic(uri_owl_Class) = all_62_1_25 & ( ~ (all_62_1_25 = 0) | ~ (all_62_2_26 = 0))) % 22.14/6.95 | % 22.14/6.95 +-Applying beta-rule and splitting (184), into two cases. % 22.14/6.95 |-Branch one: % 22.14/6.95 | (185) all_62_1_25 = 0 & ~ (all_62_0_24 = 0) & icext(uri_rdfs_Datatype, all_62_2_26) = 0 & icext(uri_owl_Class, all_62_2_26) = all_62_0_24 % 22.14/6.95 | % 22.14/6.95 | Applying alpha-rule on (185) yields: % 22.14/6.95 | (186) all_62_1_25 = 0 % 22.14/6.95 | (187) ~ (all_62_0_24 = 0) % 22.14/6.96 | (188) icext(uri_rdfs_Datatype, all_62_2_26) = 0 % 22.14/6.96 | (189) icext(uri_owl_Class, all_62_2_26) = all_62_0_24 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (28) with all_62_2_26 and discharging atoms icext(uri_rdfs_Datatype, all_62_2_26) = 0, yields: % 22.14/6.96 | (190) idc(all_62_2_26) = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (22) with all_62_0_24, all_62_2_26, uri_rdfs_Class, uri_owl_Class and discharging atoms iext(uri_owl_equivalentClass, uri_owl_Class, uri_rdfs_Class) = 0, icext(uri_owl_Class, all_62_2_26) = all_62_0_24, yields: % 22.14/6.96 | (191) all_62_0_24 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Class, all_62_2_26) = v0) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (31) with all_62_0_24, all_62_2_26 and discharging atoms icext(uri_owl_Class, all_62_2_26) = all_62_0_24, yields: % 22.14/6.96 | (192) all_62_0_24 = 0 | ? [v0] : ( ~ (v0 = 0) & ic(all_62_2_26) = v0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (191), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (193) all_62_0_24 = 0 % 22.14/6.96 | % 22.14/6.96 | Equations (193) can reduce 187 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (187) ~ (all_62_0_24 = 0) % 22.14/6.96 | (196) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Class, all_62_2_26) = v0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (192), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (193) all_62_0_24 = 0 % 22.14/6.96 | % 22.14/6.96 | Equations (193) can reduce 187 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (187) ~ (all_62_0_24 = 0) % 22.14/6.96 | (200) ? [v0] : ( ~ (v0 = 0) & ic(all_62_2_26) = v0) % 22.14/6.96 | % 22.14/6.96 | Instantiating (200) with all_82_0_28 yields: % 22.14/6.96 | (201) ~ (all_82_0_28 = 0) & ic(all_62_2_26) = all_82_0_28 % 22.14/6.96 | % 22.14/6.96 | Applying alpha-rule on (201) yields: % 22.14/6.96 | (202) ~ (all_82_0_28 = 0) % 22.14/6.96 | (203) ic(all_62_2_26) = all_82_0_28 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (2) with all_62_2_26 and discharging atoms idc(all_62_2_26) = 0, yields: % 22.14/6.96 | (204) ic(all_62_2_26) = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (26) with all_62_2_26, 0, all_82_0_28 and discharging atoms ic(all_62_2_26) = all_82_0_28, ic(all_62_2_26) = 0, yields: % 22.14/6.96 | (205) all_82_0_28 = 0 % 22.14/6.96 | % 22.14/6.96 | Equations (205) can reduce 202 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (207) ic(uri_rdfs_Datatype) = all_62_2_26 & ic(uri_owl_Class) = all_62_1_25 & ( ~ (all_62_1_25 = 0) | ~ (all_62_2_26 = 0)) % 22.14/6.96 | % 22.14/6.96 | Applying alpha-rule on (207) yields: % 22.14/6.96 | (208) ic(uri_rdfs_Datatype) = all_62_2_26 % 22.14/6.96 | (209) ic(uri_owl_Class) = all_62_1_25 % 22.14/6.96 | (210) ~ (all_62_1_25 = 0) | ~ (all_62_2_26 = 0) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (26) with uri_rdfs_Datatype, all_62_2_26, 0 and discharging atoms ic(uri_rdfs_Datatype) = all_62_2_26, ic(uri_rdfs_Datatype) = 0, yields: % 22.14/6.96 | (211) all_62_2_26 = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (26) with uri_owl_Class, all_62_1_25, 0 and discharging atoms ic(uri_owl_Class) = all_62_1_25, ic(uri_owl_Class) = 0, yields: % 22.14/6.96 | (186) all_62_1_25 = 0 % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (210), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (213) ~ (all_62_1_25 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (186) can reduce 213 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (186) all_62_1_25 = 0 % 22.14/6.96 | (216) ~ (all_62_2_26 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (211) can reduce 216 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (180) all_0_0_0 = 0 % 22.14/6.96 | (219) ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (219), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (220) ~ (all_0_1_1 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (177) can reduce 220 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (177) all_0_1_1 = 0 % 22.14/6.96 | (223) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (223), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (94) ~ (all_0_2_2 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (95) can reduce 94 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (95) all_0_2_2 = 0 % 22.14/6.96 | (227) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (227), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (48) ~ (all_0_3_3 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (49) can reduce 48 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (49) all_0_3_3 = 0 % 22.14/6.96 | (73) ~ (all_0_4_4 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (74) can reduce 73 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (220) ~ (all_0_1_1 = 0) % 22.14/6.96 | (234) ? [v0] : ? [v1] : ? [v2] : ((ic(uri_rdfs_Class) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (icext(uri_rdfs_Class, v0) = v2 & icext(uri_owl_Class, v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))) % 22.14/6.96 | % 22.14/6.96 | Instantiating (234) with all_54_0_29, all_54_1_30, all_54_2_31 yields: % 22.14/6.96 | (235) (ic(uri_rdfs_Class) = all_54_1_30 & ic(uri_owl_Class) = all_54_2_31 & ( ~ (all_54_1_30 = 0) | ~ (all_54_2_31 = 0))) | (icext(uri_rdfs_Class, all_54_2_31) = all_54_0_29 & icext(uri_owl_Class, all_54_2_31) = all_54_1_30 & ( ~ (all_54_0_29 = 0) | ~ (all_54_1_30 = 0)) & (all_54_0_29 = 0 | all_54_1_30 = 0)) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (235), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (236) ic(uri_rdfs_Class) = all_54_1_30 & ic(uri_owl_Class) = all_54_2_31 & ( ~ (all_54_1_30 = 0) | ~ (all_54_2_31 = 0)) % 22.14/6.96 | % 22.14/6.96 | Applying alpha-rule on (236) yields: % 22.14/6.96 | (237) ic(uri_rdfs_Class) = all_54_1_30 % 22.14/6.96 | (238) ic(uri_owl_Class) = all_54_2_31 % 22.14/6.96 | (239) ~ (all_54_1_30 = 0) | ~ (all_54_2_31 = 0) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (26) with uri_rdfs_Class, all_54_1_30, 0 and discharging atoms ic(uri_rdfs_Class) = all_54_1_30, ic(uri_rdfs_Class) = 0, yields: % 22.14/6.96 | (240) all_54_1_30 = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (26) with uri_owl_Class, all_54_2_31, 0 and discharging atoms ic(uri_owl_Class) = all_54_2_31, ic(uri_owl_Class) = 0, yields: % 22.14/6.96 | (241) all_54_2_31 = 0 % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (239), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (242) ~ (all_54_1_30 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (240) can reduce 242 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (240) all_54_1_30 = 0 % 22.14/6.96 | (245) ~ (all_54_2_31 = 0) % 22.14/6.96 | % 22.14/6.96 | Equations (241) can reduce 245 to: % 22.14/6.96 | (50) $false % 22.14/6.96 | % 22.14/6.96 |-The branch is then unsatisfiable % 22.14/6.96 |-Branch two: % 22.14/6.96 | (247) icext(uri_rdfs_Class, all_54_2_31) = all_54_0_29 & icext(uri_owl_Class, all_54_2_31) = all_54_1_30 & ( ~ (all_54_0_29 = 0) | ~ (all_54_1_30 = 0)) & (all_54_0_29 = 0 | all_54_1_30 = 0) % 22.14/6.96 | % 22.14/6.96 | Applying alpha-rule on (247) yields: % 22.14/6.96 | (248) icext(uri_rdfs_Class, all_54_2_31) = all_54_0_29 % 22.14/6.96 | (249) icext(uri_owl_Class, all_54_2_31) = all_54_1_30 % 22.14/6.96 | (250) ~ (all_54_0_29 = 0) | ~ (all_54_1_30 = 0) % 22.14/6.96 | (251) all_54_0_29 = 0 | all_54_1_30 = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (32) with uri_owl_Class, uri_owl_Class, all_54_1_30, 0 and discharging atoms icext(uri_owl_Class, uri_owl_Class) = 0, yields: % 22.14/6.96 | (252) all_54_1_30 = 0 | ~ (icext(uri_owl_Class, uri_owl_Class) = all_54_1_30) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (32) with uri_owl_Class, all_54_2_31, all_54_1_30, all_54_0_29 and discharging atoms icext(uri_owl_Class, all_54_2_31) = all_54_1_30, yields: % 22.14/6.96 | (253) all_54_0_29 = all_54_1_30 | ~ (icext(uri_owl_Class, all_54_2_31) = all_54_0_29) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (35) with all_54_2_31 yields: % 22.14/6.96 | (254) ~ (icext(uri_rdfs_Class, all_54_2_31) = 0) | ic(all_54_2_31) = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (6) with all_54_0_29, all_54_2_31 and discharging atoms icext(uri_rdfs_Class, all_54_2_31) = all_54_0_29, yields: % 22.14/6.96 | (255) all_54_0_29 = 0 | ? [v0] : ( ~ (v0 = 0) & ic(all_54_2_31) = v0) % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (8) with all_54_2_31 yields: % 22.14/6.96 | (256) ~ (icext(uri_owl_Class, all_54_2_31) = 0) | ic(all_54_2_31) = 0 % 22.14/6.96 | % 22.14/6.96 | Instantiating formula (31) with all_54_1_30, all_54_2_31 and discharging atoms icext(uri_owl_Class, all_54_2_31) = all_54_1_30, yields: % 22.14/6.96 | (257) all_54_1_30 = 0 | ? [v0] : ( ~ (v0 = 0) & ic(all_54_2_31) = v0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (253), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (258) ~ (icext(uri_owl_Class, all_54_2_31) = all_54_0_29) % 22.14/6.96 | % 22.14/6.96 | Using (249) and (258) yields: % 22.14/6.96 | (259) ~ (all_54_0_29 = all_54_1_30) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (252), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (260) ~ (icext(uri_owl_Class, uri_owl_Class) = all_54_1_30) % 22.14/6.96 | % 22.14/6.96 | Using (67) and (260) yields: % 22.14/6.96 | (242) ~ (all_54_1_30 = 0) % 22.14/6.96 | % 22.14/6.96 +-Applying beta-rule and splitting (251), into two cases. % 22.14/6.96 |-Branch one: % 22.14/6.96 | (262) all_54_0_29 = 0 % 22.14/6.96 | % 22.14/6.96 | Equations (262) can reduce 259 to: % 22.14/6.97 | (263) ~ (all_54_1_30 = 0) % 22.14/6.97 | % 22.14/6.97 | Simplifying 263 yields: % 22.14/6.97 | (242) ~ (all_54_1_30 = 0) % 22.14/6.97 | % 22.14/6.97 | From (262) and (248) follows: % 22.14/6.97 | (265) icext(uri_rdfs_Class, all_54_2_31) = 0 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (257), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (240) all_54_1_30 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (240) can reduce 242 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (242) ~ (all_54_1_30 = 0) % 22.14/6.97 | (269) ? [v0] : ( ~ (v0 = 0) & ic(all_54_2_31) = v0) % 22.14/6.97 | % 22.14/6.97 | Instantiating (269) with all_128_0_32 yields: % 22.14/6.97 | (270) ~ (all_128_0_32 = 0) & ic(all_54_2_31) = all_128_0_32 % 22.14/6.97 | % 22.14/6.97 | Applying alpha-rule on (270) yields: % 22.14/6.97 | (271) ~ (all_128_0_32 = 0) % 22.14/6.97 | (272) ic(all_54_2_31) = all_128_0_32 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (254), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (273) ~ (icext(uri_rdfs_Class, all_54_2_31) = 0) % 22.14/6.97 | % 22.14/6.97 | Using (265) and (273) yields: % 22.14/6.97 | (163) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (265) icext(uri_rdfs_Class, all_54_2_31) = 0 % 22.14/6.97 | (276) ic(all_54_2_31) = 0 % 22.14/6.97 | % 22.14/6.97 | Instantiating formula (26) with all_54_2_31, 0, all_128_0_32 and discharging atoms ic(all_54_2_31) = all_128_0_32, ic(all_54_2_31) = 0, yields: % 22.14/6.97 | (277) all_128_0_32 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (277) can reduce 271 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (279) ~ (all_54_0_29 = 0) % 22.14/6.97 | (240) all_54_1_30 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (240) can reduce 242 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (282) icext(uri_owl_Class, uri_owl_Class) = all_54_1_30 % 22.14/6.97 | (240) all_54_1_30 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (240) can reduce 259 to: % 22.14/6.97 | (279) ~ (all_54_0_29 = 0) % 22.14/6.97 | % 22.14/6.97 | From (240) and (249) follows: % 22.14/6.97 | (285) icext(uri_owl_Class, all_54_2_31) = 0 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (256), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (286) ~ (icext(uri_owl_Class, all_54_2_31) = 0) % 22.14/6.97 | % 22.14/6.97 | Using (285) and (286) yields: % 22.14/6.97 | (163) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (285) icext(uri_owl_Class, all_54_2_31) = 0 % 22.14/6.97 | (276) ic(all_54_2_31) = 0 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (255), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (262) all_54_0_29 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (262) can reduce 279 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (279) ~ (all_54_0_29 = 0) % 22.14/6.97 | (269) ? [v0] : ( ~ (v0 = 0) & ic(all_54_2_31) = v0) % 22.14/6.97 | % 22.14/6.97 | Instantiating (269) with all_125_0_33 yields: % 22.14/6.97 | (294) ~ (all_125_0_33 = 0) & ic(all_54_2_31) = all_125_0_33 % 22.14/6.97 | % 22.14/6.97 | Applying alpha-rule on (294) yields: % 22.14/6.97 | (295) ~ (all_125_0_33 = 0) % 22.14/6.97 | (296) ic(all_54_2_31) = all_125_0_33 % 22.14/6.97 | % 22.14/6.97 | Instantiating formula (26) with all_54_2_31, 0, all_125_0_33 and discharging atoms ic(all_54_2_31) = all_125_0_33, ic(all_54_2_31) = 0, yields: % 22.14/6.97 | (297) all_125_0_33 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (297) can reduce 295 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (299) icext(uri_owl_Class, all_54_2_31) = all_54_0_29 % 22.14/6.97 | (300) all_54_0_29 = all_54_1_30 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (251), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (262) all_54_0_29 = 0 % 22.14/6.97 | % 22.14/6.97 | Combining equations (262,300) yields a new equation: % 22.14/6.97 | (240) all_54_1_30 = 0 % 22.14/6.97 | % 22.14/6.97 | Combining equations (240,300) yields a new equation: % 22.14/6.97 | (262) all_54_0_29 = 0 % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (250), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (279) ~ (all_54_0_29 = 0) % 22.14/6.97 | % 22.14/6.97 | Equations (262) can reduce 279 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (262) all_54_0_29 = 0 % 22.14/6.97 | (242) ~ (all_54_1_30 = 0) % 22.14/6.97 | % 22.14/6.97 | Equations (240) can reduce 242 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (279) ~ (all_54_0_29 = 0) % 22.14/6.97 | (240) all_54_1_30 = 0 % 22.14/6.97 | % 22.14/6.97 | Combining equations (240,300) yields a new equation: % 22.14/6.97 | (262) all_54_0_29 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (262) can reduce 279 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (94) ~ (all_0_2_2 = 0) % 22.14/6.97 | (77) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_owl_Class) = v0) % 22.14/6.97 | % 22.14/6.97 | Equations (131) can reduce 94 to: % 22.14/6.97 | (73) ~ (all_0_4_4 = 0) % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (40), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (95) all_0_2_2 = 0 % 22.14/6.97 | % 22.14/6.97 | Combining equations (95,131) yields a new equation: % 22.14/6.97 | (74) all_0_4_4 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (74) can reduce 73 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (94) ~ (all_0_2_2 = 0) % 22.14/6.97 | (98) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.97 | % 22.14/6.97 | Equations (131) can reduce 94 to: % 22.14/6.97 | (73) ~ (all_0_4_4 = 0) % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (43), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (322) ~ (iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_4_4) % 22.14/6.97 | % 22.14/6.97 | Using (132) and (322) yields: % 22.14/6.97 | (163) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (132) iext(uri_rdfs_subClassOf, uri_owl_Class, uri_owl_Thing) = all_0_4_4 % 22.14/6.97 | (325) all_0_4_4 = 0 | ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.97 | % 22.14/6.97 +-Applying beta-rule and splitting (325), into two cases. % 22.14/6.97 |-Branch one: % 22.14/6.97 | (74) all_0_4_4 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (74) can reduce 73 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (73) ~ (all_0_4_4 = 0) % 22.14/6.97 | (98) ? [v0] : ? [v1] : ? [v2] : ((v1 = 0 & ~ (v2 = 0) & icext(uri_owl_Thing, v0) = v2 & icext(uri_owl_Class, v0) = 0) | (ic(uri_owl_Thing) = v1 & ic(uri_owl_Class) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 22.14/6.97 | % 22.14/6.97 | Instantiating formula (24) with uri_rdf_type, uri_owl_Class, uri_owl_Thing, 0, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = all_0_4_4, iext(uri_rdf_type, uri_owl_Class, uri_owl_Thing) = 0, yields: % 22.14/6.97 | (74) all_0_4_4 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (74) can reduce 73 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 |-Branch two: % 22.14/6.97 | (48) ~ (all_0_3_3 = 0) % 22.14/6.97 | (52) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Class, uri_owl_Class) = v0) % 22.14/6.97 | % 22.14/6.97 | Instantiating formula (24) with uri_rdf_type, uri_owl_Class, uri_owl_Class, 0, all_0_3_3 and discharging atoms iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = all_0_3_3, iext(uri_rdf_type, uri_owl_Class, uri_owl_Class) = 0, yields: % 22.14/6.97 | (49) all_0_3_3 = 0 % 22.14/6.97 | % 22.14/6.97 | Equations (49) can reduce 48 to: % 22.14/6.97 | (50) $false % 22.14/6.97 | % 22.14/6.97 |-The branch is then unsatisfiable % 22.14/6.97 % SZS output end Proof for theBenchmark % 22.14/6.97 % 22.14/6.97 6353ms %------------------------------------------------------------------------------