TSTP Solution File: SWB005+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWB005+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:59:34 EDT 2022
% Result : Theorem 3.76s 1.58s
% Output : Proof 12.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWB005+2 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 06:06:58 EDT 2022
% 0.12/0.34 % 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
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.90 Prover 0: Preprocessing ...
% 1.55/0.98 Prover 0: Warning: ignoring some quantifiers
% 1.55/1.00 Prover 0: Constructing countermodel ...
% 2.60/1.29 Prover 0: gave up
% 2.60/1.29 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.60/1.30 Prover 1: Preprocessing ...
% 3.06/1.38 Prover 1: Constructing countermodel ...
% 3.76/1.58 Prover 1: proved (297ms)
% 3.76/1.58
% 3.76/1.58 No countermodel exists, formula is valid
% 3.76/1.58 % SZS status Theorem for theBenchmark
% 3.76/1.58
% 3.76/1.58 Generating proof ... found it (size 608)
% 11.22/3.38
% 11.22/3.38 % SZS output start Proof for theBenchmark
% 11.22/3.38 Assumed formulas after preprocessing and simplification:
% 11.22/3.38 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (iext(uri_ex_p, uri_ex_s, uri_ex_o) = 0 & iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = v7 & iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = v6 & iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) = v5 & iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = v3 & iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = v2 & iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = v4 & iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = v1 & iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = v0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (iext(v12, v11, v10) = v9) | ~ (iext(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (icext(v11, v10) = v9) | ~ (icext(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (iext(uri_rdf_type, v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & icext(v9, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ip(v10) = v9) | ~ (ip(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ir(v10) = v9) | ~ (ir(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (iext(v9, v8, v10) = 0) | ip(v9) = 0) & ! [v8] : ! [v9] : (v9 = 0 | ~ (icext(uri_owl_ObjectProperty, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ip(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (icext(uri_owl_Thing, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ir(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (icext(uri_rdfs_Resource, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ir(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (iext(uri_rdf_type, v8, uri_rdf_Property) = v9) | ? [v10] : ( ~ (v10 = 0) & ip(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (ir(v8) = v9)) & ! [v8] : ! [v9] : ( ~ (iext(uri_rdf_type, v8, v9) = 0) | icext(v9, v8) = 0) & ! [v8] : ( ~ (icext(uri_owl_ObjectProperty, v8) = 0) | ip(v8) = 0) & ! [v8] : ( ~ (icext(uri_owl_Thing, v8) = 0) | ir(v8) = 0) & ! [v8] : ( ~ (icext(uri_rdfs_Resource, v8) = 0) | ir(v8) = 0) & ! [v8] : ( ~ (iext(uri_rdf_type, v8, uri_rdf_Property) = 0) | ip(v8) = 0) & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 11.22/3.41 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 11.22/3.41 | (1) iext(uri_ex_p, uri_ex_s, uri_ex_o) = 0 & iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = all_0_0_0 & iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = all_0_1_1 & iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) = all_0_2_2 & iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_4_4 & iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5 & iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3 & iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6 & iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ir(v2) = v1) | ~ (ir(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(v1, v0, v2) = 0) | ip(v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_ObjectProperty, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ip(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Thing, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Resource, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = v1) | ? [v2] : ( ~ (v2 = 0) & ip(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (ir(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0) & ! [v0] : ( ~ (icext(uri_owl_ObjectProperty, v0) = 0) | ip(v0) = 0) & ! [v0] : ( ~ (icext(uri_owl_Thing, v0) = 0) | ir(v0) = 0) & ! [v0] : ( ~ (icext(uri_rdfs_Resource, v0) = 0) | ir(v0) = 0) & ! [v0] : ( ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = 0) | ip(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) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0))
% 11.22/3.42 |
% 11.22/3.42 | Applying alpha-rule on (1) yields:
% 11.22/3.42 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (iext(v4, v3, v2) = v1) | ~ (iext(v4, v3, v2) = v0))
% 11.22/3.42 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (icext(v3, v2) = v1) | ~ (icext(v3, v2) = v0))
% 11.22/3.42 | (4) ! [v0] : ( ~ (icext(uri_owl_Thing, v0) = 0) | ir(v0) = 0)
% 11.22/3.42 | (5) iext(uri_ex_p, uri_ex_s, uri_ex_o) = 0
% 11.73/3.42 | (6) iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) = all_0_2_2
% 11.73/3.42 | (7) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6
% 11.73/3.42 | (8) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3
% 11.73/3.42 | (9) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5
% 11.73/3.42 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_rdfs_Resource, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2))
% 11.73/3.42 | (11) iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7
% 11.73/3.42 | (12) ! [v0] : ( ~ (icext(uri_owl_ObjectProperty, v0) = 0) | ip(v0) = 0)
% 11.73/3.42 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ir(v2) = v1) | ~ (ir(v2) = v0))
% 11.73/3.42 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_Thing, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ir(v0) = v2))
% 11.73/3.42 | (15) ! [v0] : ! [v1] : (v1 = 0 | ~ (icext(uri_owl_ObjectProperty, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ip(v0) = v2))
% 11.73/3.42 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (iext(v1, v0, v2) = 0) | ip(v1) = 0)
% 11.73/3.42 | (17) ! [v0] : ( ~ (icext(uri_rdfs_Resource, v0) = 0) | ir(v0) = 0)
% 11.73/3.42 | (18) iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = all_0_0_0
% 11.73/3.42 | (19) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_4_4
% 11.73/3.42 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = v1) | ? [v2] : ( ~ (v2 = 0) & ip(v0) = v2))
% 11.73/3.42 | (21) iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = all_0_1_1
% 11.73/3.42 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ip(v2) = v1) | ~ (ip(v2) = v0))
% 11.73/3.42 | (23) ! [v0] : ( ~ (iext(uri_rdf_type, v0, uri_rdf_Property) = 0) | ip(v0) = 0)
% 11.73/3.42 | (24) ~ (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) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 11.73/3.42 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (iext(uri_rdf_type, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & icext(v1, v0) = v3))
% 11.73/3.42 | (26) ! [v0] : ! [v1] : ( ~ (iext(uri_rdf_type, v0, v1) = 0) | icext(v1, v0) = 0)
% 11.73/3.42 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (ir(v0) = v1))
% 11.73/3.42 |
% 11.73/3.42 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_owl_Thing, all_0_4_4, all_0_0_0 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_4_4, yields:
% 11.73/3.42 | (28) all_0_0_0 = all_0_4_4 | ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_0_0)
% 11.73/3.42 |
% 11.73/3.42 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_owl_Thing, all_0_4_4, all_0_2_2 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_4_4, yields:
% 11.73/3.42 | (29) all_0_2_2 = all_0_4_4 | ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_2_2)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdfs_Resource, all_0_5_5, all_0_1_1 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5, yields:
% 11.73/3.43 | (30) all_0_1_1 = all_0_5_5 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_1_1)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdfs_Resource, all_0_5_5, all_0_2_2 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5, yields:
% 11.73/3.43 | (31) all_0_2_2 = all_0_5_5 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_2_2)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdfs_Resource, all_0_5_5, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5, yields:
% 11.73/3.43 | (32) all_0_4_4 = all_0_5_5 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_4_4)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdf_Property, all_0_3_3, all_0_2_2 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3, yields:
% 11.73/3.43 | (33) all_0_2_2 = all_0_3_3 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdf_Property, all_0_3_3, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3, yields:
% 11.73/3.43 | (34) all_0_3_3 = all_0_4_4 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_p, uri_rdf_Property, all_0_3_3, all_0_5_5 and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3, yields:
% 11.73/3.43 | (35) all_0_3_3 = all_0_5_5 | ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_5_5)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_s, uri_owl_Thing, all_0_6_6, all_0_0_0 and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6, yields:
% 11.73/3.43 | (36) all_0_0_0 = all_0_6_6 | ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_0_0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_s, uri_owl_Thing, all_0_6_6, all_0_4_4 and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6, yields:
% 11.73/3.43 | (37) all_0_4_4 = all_0_6_6 | ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_4_4)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_s, uri_rdfs_Resource, all_0_7_7, all_0_1_1 and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7, yields:
% 11.73/3.43 | (38) all_0_1_1 = all_0_7_7 | ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_1_1)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_s, uri_rdfs_Resource, all_0_7_7, all_0_5_5 and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7, yields:
% 11.73/3.43 | (39) all_0_5_5 = all_0_7_7 | ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_5_5)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (2) with uri_rdf_type, uri_ex_s, uri_rdfs_Resource, all_0_7_7, all_0_6_6 and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7, yields:
% 11.73/3.43 | (40) all_0_6_6 = all_0_7_7 | ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_6_6)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (16) with uri_ex_o, uri_ex_p, uri_ex_s and discharging atoms iext(uri_ex_p, uri_ex_s, uri_ex_o) = 0, yields:
% 11.73/3.43 | (41) ip(uri_ex_p) = 0
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (26) with uri_owl_Thing, uri_ex_o yields:
% 11.73/3.43 | (42) ~ (iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = 0) | icext(uri_owl_Thing, uri_ex_o) = 0
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_0_0, uri_owl_Thing, uri_ex_o and discharging atoms iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = all_0_0_0, yields:
% 11.73/3.43 | (43) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_o) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (26) with uri_rdfs_Resource, uri_ex_o yields:
% 11.73/3.43 | (44) ~ (iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = 0) | icext(uri_rdfs_Resource, uri_ex_o) = 0
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_1_1, uri_rdfs_Resource, uri_ex_o and discharging atoms iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = all_0_1_1, yields:
% 11.73/3.43 | (45) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_2_2, uri_owl_ObjectProperty, uri_ex_p and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_owl_ObjectProperty) = all_0_2_2, yields:
% 11.73/3.43 | (46) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_4_4, uri_owl_Thing, uri_ex_p and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_4_4, yields:
% 11.73/3.43 | (47) all_0_4_4 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_5_5, uri_rdfs_Resource, uri_ex_p and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5, yields:
% 11.73/3.43 | (48) all_0_5_5 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (20) with all_0_3_3, uri_ex_p and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_3_3, yields:
% 11.73/3.43 | (49) all_0_3_3 = 0 | ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (26) with uri_rdf_Property, uri_ex_p yields:
% 11.73/3.43 | (50) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0) | icext(uri_rdf_Property, uri_ex_p) = 0
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (16) with uri_rdf_Property, uri_rdf_type, uri_ex_p yields:
% 11.73/3.43 | (51) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0) | ip(uri_rdf_type) = 0
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_6_6, uri_owl_Thing, uri_ex_s and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6, yields:
% 11.73/3.43 | (52) all_0_6_6 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.43 |
% 11.73/3.43 | Instantiating formula (25) with all_0_7_7, uri_rdfs_Resource, uri_ex_s and discharging atoms iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7, yields:
% 11.73/3.43 | (53) all_0_7_7 = 0 | ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.43 |
% 11.73/3.43 +-Applying beta-rule and splitting (49), into two cases.
% 11.73/3.43 |-Branch one:
% 11.73/3.43 | (54) all_0_3_3 = 0
% 11.73/3.43 |
% 11.73/3.43 | From (54) and (8) follows:
% 11.73/3.43 | (55) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0
% 11.73/3.43 |
% 11.73/3.43 +-Applying beta-rule and splitting (51), into two cases.
% 11.73/3.43 |-Branch one:
% 11.73/3.43 | (56) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0)
% 11.73/3.43 |
% 11.73/3.43 | Using (55) and (56) yields:
% 11.73/3.43 | (57) $false
% 11.73/3.43 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (55) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0
% 11.73/3.44 | (59) ip(uri_rdf_type) = 0
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (50), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (56) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0)
% 11.73/3.44 |
% 11.73/3.44 | Using (55) and (56) yields:
% 11.73/3.44 | (57) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (55) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = 0
% 11.73/3.44 | (63) icext(uri_rdf_Property, uri_ex_p) = 0
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (37), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (64) ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_4_4)
% 11.73/3.44 |
% 11.73/3.44 | Using (7) and (64) yields:
% 11.73/3.44 | (65) ~ (all_0_4_4 = all_0_6_6)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (34), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (66) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4)
% 11.73/3.44 |
% 11.73/3.44 | Using (55) and (66) yields:
% 11.73/3.44 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (68) all_0_4_4 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (68) can reduce 67 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.44 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.44 |
% 11.73/3.44 | Instantiating (71) with all_105_0_106 yields:
% 11.73/3.44 | (72) ~ (all_105_0_106 = 0) & icext(uri_owl_Thing, uri_ex_p) = all_105_0_106
% 11.73/3.44 |
% 11.73/3.44 | Applying alpha-rule on (72) yields:
% 11.73/3.44 | (73) ~ (all_105_0_106 = 0)
% 11.73/3.44 | (74) icext(uri_owl_Thing, uri_ex_p) = all_105_0_106
% 11.73/3.44 |
% 11.73/3.44 | Instantiating formula (14) with all_105_0_106, uri_ex_p and discharging atoms icext(uri_owl_Thing, uri_ex_p) = all_105_0_106, yields:
% 11.73/3.44 | (75) all_105_0_106 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (75), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (76) all_105_0_106 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (76) can reduce 73 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (73) ~ (all_105_0_106 = 0)
% 11.73/3.44 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.44 |
% 11.73/3.44 | Instantiating (79) with all_121_0_107 yields:
% 11.73/3.44 | (80) ~ (all_121_0_107 = 0) & ir(uri_ex_p) = all_121_0_107
% 11.73/3.44 |
% 11.73/3.44 | Applying alpha-rule on (80) yields:
% 11.73/3.44 | (81) ~ (all_121_0_107 = 0)
% 11.73/3.44 | (82) ir(uri_ex_p) = all_121_0_107
% 11.73/3.44 |
% 11.73/3.44 | Instantiating formula (27) with all_121_0_107, uri_ex_p and discharging atoms ir(uri_ex_p) = all_121_0_107, yields:
% 11.73/3.44 | (83) all_121_0_107 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (83) can reduce 81 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (85) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4
% 11.73/3.44 | (86) all_0_3_3 = all_0_4_4
% 11.73/3.44 |
% 11.73/3.44 | Combining equations (54,86) yields a new equation:
% 11.73/3.44 | (68) all_0_4_4 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (68) can reduce 65 to:
% 11.73/3.44 | (88) ~ (all_0_6_6 = 0)
% 11.73/3.44 |
% 11.73/3.44 | Simplifying 88 yields:
% 11.73/3.44 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (52), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (90) all_0_6_6 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (90) can reduce 89 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.44 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.44 |
% 11.73/3.44 | Instantiating (93) with all_108_0_108 yields:
% 11.73/3.44 | (94) ~ (all_108_0_108 = 0) & icext(uri_owl_Thing, uri_ex_s) = all_108_0_108
% 11.73/3.44 |
% 11.73/3.44 | Applying alpha-rule on (94) yields:
% 11.73/3.44 | (95) ~ (all_108_0_108 = 0)
% 11.73/3.44 | (96) icext(uri_owl_Thing, uri_ex_s) = all_108_0_108
% 11.73/3.44 |
% 11.73/3.44 | Instantiating formula (14) with all_108_0_108, uri_ex_s and discharging atoms icext(uri_owl_Thing, uri_ex_s) = all_108_0_108, yields:
% 11.73/3.44 | (97) all_108_0_108 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_s) = v0)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (97), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (98) all_108_0_108 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (98) can reduce 95 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (95) ~ (all_108_0_108 = 0)
% 11.73/3.44 | (101) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_s) = v0)
% 11.73/3.44 |
% 11.73/3.44 | Instantiating (101) with all_121_0_109 yields:
% 11.73/3.44 | (102) ~ (all_121_0_109 = 0) & ir(uri_ex_s) = all_121_0_109
% 11.73/3.44 |
% 11.73/3.44 | Applying alpha-rule on (102) yields:
% 11.73/3.44 | (103) ~ (all_121_0_109 = 0)
% 11.73/3.44 | (104) ir(uri_ex_s) = all_121_0_109
% 11.73/3.44 |
% 11.73/3.44 | Instantiating formula (27) with all_121_0_109, uri_ex_s and discharging atoms ir(uri_ex_s) = all_121_0_109, yields:
% 11.73/3.44 | (105) all_121_0_109 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (105) can reduce 103 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (107) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_4_4
% 11.73/3.44 | (108) all_0_4_4 = all_0_6_6
% 11.73/3.44 |
% 11.73/3.44 | From (108) and (19) follows:
% 11.73/3.44 | (109) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_6_6
% 11.73/3.44 |
% 11.73/3.44 | From (108) and (107) follows:
% 11.73/3.44 | (7) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_6_6
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (31), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (111) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_2_2)
% 11.73/3.44 |
% 11.73/3.44 | Using (9) and (111) yields:
% 11.73/3.44 | (112) ~ (all_0_2_2 = all_0_5_5)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (33), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (113) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2)
% 11.73/3.44 |
% 11.73/3.44 | Using (55) and (113) yields:
% 11.73/3.44 | (114) ~ (all_0_2_2 = 0)
% 11.73/3.44 |
% 11.73/3.44 +-Applying beta-rule and splitting (46), into two cases.
% 11.73/3.44 |-Branch one:
% 11.73/3.44 | (115) all_0_2_2 = 0
% 11.73/3.44 |
% 11.73/3.44 | Equations (115) can reduce 114 to:
% 11.73/3.44 | (69) $false
% 11.73/3.44 |
% 11.73/3.44 |-The branch is then unsatisfiable
% 11.73/3.44 |-Branch two:
% 11.73/3.44 | (114) ~ (all_0_2_2 = 0)
% 11.73/3.44 | (118) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 11.73/3.44 |
% 11.73/3.44 | Instantiating (118) with all_83_0_141 yields:
% 11.73/3.44 | (119) ~ (all_83_0_141 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = all_83_0_141
% 11.73/3.44 |
% 11.73/3.44 | Applying alpha-rule on (119) yields:
% 11.73/3.45 | (120) ~ (all_83_0_141 = 0)
% 11.73/3.45 | (121) icext(uri_owl_ObjectProperty, uri_ex_p) = all_83_0_141
% 11.73/3.45 |
% 11.73/3.45 | Instantiating formula (15) with all_83_0_141, uri_ex_p and discharging atoms icext(uri_owl_ObjectProperty, uri_ex_p) = all_83_0_141, yields:
% 11.73/3.45 | (122) all_83_0_141 = 0 | ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (122), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (123) all_83_0_141 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (123) can reduce 120 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (120) ~ (all_83_0_141 = 0)
% 11.73/3.45 | (126) ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 | Instantiating (126) with all_96_0_142 yields:
% 11.73/3.45 | (127) ~ (all_96_0_142 = 0) & ip(uri_ex_p) = all_96_0_142
% 11.73/3.45 |
% 11.73/3.45 | Applying alpha-rule on (127) yields:
% 11.73/3.45 | (128) ~ (all_96_0_142 = 0)
% 11.73/3.45 | (129) ip(uri_ex_p) = all_96_0_142
% 11.73/3.45 |
% 11.73/3.45 | Instantiating formula (22) with uri_ex_p, all_96_0_142, 0 and discharging atoms ip(uri_ex_p) = all_96_0_142, ip(uri_ex_p) = 0, yields:
% 11.73/3.45 | (130) all_96_0_142 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (130) can reduce 128 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (132) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2
% 11.73/3.45 | (133) all_0_2_2 = all_0_3_3
% 11.73/3.45 |
% 11.73/3.45 | Combining equations (54,133) yields a new equation:
% 11.73/3.45 | (115) all_0_2_2 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (115) can reduce 112 to:
% 11.73/3.45 | (135) ~ (all_0_5_5 = 0)
% 11.73/3.45 |
% 11.73/3.45 | Simplifying 135 yields:
% 11.73/3.45 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (48), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (137) all_0_5_5 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (137) can reduce 136 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.45 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 | Instantiating (140) with all_83_0_143 yields:
% 11.73/3.45 | (141) ~ (all_83_0_143 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_83_0_143
% 11.73/3.45 |
% 11.73/3.45 | Applying alpha-rule on (141) yields:
% 11.73/3.45 | (142) ~ (all_83_0_143 = 0)
% 11.73/3.45 | (143) icext(uri_rdfs_Resource, uri_ex_p) = all_83_0_143
% 11.73/3.45 |
% 11.73/3.45 | Instantiating formula (10) with all_83_0_143, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_83_0_143, yields:
% 11.73/3.45 | (144) all_83_0_143 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (144), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (145) all_83_0_143 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (145) can reduce 142 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (142) ~ (all_83_0_143 = 0)
% 11.73/3.45 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 | Instantiating (79) with all_100_0_144 yields:
% 11.73/3.45 | (149) ~ (all_100_0_144 = 0) & ir(uri_ex_p) = all_100_0_144
% 11.73/3.45 |
% 11.73/3.45 | Applying alpha-rule on (149) yields:
% 11.73/3.45 | (150) ~ (all_100_0_144 = 0)
% 11.73/3.45 | (151) ir(uri_ex_p) = all_100_0_144
% 11.73/3.45 |
% 11.73/3.45 | Instantiating formula (27) with all_100_0_144, uri_ex_p and discharging atoms ir(uri_ex_p) = all_100_0_144, yields:
% 11.73/3.45 | (152) all_100_0_144 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (152) can reduce 150 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (154) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_2_2
% 11.73/3.45 | (155) all_0_2_2 = all_0_5_5
% 11.73/3.45 |
% 11.73/3.45 | From (155) and (154) follows:
% 11.73/3.45 | (9) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_5_5
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (40), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (157) ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_6_6)
% 11.73/3.45 |
% 11.73/3.45 | Using (11) and (157) yields:
% 11.73/3.45 | (158) ~ (all_0_6_6 = all_0_7_7)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (34), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (66) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4)
% 11.73/3.45 |
% 11.73/3.45 | From (108) and (66) follows:
% 11.73/3.45 | (160) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_6_6)
% 11.73/3.45 |
% 11.73/3.45 | Using (55) and (160) yields:
% 11.73/3.45 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (52), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (90) all_0_6_6 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (90) can reduce 89 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.45 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (68) all_0_4_4 = 0
% 11.73/3.45 |
% 11.73/3.45 | Combining equations (68,108) yields a new equation:
% 11.73/3.45 | (90) all_0_6_6 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (90) can reduce 89 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.45 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 | Instantiating (71) with all_99_0_146 yields:
% 11.73/3.45 | (171) ~ (all_99_0_146 = 0) & icext(uri_owl_Thing, uri_ex_p) = all_99_0_146
% 11.73/3.45 |
% 11.73/3.45 | Applying alpha-rule on (171) yields:
% 11.73/3.45 | (172) ~ (all_99_0_146 = 0)
% 11.73/3.45 | (173) icext(uri_owl_Thing, uri_ex_p) = all_99_0_146
% 11.73/3.45 |
% 11.73/3.45 | Instantiating formula (14) with all_99_0_146, uri_ex_p and discharging atoms icext(uri_owl_Thing, uri_ex_p) = all_99_0_146, yields:
% 11.73/3.45 | (174) all_99_0_146 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 +-Applying beta-rule and splitting (174), into two cases.
% 11.73/3.45 |-Branch one:
% 11.73/3.45 | (175) all_99_0_146 = 0
% 11.73/3.45 |
% 11.73/3.45 | Equations (175) can reduce 172 to:
% 11.73/3.45 | (69) $false
% 11.73/3.45 |
% 11.73/3.45 |-The branch is then unsatisfiable
% 11.73/3.45 |-Branch two:
% 11.73/3.45 | (172) ~ (all_99_0_146 = 0)
% 11.73/3.45 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.45 |
% 11.73/3.45 | Instantiating (79) with all_115_0_147 yields:
% 11.73/3.45 | (179) ~ (all_115_0_147 = 0) & ir(uri_ex_p) = all_115_0_147
% 11.73/3.45 |
% 11.73/3.45 | Applying alpha-rule on (179) yields:
% 11.73/3.45 | (180) ~ (all_115_0_147 = 0)
% 11.73/3.46 | (181) ir(uri_ex_p) = all_115_0_147
% 11.73/3.46 |
% 11.73/3.46 | Instantiating formula (27) with all_115_0_147, uri_ex_p and discharging atoms ir(uri_ex_p) = all_115_0_147, yields:
% 11.73/3.46 | (182) all_115_0_147 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (182) can reduce 180 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (85) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4
% 11.73/3.46 | (86) all_0_3_3 = all_0_4_4
% 11.73/3.46 |
% 11.73/3.46 | Combining equations (54,86) yields a new equation:
% 11.73/3.46 | (68) all_0_4_4 = 0
% 11.73/3.46 |
% 11.73/3.46 | Combining equations (68,108) yields a new equation:
% 11.73/3.46 | (90) all_0_6_6 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (90) can reduce 158 to:
% 11.73/3.46 | (188) ~ (all_0_7_7 = 0)
% 11.73/3.46 |
% 11.73/3.46 | Simplifying 188 yields:
% 11.73/3.46 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (53), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (190) all_0_7_7 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (190) can reduce 189 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.46 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.46 |
% 11.73/3.46 | Instantiating (193) with all_101_0_149 yields:
% 11.73/3.46 | (194) ~ (all_101_0_149 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = all_101_0_149
% 11.73/3.46 |
% 11.73/3.46 | Applying alpha-rule on (194) yields:
% 11.73/3.46 | (195) ~ (all_101_0_149 = 0)
% 11.73/3.46 | (196) icext(uri_rdfs_Resource, uri_ex_s) = all_101_0_149
% 11.73/3.46 |
% 11.73/3.46 | Instantiating formula (10) with all_101_0_149, uri_ex_s and discharging atoms icext(uri_rdfs_Resource, uri_ex_s) = all_101_0_149, yields:
% 11.73/3.46 | (197) all_101_0_149 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_s) = v0)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (197), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (198) all_101_0_149 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (198) can reduce 195 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (195) ~ (all_101_0_149 = 0)
% 11.73/3.46 | (101) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_s) = v0)
% 11.73/3.46 |
% 11.73/3.46 | Instantiating (101) with all_117_0_150 yields:
% 11.73/3.46 | (202) ~ (all_117_0_150 = 0) & ir(uri_ex_s) = all_117_0_150
% 11.73/3.46 |
% 11.73/3.46 | Applying alpha-rule on (202) yields:
% 11.73/3.46 | (203) ~ (all_117_0_150 = 0)
% 11.73/3.46 | (204) ir(uri_ex_s) = all_117_0_150
% 11.73/3.46 |
% 11.73/3.46 | Instantiating formula (27) with all_117_0_150, uri_ex_s and discharging atoms ir(uri_ex_s) = all_117_0_150, yields:
% 11.73/3.46 | (205) all_117_0_150 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (205) can reduce 203 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (207) iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_6_6
% 11.73/3.46 | (208) all_0_6_6 = all_0_7_7
% 11.73/3.46 |
% 11.73/3.46 | Combining equations (208,108) yields a new equation:
% 11.73/3.46 | (209) all_0_4_4 = all_0_7_7
% 11.73/3.46 |
% 11.73/3.46 | From (208) and (109) follows:
% 11.73/3.46 | (210) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_7_7
% 11.73/3.46 |
% 11.73/3.46 | From (208) and (7) follows:
% 11.73/3.46 | (211) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_7_7
% 11.73/3.46 |
% 11.73/3.46 | From (208) and (207) follows:
% 11.73/3.46 | (11) iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (38), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (213) ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_1_1)
% 11.73/3.46 |
% 11.73/3.46 | Using (11) and (213) yields:
% 11.73/3.46 | (214) ~ (all_0_1_1 = all_0_7_7)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (28), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (215) ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_0_0)
% 11.73/3.46 |
% 11.73/3.46 | Using (210) and (215) yields:
% 11.73/3.46 | (216) ~ (all_0_0_0 = all_0_7_7)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (34), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (66) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4)
% 11.73/3.46 |
% 11.73/3.46 | From (209) and (66) follows:
% 11.73/3.46 | (218) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_7_7)
% 11.73/3.46 |
% 11.73/3.46 | Using (55) and (218) yields:
% 11.73/3.46 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (53), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (190) all_0_7_7 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (190) can reduce 189 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.46 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (52), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (90) all_0_6_6 = 0
% 11.73/3.46 |
% 11.73/3.46 | Combining equations (90,208) yields a new equation:
% 11.73/3.46 | (190) all_0_7_7 = 0
% 11.73/3.46 |
% 11.73/3.46 | Equations (190) can reduce 189 to:
% 11.73/3.46 | (69) $false
% 11.73/3.46 |
% 11.73/3.46 |-The branch is then unsatisfiable
% 11.73/3.46 |-Branch two:
% 11.73/3.46 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.46 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.46 |
% 11.73/3.46 | Equations (208) can reduce 89 to:
% 11.73/3.46 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.46 |
% 11.73/3.46 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.46 |-Branch one:
% 11.73/3.46 | (68) all_0_4_4 = 0
% 11.73/3.46 |
% 11.73/3.46 | Combining equations (209,68) yields a new equation:
% 11.73/3.46 | (231) all_0_7_7 = 0
% 11.73/3.46 |
% 11.73/3.46 | Simplifying 231 yields:
% 11.73/3.46 | (190) all_0_7_7 = 0
% 11.73/3.46 |
% 11.73/3.47 | Equations (190) can reduce 189 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.47 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (71) with all_100_0_153 yields:
% 11.73/3.47 | (236) ~ (all_100_0_153 = 0) & icext(uri_owl_Thing, uri_ex_p) = all_100_0_153
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (236) yields:
% 11.73/3.47 | (237) ~ (all_100_0_153 = 0)
% 11.73/3.47 | (238) icext(uri_owl_Thing, uri_ex_p) = all_100_0_153
% 11.73/3.47 |
% 11.73/3.47 | Instantiating formula (14) with all_100_0_153, uri_ex_p and discharging atoms icext(uri_owl_Thing, uri_ex_p) = all_100_0_153, yields:
% 11.73/3.47 | (239) all_100_0_153 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.47 |
% 11.73/3.47 +-Applying beta-rule and splitting (239), into two cases.
% 11.73/3.47 |-Branch one:
% 11.73/3.47 | (240) all_100_0_153 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (240) can reduce 237 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (237) ~ (all_100_0_153 = 0)
% 11.73/3.47 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (79) with all_116_0_154 yields:
% 11.73/3.47 | (244) ~ (all_116_0_154 = 0) & ir(uri_ex_p) = all_116_0_154
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (244) yields:
% 11.73/3.47 | (245) ~ (all_116_0_154 = 0)
% 11.73/3.47 | (246) ir(uri_ex_p) = all_116_0_154
% 11.73/3.47 |
% 11.73/3.47 | Instantiating formula (27) with all_116_0_154, uri_ex_p and discharging atoms ir(uri_ex_p) = all_116_0_154, yields:
% 11.73/3.47 | (247) all_116_0_154 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (247) can reduce 245 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (85) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4
% 11.73/3.47 | (86) all_0_3_3 = all_0_4_4
% 11.73/3.47 |
% 11.73/3.47 | Combining equations (54,86) yields a new equation:
% 11.73/3.47 | (68) all_0_4_4 = 0
% 11.73/3.47 |
% 11.73/3.47 | Combining equations (68,209) yields a new equation:
% 11.73/3.47 | (190) all_0_7_7 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (190) can reduce 216 to:
% 11.73/3.47 | (253) ~ (all_0_0_0 = 0)
% 11.73/3.47 |
% 11.73/3.47 | Equations (190) can reduce 214 to:
% 11.73/3.47 | (254) ~ (all_0_1_1 = 0)
% 11.73/3.47 |
% 11.73/3.47 +-Applying beta-rule and splitting (43), into two cases.
% 11.73/3.47 |-Branch one:
% 11.73/3.47 | (255) all_0_0_0 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (255) can reduce 253 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (253) ~ (all_0_0_0 = 0)
% 11.73/3.47 | (258) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (258) with all_97_0_157 yields:
% 11.73/3.47 | (259) ~ (all_97_0_157 = 0) & icext(uri_owl_Thing, uri_ex_o) = all_97_0_157
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (259) yields:
% 11.73/3.47 | (260) ~ (all_97_0_157 = 0)
% 11.73/3.47 | (261) icext(uri_owl_Thing, uri_ex_o) = all_97_0_157
% 11.73/3.47 |
% 11.73/3.47 +-Applying beta-rule and splitting (45), into two cases.
% 11.73/3.47 |-Branch one:
% 11.73/3.47 | (262) all_0_1_1 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (262) can reduce 254 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (254) ~ (all_0_1_1 = 0)
% 11.73/3.47 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (265) with all_107_0_158 yields:
% 11.73/3.47 | (266) ~ (all_107_0_158 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = all_107_0_158
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (266) yields:
% 11.73/3.47 | (267) ~ (all_107_0_158 = 0)
% 11.73/3.47 | (268) icext(uri_rdfs_Resource, uri_ex_o) = all_107_0_158
% 11.73/3.47 |
% 11.73/3.47 | Instantiating formula (14) with all_97_0_157, uri_ex_o and discharging atoms icext(uri_owl_Thing, uri_ex_o) = all_97_0_157, yields:
% 11.73/3.47 | (269) all_97_0_157 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating formula (10) with all_107_0_158, uri_ex_o and discharging atoms icext(uri_rdfs_Resource, uri_ex_o) = all_107_0_158, yields:
% 11.73/3.47 | (270) all_107_0_158 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 +-Applying beta-rule and splitting (270), into two cases.
% 11.73/3.47 |-Branch one:
% 11.73/3.47 | (271) all_107_0_158 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (271) can reduce 267 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (267) ~ (all_107_0_158 = 0)
% 11.73/3.47 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (274) with all_123_0_159 yields:
% 11.73/3.47 | (275) ~ (all_123_0_159 = 0) & ir(uri_ex_o) = all_123_0_159
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (275) yields:
% 11.73/3.47 | (276) ~ (all_123_0_159 = 0)
% 11.73/3.47 | (277) ir(uri_ex_o) = all_123_0_159
% 11.73/3.47 |
% 11.73/3.47 +-Applying beta-rule and splitting (269), into two cases.
% 11.73/3.47 |-Branch one:
% 11.73/3.47 | (278) all_97_0_157 = 0
% 11.73/3.47 |
% 11.73/3.47 | Equations (278) can reduce 260 to:
% 11.73/3.47 | (69) $false
% 11.73/3.47 |
% 11.73/3.47 |-The branch is then unsatisfiable
% 11.73/3.47 |-Branch two:
% 11.73/3.47 | (260) ~ (all_97_0_157 = 0)
% 11.73/3.47 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.47 |
% 11.73/3.47 | Instantiating (274) with all_128_0_160 yields:
% 11.73/3.47 | (282) ~ (all_128_0_160 = 0) & ir(uri_ex_o) = all_128_0_160
% 11.73/3.47 |
% 11.73/3.47 | Applying alpha-rule on (282) yields:
% 11.73/3.47 | (283) ~ (all_128_0_160 = 0)
% 11.73/3.48 | (284) ir(uri_ex_o) = all_128_0_160
% 11.73/3.48 |
% 11.73/3.48 | Instantiating formula (27) with all_128_0_160, uri_ex_o and discharging atoms ir(uri_ex_o) = all_128_0_160, yields:
% 11.73/3.48 | (285) all_128_0_160 = 0
% 11.73/3.48 |
% 11.73/3.48 | Instantiating formula (13) with uri_ex_o, all_123_0_159, all_128_0_160 and discharging atoms ir(uri_ex_o) = all_128_0_160, ir(uri_ex_o) = all_123_0_159, yields:
% 11.73/3.48 | (286) all_128_0_160 = all_123_0_159
% 11.73/3.48 |
% 11.73/3.48 | Combining equations (285,286) yields a new equation:
% 11.73/3.48 | (287) all_123_0_159 = 0
% 11.73/3.48 |
% 11.73/3.48 | Equations (287) can reduce 276 to:
% 11.73/3.48 | (69) $false
% 11.73/3.48 |
% 11.73/3.48 |-The branch is then unsatisfiable
% 11.73/3.48 |-Branch two:
% 11.73/3.48 | (289) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_0_0
% 11.73/3.48 | (290) all_0_0_0 = all_0_4_4
% 11.73/3.48 |
% 11.73/3.48 | Combining equations (209,290) yields a new equation:
% 11.73/3.48 | (291) all_0_0_0 = all_0_7_7
% 11.73/3.48 |
% 11.73/3.48 | From (291) and (18) follows:
% 11.73/3.48 | (292) iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = all_0_7_7
% 11.73/3.48 |
% 11.73/3.48 | From (291) and (289) follows:
% 11.73/3.48 | (210) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_7_7
% 11.73/3.48 |
% 11.73/3.48 +-Applying beta-rule and splitting (36), into two cases.
% 11.73/3.48 |-Branch one:
% 11.73/3.48 | (294) ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_0_0)
% 11.73/3.48 |
% 11.73/3.48 | From (291) and (294) follows:
% 11.73/3.48 | (295) ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_7_7)
% 11.73/3.48 |
% 11.73/3.48 | Using (211) and (295) yields:
% 11.73/3.48 | (57) $false
% 11.73/3.48 |
% 11.73/3.48 |-The branch is then unsatisfiable
% 11.73/3.48 |-Branch two:
% 11.73/3.48 | (297) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_0_0
% 11.73/3.48 | (298) all_0_0_0 = all_0_6_6
% 11.73/3.48 |
% 11.73/3.48 | Combining equations (298,291) yields a new equation:
% 11.73/3.48 | (299) all_0_6_6 = all_0_7_7
% 11.73/3.48 |
% 11.73/3.48 | Simplifying 299 yields:
% 11.73/3.48 | (208) all_0_6_6 = all_0_7_7
% 11.73/3.48 |
% 11.73/3.48 +-Applying beta-rule and splitting (32), into two cases.
% 11.73/3.48 |-Branch one:
% 11.73/3.48 | (301) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_4_4)
% 11.73/3.48 |
% 11.73/3.48 | From (209) and (301) follows:
% 11.73/3.48 | (302) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_7_7)
% 11.73/3.48 |
% 11.73/3.48 | Using (9) and (302) yields:
% 11.73/3.48 | (303) ~ (all_0_5_5 = all_0_7_7)
% 11.73/3.48 |
% 11.73/3.48 +-Applying beta-rule and splitting (33), into two cases.
% 11.73/3.48 |-Branch one:
% 11.73/3.48 | (113) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2)
% 11.73/3.48 |
% 11.73/3.48 | From (155) and (113) follows:
% 11.73/3.48 | (305) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_5_5)
% 11.73/3.48 |
% 11.73/3.48 | Using (55) and (305) yields:
% 11.73/3.48 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.48 |
% 11.73/3.48 +-Applying beta-rule and splitting (48), into two cases.
% 11.73/3.48 |-Branch one:
% 11.73/3.48 | (137) all_0_5_5 = 0
% 11.73/3.48 |
% 11.73/3.48 | Equations (137) can reduce 136 to:
% 11.73/3.48 | (69) $false
% 11.73/3.48 |
% 11.73/3.48 |-The branch is then unsatisfiable
% 11.73/3.48 |-Branch two:
% 11.73/3.48 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.48 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 11.73/3.48 |
% 11.73/3.48 | Instantiating (140) with all_115_0_161 yields:
% 11.73/3.48 | (311) ~ (all_115_0_161 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_115_0_161
% 11.73/3.48 |
% 11.73/3.48 | Applying alpha-rule on (311) yields:
% 11.73/3.48 | (312) ~ (all_115_0_161 = 0)
% 11.73/3.48 | (313) icext(uri_rdfs_Resource, uri_ex_p) = all_115_0_161
% 11.73/3.48 |
% 11.73/3.48 | Instantiating formula (10) with all_115_0_161, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_115_0_161, yields:
% 11.73/3.48 | (314) all_115_0_161 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.48 |
% 11.73/3.48 +-Applying beta-rule and splitting (314), into two cases.
% 11.73/3.48 |-Branch one:
% 11.73/3.48 | (315) all_115_0_161 = 0
% 11.73/3.48 |
% 11.73/3.48 | Equations (315) can reduce 312 to:
% 11.73/3.48 | (69) $false
% 11.73/3.48 |
% 11.73/3.48 |-The branch is then unsatisfiable
% 11.73/3.48 |-Branch two:
% 11.73/3.48 | (312) ~ (all_115_0_161 = 0)
% 11.73/3.48 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.48 |
% 11.73/3.48 | Instantiating (79) with all_217_0_168 yields:
% 11.73/3.48 | (319) ~ (all_217_0_168 = 0) & ir(uri_ex_p) = all_217_0_168
% 11.73/3.48 |
% 11.73/3.48 | Applying alpha-rule on (319) yields:
% 11.73/3.48 | (320) ~ (all_217_0_168 = 0)
% 11.73/3.48 | (321) ir(uri_ex_p) = all_217_0_168
% 11.73/3.48 |
% 11.73/3.48 | Instantiating formula (27) with all_217_0_168, uri_ex_p and discharging atoms ir(uri_ex_p) = all_217_0_168, yields:
% 11.73/3.48 | (322) all_217_0_168 = 0
% 11.73/3.48 |
% 11.73/3.49 | Equations (322) can reduce 320 to:
% 11.73/3.49 | (69) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (132) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2
% 11.73/3.49 | (133) all_0_2_2 = all_0_3_3
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (133,155) yields a new equation:
% 11.73/3.49 | (326) all_0_3_3 = all_0_5_5
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 326 yields:
% 11.73/3.49 | (327) all_0_3_3 = all_0_5_5
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (327,54) yields a new equation:
% 11.73/3.49 | (328) all_0_5_5 = 0
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 328 yields:
% 11.73/3.49 | (137) all_0_5_5 = 0
% 11.73/3.49 |
% 11.73/3.49 | Equations (137) can reduce 303 to:
% 11.73/3.49 | (188) ~ (all_0_7_7 = 0)
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 188 yields:
% 11.73/3.49 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.49 |
% 11.73/3.49 +-Applying beta-rule and splitting (53), into two cases.
% 11.73/3.49 |-Branch one:
% 11.73/3.49 | (190) all_0_7_7 = 0
% 11.73/3.49 |
% 11.73/3.49 | Equations (190) can reduce 189 to:
% 11.73/3.49 | (69) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.49 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.49 |
% 11.73/3.49 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.49 |-Branch one:
% 11.73/3.49 | (68) all_0_4_4 = 0
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (209,68) yields a new equation:
% 11.73/3.49 | (231) all_0_7_7 = 0
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 231 yields:
% 11.73/3.49 | (190) all_0_7_7 = 0
% 11.73/3.49 |
% 11.73/3.49 | Equations (190) can reduce 189 to:
% 11.73/3.49 | (69) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.49 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.49 |
% 11.73/3.49 | Instantiating (71) with all_123_0_174 yields:
% 11.73/3.49 | (342) ~ (all_123_0_174 = 0) & icext(uri_owl_Thing, uri_ex_p) = all_123_0_174
% 11.73/3.49 |
% 11.73/3.49 | Applying alpha-rule on (342) yields:
% 11.73/3.49 | (343) ~ (all_123_0_174 = 0)
% 11.73/3.49 | (344) icext(uri_owl_Thing, uri_ex_p) = all_123_0_174
% 11.73/3.49 |
% 11.73/3.49 | Instantiating formula (14) with all_123_0_174, uri_ex_p and discharging atoms icext(uri_owl_Thing, uri_ex_p) = all_123_0_174, yields:
% 11.73/3.49 | (345) all_123_0_174 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.49 |
% 11.73/3.49 +-Applying beta-rule and splitting (345), into two cases.
% 11.73/3.49 |-Branch one:
% 11.73/3.49 | (346) all_123_0_174 = 0
% 11.73/3.49 |
% 11.73/3.49 | Equations (346) can reduce 343 to:
% 11.73/3.49 | (69) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (343) ~ (all_123_0_174 = 0)
% 11.73/3.49 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.49 |
% 11.73/3.49 | Instantiating (79) with all_196_0_178 yields:
% 11.73/3.49 | (350) ~ (all_196_0_178 = 0) & ir(uri_ex_p) = all_196_0_178
% 11.73/3.49 |
% 11.73/3.49 | Applying alpha-rule on (350) yields:
% 11.73/3.49 | (351) ~ (all_196_0_178 = 0)
% 11.73/3.49 | (352) ir(uri_ex_p) = all_196_0_178
% 11.73/3.49 |
% 11.73/3.49 | Instantiating formula (27) with all_196_0_178, uri_ex_p and discharging atoms ir(uri_ex_p) = all_196_0_178, yields:
% 11.73/3.49 | (353) all_196_0_178 = 0
% 11.73/3.49 |
% 11.73/3.49 | Equations (353) can reduce 351 to:
% 11.73/3.49 | (69) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (355) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_4_4
% 11.73/3.49 | (356) all_0_4_4 = all_0_5_5
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (356,209) yields a new equation:
% 11.73/3.49 | (357) all_0_5_5 = all_0_7_7
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 357 yields:
% 11.73/3.49 | (358) all_0_5_5 = all_0_7_7
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (358,155) yields a new equation:
% 11.73/3.49 | (359) all_0_2_2 = all_0_7_7
% 11.73/3.49 |
% 11.73/3.49 +-Applying beta-rule and splitting (29), into two cases.
% 11.73/3.49 |-Branch one:
% 11.73/3.49 | (360) ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_2_2)
% 11.73/3.49 |
% 11.73/3.49 | From (359) and (360) follows:
% 11.73/3.49 | (361) ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_7_7)
% 11.73/3.49 |
% 11.73/3.49 | Using (210) and (361) yields:
% 11.73/3.49 | (57) $false
% 11.73/3.49 |
% 11.73/3.49 |-The branch is then unsatisfiable
% 11.73/3.49 |-Branch two:
% 11.73/3.49 | (363) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_2_2
% 11.73/3.49 | (364) all_0_2_2 = all_0_4_4
% 11.73/3.49 |
% 11.73/3.49 | Combining equations (364,359) yields a new equation:
% 11.73/3.49 | (365) all_0_4_4 = all_0_7_7
% 11.73/3.49 |
% 11.73/3.49 | Simplifying 365 yields:
% 11.73/3.49 | (209) all_0_4_4 = all_0_7_7
% 11.73/3.49 |
% 11.73/3.49 +-Applying beta-rule and splitting (39), into two cases.
% 11.73/3.49 |-Branch one:
% 11.73/3.49 | (367) ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_5_5)
% 11.73/3.49 |
% 11.73/3.49 | From (358) and (367) follows:
% 11.73/3.49 | (368) ~ (iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_7_7)
% 11.73/3.49 |
% 11.73/3.50 | Using (11) and (368) yields:
% 11.73/3.50 | (57) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (370) iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_5_5
% 11.73/3.50 | (358) all_0_5_5 = all_0_7_7
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (33), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (113) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2)
% 11.73/3.50 |
% 11.73/3.50 | From (359) and (113) follows:
% 11.73/3.50 | (218) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_7_7)
% 11.73/3.50 |
% 11.73/3.50 | Using (55) and (218) yields:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (43), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (255) all_0_0_0 = 0
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (255,291) yields a new equation:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (253) ~ (all_0_0_0 = 0)
% 11.73/3.50 | (258) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_o) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Equations (291) can reduce 253 to:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (46), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (115) all_0_2_2 = 0
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (115,359) yields a new equation:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (114) ~ (all_0_2_2 = 0)
% 11.73/3.50 | (118) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Equations (359) can reduce 114 to:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (53), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (68) all_0_4_4 = 0
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (209,68) yields a new equation:
% 11.73/3.50 | (231) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Simplifying 231 yields:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.50 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Equations (209) can reduce 67 to:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (52), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (90) all_0_6_6 = 0
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (90,208) yields a new equation:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.50 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Equations (208) can reduce 89 to:
% 11.73/3.50 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (48), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (137) all_0_5_5 = 0
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (358,137) yields a new equation:
% 11.73/3.50 | (231) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Simplifying 231 yields:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 189 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.50 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Instantiating (140) with all_148_0_187 yields:
% 11.73/3.50 | (410) ~ (all_148_0_187 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_148_0_187
% 11.73/3.50 |
% 11.73/3.50 | Applying alpha-rule on (410) yields:
% 11.73/3.50 | (411) ~ (all_148_0_187 = 0)
% 11.73/3.50 | (412) icext(uri_rdfs_Resource, uri_ex_p) = all_148_0_187
% 11.73/3.50 |
% 11.73/3.50 | Instantiating formula (10) with all_148_0_187, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_148_0_187, yields:
% 11.73/3.50 | (413) all_148_0_187 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (413), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (414) all_148_0_187 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (414) can reduce 411 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (411) ~ (all_148_0_187 = 0)
% 11.73/3.50 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Instantiating (79) with all_182_0_188 yields:
% 11.73/3.50 | (418) ~ (all_182_0_188 = 0) & ir(uri_ex_p) = all_182_0_188
% 11.73/3.50 |
% 11.73/3.50 | Applying alpha-rule on (418) yields:
% 11.73/3.50 | (419) ~ (all_182_0_188 = 0)
% 11.73/3.50 | (420) ir(uri_ex_p) = all_182_0_188
% 11.73/3.50 |
% 11.73/3.50 | Instantiating formula (27) with all_182_0_188, uri_ex_p and discharging atoms ir(uri_ex_p) = all_182_0_188, yields:
% 11.73/3.50 | (421) all_182_0_188 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (421) can reduce 419 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (132) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2
% 11.73/3.50 | (133) all_0_2_2 = all_0_3_3
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (133,359) yields a new equation:
% 11.73/3.50 | (425) all_0_3_3 = all_0_7_7
% 11.73/3.50 |
% 11.73/3.50 | Simplifying 425 yields:
% 11.73/3.50 | (426) all_0_3_3 = all_0_7_7
% 11.73/3.50 |
% 11.73/3.50 | Combining equations (426,54) yields a new equation:
% 11.73/3.50 | (231) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Simplifying 231 yields:
% 11.73/3.50 | (190) all_0_7_7 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (190) can reduce 214 to:
% 11.73/3.50 | (254) ~ (all_0_1_1 = 0)
% 11.73/3.50 |
% 11.73/3.50 | From (190) and (292) follows:
% 11.73/3.50 | (430) iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = 0
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (42), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (431) ~ (iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = 0)
% 11.73/3.50 |
% 11.73/3.50 | Using (430) and (431) yields:
% 11.73/3.50 | (57) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (430) iext(uri_rdf_type, uri_ex_o, uri_owl_Thing) = 0
% 11.73/3.50 | (434) icext(uri_owl_Thing, uri_ex_o) = 0
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (45), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (262) all_0_1_1 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (262) can reduce 254 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (254) ~ (all_0_1_1 = 0)
% 11.73/3.50 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Instantiating (265) with all_134_0_192 yields:
% 11.73/3.50 | (439) ~ (all_134_0_192 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = all_134_0_192
% 11.73/3.50 |
% 11.73/3.50 | Applying alpha-rule on (439) yields:
% 11.73/3.50 | (440) ~ (all_134_0_192 = 0)
% 11.73/3.50 | (441) icext(uri_rdfs_Resource, uri_ex_o) = all_134_0_192
% 11.73/3.50 |
% 11.73/3.50 | Instantiating formula (4) with uri_ex_o and discharging atoms icext(uri_owl_Thing, uri_ex_o) = 0, yields:
% 11.73/3.50 | (442) ir(uri_ex_o) = 0
% 11.73/3.50 |
% 11.73/3.50 | Instantiating formula (10) with all_134_0_192, uri_ex_o and discharging atoms icext(uri_rdfs_Resource, uri_ex_o) = all_134_0_192, yields:
% 11.73/3.50 | (443) all_134_0_192 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.50 |
% 11.73/3.50 +-Applying beta-rule and splitting (443), into two cases.
% 11.73/3.50 |-Branch one:
% 11.73/3.50 | (444) all_134_0_192 = 0
% 11.73/3.50 |
% 11.73/3.50 | Equations (444) can reduce 440 to:
% 11.73/3.50 | (69) $false
% 11.73/3.50 |
% 11.73/3.50 |-The branch is then unsatisfiable
% 11.73/3.50 |-Branch two:
% 11.73/3.50 | (440) ~ (all_134_0_192 = 0)
% 11.73/3.50 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 11.73/3.50 |
% 11.73/3.50 | Instantiating (274) with all_180_0_193 yields:
% 11.73/3.50 | (448) ~ (all_180_0_193 = 0) & ir(uri_ex_o) = all_180_0_193
% 11.73/3.50 |
% 11.73/3.50 | Applying alpha-rule on (448) yields:
% 11.73/3.50 | (449) ~ (all_180_0_193 = 0)
% 11.73/3.50 | (450) ir(uri_ex_o) = all_180_0_193
% 11.73/3.50 |
% 11.73/3.50 | Instantiating formula (13) with uri_ex_o, 0, all_180_0_193 and discharging atoms ir(uri_ex_o) = all_180_0_193, ir(uri_ex_o) = 0, yields:
% 11.73/3.51 | (451) all_180_0_193 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (451) can reduce 449 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (453) iext(uri_rdf_type, uri_ex_s, uri_rdfs_Resource) = all_0_1_1
% 11.73/3.51 | (454) all_0_1_1 = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 | From (454) and (21) follows:
% 11.73/3.51 | (455) iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (36), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (294) ~ (iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_0_0)
% 11.73/3.51 |
% 11.73/3.51 | Using (211) and (294) yields:
% 11.73/3.51 | (216) ~ (all_0_0_0 = all_0_7_7)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (32), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (301) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_4_4)
% 11.73/3.51 |
% 11.73/3.51 | From (209) and (301) follows:
% 11.73/3.51 | (302) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_7_7)
% 11.73/3.51 |
% 11.73/3.51 | Using (9) and (302) yields:
% 11.73/3.51 | (303) ~ (all_0_5_5 = all_0_7_7)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (35), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (305) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_5_5)
% 11.73/3.51 |
% 11.73/3.51 | Using (55) and (305) yields:
% 11.73/3.51 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (46), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (115) all_0_2_2 = 0
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (115,155) yields a new equation:
% 11.73/3.51 | (137) all_0_5_5 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (137) can reduce 136 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (114) ~ (all_0_2_2 = 0)
% 11.73/3.51 | (118) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Equations (155) can reduce 114 to:
% 11.73/3.51 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (48), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (137) all_0_5_5 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (137) can reduce 136 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (136) ~ (all_0_5_5 = 0)
% 11.73/3.51 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Instantiating (140) with all_102_0_195 yields:
% 11.73/3.51 | (473) ~ (all_102_0_195 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_102_0_195
% 11.73/3.51 |
% 11.73/3.51 | Applying alpha-rule on (473) yields:
% 11.73/3.51 | (474) ~ (all_102_0_195 = 0)
% 11.73/3.51 | (475) icext(uri_rdfs_Resource, uri_ex_p) = all_102_0_195
% 11.73/3.51 |
% 11.73/3.51 | Instantiating formula (10) with all_102_0_195, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_102_0_195, yields:
% 11.73/3.51 | (476) all_102_0_195 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (476), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (477) all_102_0_195 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (477) can reduce 474 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (474) ~ (all_102_0_195 = 0)
% 11.73/3.51 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Instantiating (79) with all_118_0_196 yields:
% 11.73/3.51 | (481) ~ (all_118_0_196 = 0) & ir(uri_ex_p) = all_118_0_196
% 11.73/3.51 |
% 11.73/3.51 | Applying alpha-rule on (481) yields:
% 11.73/3.51 | (482) ~ (all_118_0_196 = 0)
% 11.73/3.51 | (483) ir(uri_ex_p) = all_118_0_196
% 11.73/3.51 |
% 11.73/3.51 | Instantiating formula (27) with all_118_0_196, uri_ex_p and discharging atoms ir(uri_ex_p) = all_118_0_196, yields:
% 11.73/3.51 | (484) all_118_0_196 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (484) can reduce 482 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (486) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_5_5
% 11.73/3.51 | (327) all_0_3_3 = all_0_5_5
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (54,327) yields a new equation:
% 11.73/3.51 | (137) all_0_5_5 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (137) can reduce 303 to:
% 11.73/3.51 | (188) ~ (all_0_7_7 = 0)
% 11.73/3.51 |
% 11.73/3.51 | Simplifying 188 yields:
% 11.73/3.51 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (53), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (190) all_0_7_7 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (190) can reduce 189 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.51 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (52), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (90) all_0_6_6 = 0
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (90,208) yields a new equation:
% 11.73/3.51 | (190) all_0_7_7 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (190) can reduce 189 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (89) ~ (all_0_6_6 = 0)
% 11.73/3.51 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Equations (208) can reduce 89 to:
% 11.73/3.51 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (45), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (262) all_0_1_1 = 0
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (262,454) yields a new equation:
% 11.73/3.51 | (190) all_0_7_7 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (190) can reduce 189 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (254) ~ (all_0_1_1 = 0)
% 11.73/3.51 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Equations (454) can reduce 254 to:
% 11.73/3.51 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (47), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (68) all_0_4_4 = 0
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (209,68) yields a new equation:
% 11.73/3.51 | (231) all_0_7_7 = 0
% 11.73/3.51 |
% 11.73/3.51 | Simplifying 231 yields:
% 11.73/3.51 | (190) all_0_7_7 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (190) can reduce 189 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (67) ~ (all_0_4_4 = 0)
% 11.73/3.51 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Instantiating (71) with all_119_0_201 yields:
% 11.73/3.51 | (513) ~ (all_119_0_201 = 0) & icext(uri_owl_Thing, uri_ex_p) = all_119_0_201
% 11.73/3.51 |
% 11.73/3.51 | Applying alpha-rule on (513) yields:
% 11.73/3.51 | (514) ~ (all_119_0_201 = 0)
% 11.73/3.51 | (515) icext(uri_owl_Thing, uri_ex_p) = all_119_0_201
% 11.73/3.51 |
% 11.73/3.51 | Instantiating formula (14) with all_119_0_201, uri_ex_p and discharging atoms icext(uri_owl_Thing, uri_ex_p) = all_119_0_201, yields:
% 11.73/3.51 | (516) all_119_0_201 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (516), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (517) all_119_0_201 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (517) can reduce 514 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (514) ~ (all_119_0_201 = 0)
% 11.73/3.51 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 11.73/3.51 |
% 11.73/3.51 | Instantiating (79) with all_132_0_202 yields:
% 11.73/3.51 | (521) ~ (all_132_0_202 = 0) & ir(uri_ex_p) = all_132_0_202
% 11.73/3.51 |
% 11.73/3.51 | Applying alpha-rule on (521) yields:
% 11.73/3.51 | (522) ~ (all_132_0_202 = 0)
% 11.73/3.51 | (523) ir(uri_ex_p) = all_132_0_202
% 11.73/3.51 |
% 11.73/3.51 | Instantiating formula (27) with all_132_0_202, uri_ex_p and discharging atoms ir(uri_ex_p) = all_132_0_202, yields:
% 11.73/3.51 | (524) all_132_0_202 = 0
% 11.73/3.51 |
% 11.73/3.51 | Equations (524) can reduce 522 to:
% 11.73/3.51 | (69) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (355) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_4_4
% 11.73/3.51 | (356) all_0_4_4 = all_0_5_5
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (356,209) yields a new equation:
% 11.73/3.51 | (357) all_0_5_5 = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 | Simplifying 357 yields:
% 11.73/3.51 | (358) all_0_5_5 = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 | Combining equations (358,155) yields a new equation:
% 11.73/3.51 | (359) all_0_2_2 = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 | From (358) and (9) follows:
% 11.73/3.51 | (531) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_7_7
% 11.73/3.51 |
% 11.73/3.51 +-Applying beta-rule and splitting (30), into two cases.
% 11.73/3.51 |-Branch one:
% 11.73/3.51 | (532) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_1_1)
% 11.73/3.51 |
% 11.73/3.51 | From (454) and (532) follows:
% 11.73/3.51 | (302) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_7_7)
% 11.73/3.51 |
% 11.73/3.51 | Using (531) and (302) yields:
% 11.73/3.51 | (57) $false
% 11.73/3.51 |
% 11.73/3.51 |-The branch is then unsatisfiable
% 11.73/3.51 |-Branch two:
% 11.73/3.51 | (535) iext(uri_rdf_type, uri_ex_p, uri_rdfs_Resource) = all_0_1_1
% 11.73/3.52 | (536) all_0_1_1 = all_0_5_5
% 11.73/3.52 |
% 11.73/3.52 | Combining equations (536,454) yields a new equation:
% 11.73/3.52 | (357) all_0_5_5 = all_0_7_7
% 11.73/3.52 |
% 11.73/3.52 | Simplifying 357 yields:
% 11.73/3.52 | (358) all_0_5_5 = all_0_7_7
% 11.73/3.52 |
% 11.73/3.52 +-Applying beta-rule and splitting (33), into two cases.
% 11.73/3.52 |-Branch one:
% 11.73/3.52 | (113) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2)
% 11.73/3.52 |
% 11.73/3.52 | From (359) and (113) follows:
% 11.73/3.52 | (218) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_7_7)
% 11.73/3.52 |
% 11.73/3.52 | Using (55) and (218) yields:
% 11.73/3.52 | (189) ~ (all_0_7_7 = 0)
% 11.73/3.52 |
% 11.73/3.52 +-Applying beta-rule and splitting (45), into two cases.
% 11.73/3.52 |-Branch one:
% 11.73/3.52 | (262) all_0_1_1 = 0
% 11.73/3.52 |
% 12.23/3.52 | Combining equations (262,454) yields a new equation:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 189 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (254) ~ (all_0_1_1 = 0)
% 12.23/3.52 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Equations (454) can reduce 254 to:
% 12.23/3.52 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (52), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (90) all_0_6_6 = 0
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (90,208) yields a new equation:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 189 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (89) ~ (all_0_6_6 = 0)
% 12.23/3.52 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Equations (208) can reduce 89 to:
% 12.23/3.52 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (53), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 189 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.52 | (193) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_s) = v0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (46), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (115) all_0_2_2 = 0
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (115,359) yields a new equation:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 189 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (114) ~ (all_0_2_2 = 0)
% 12.23/3.52 | (118) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Equations (359) can reduce 114 to:
% 12.23/3.52 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (48), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (137) all_0_5_5 = 0
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (358,137) yields a new equation:
% 12.23/3.52 | (231) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Simplifying 231 yields:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 189 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (136) ~ (all_0_5_5 = 0)
% 12.23/3.52 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Instantiating (140) with all_131_0_210 yields:
% 12.23/3.52 | (570) ~ (all_131_0_210 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_131_0_210
% 12.23/3.52 |
% 12.23/3.52 | Applying alpha-rule on (570) yields:
% 12.23/3.52 | (571) ~ (all_131_0_210 = 0)
% 12.23/3.52 | (572) icext(uri_rdfs_Resource, uri_ex_p) = all_131_0_210
% 12.23/3.52 |
% 12.23/3.52 | Instantiating formula (10) with all_131_0_210, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_131_0_210, yields:
% 12.23/3.52 | (573) all_131_0_210 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (573), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (574) all_131_0_210 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (574) can reduce 571 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (571) ~ (all_131_0_210 = 0)
% 12.23/3.52 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Instantiating (79) with all_186_0_212 yields:
% 12.23/3.52 | (578) ~ (all_186_0_212 = 0) & ir(uri_ex_p) = all_186_0_212
% 12.23/3.52 |
% 12.23/3.52 | Applying alpha-rule on (578) yields:
% 12.23/3.52 | (579) ~ (all_186_0_212 = 0)
% 12.23/3.52 | (580) ir(uri_ex_p) = all_186_0_212
% 12.23/3.52 |
% 12.23/3.52 | Instantiating formula (27) with all_186_0_212, uri_ex_p and discharging atoms ir(uri_ex_p) = all_186_0_212, yields:
% 12.23/3.52 | (581) all_186_0_212 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (581) can reduce 579 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (132) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_2_2
% 12.23/3.52 | (133) all_0_2_2 = all_0_3_3
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (133,359) yields a new equation:
% 12.23/3.52 | (425) all_0_3_3 = all_0_7_7
% 12.23/3.52 |
% 12.23/3.52 | Simplifying 425 yields:
% 12.23/3.52 | (426) all_0_3_3 = all_0_7_7
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (426,54) yields a new equation:
% 12.23/3.52 | (231) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Simplifying 231 yields:
% 12.23/3.52 | (190) all_0_7_7 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (190) can reduce 216 to:
% 12.23/3.52 | (253) ~ (all_0_0_0 = 0)
% 12.23/3.52 |
% 12.23/3.52 | From (190) and (455) follows:
% 12.23/3.52 | (590) iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = 0
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (44), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (591) ~ (iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = 0)
% 12.23/3.52 |
% 12.23/3.52 | Using (590) and (591) yields:
% 12.23/3.52 | (57) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (590) iext(uri_rdf_type, uri_ex_o, uri_rdfs_Resource) = 0
% 12.23/3.52 | (594) icext(uri_rdfs_Resource, uri_ex_o) = 0
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (43), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (255) all_0_0_0 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (255) can reduce 253 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (253) ~ (all_0_0_0 = 0)
% 12.23/3.52 | (258) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_o) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Instantiating (258) with all_130_0_216 yields:
% 12.23/3.52 | (599) ~ (all_130_0_216 = 0) & icext(uri_owl_Thing, uri_ex_o) = all_130_0_216
% 12.23/3.52 |
% 12.23/3.52 | Applying alpha-rule on (599) yields:
% 12.23/3.52 | (600) ~ (all_130_0_216 = 0)
% 12.23/3.52 | (601) icext(uri_owl_Thing, uri_ex_o) = all_130_0_216
% 12.23/3.52 |
% 12.23/3.52 | Instantiating formula (14) with all_130_0_216, uri_ex_o and discharging atoms icext(uri_owl_Thing, uri_ex_o) = all_130_0_216, yields:
% 12.23/3.52 | (602) all_130_0_216 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Instantiating formula (17) with uri_ex_o and discharging atoms icext(uri_rdfs_Resource, uri_ex_o) = 0, yields:
% 12.23/3.52 | (442) ir(uri_ex_o) = 0
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (602), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (604) all_130_0_216 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (604) can reduce 600 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (600) ~ (all_130_0_216 = 0)
% 12.23/3.52 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.52 |
% 12.23/3.52 | Instantiating (274) with all_184_0_217 yields:
% 12.23/3.52 | (608) ~ (all_184_0_217 = 0) & ir(uri_ex_o) = all_184_0_217
% 12.23/3.52 |
% 12.23/3.52 | Applying alpha-rule on (608) yields:
% 12.23/3.52 | (609) ~ (all_184_0_217 = 0)
% 12.23/3.52 | (610) ir(uri_ex_o) = all_184_0_217
% 12.23/3.52 |
% 12.23/3.52 | Instantiating formula (13) with uri_ex_o, 0, all_184_0_217 and discharging atoms ir(uri_ex_o) = all_184_0_217, ir(uri_ex_o) = 0, yields:
% 12.23/3.52 | (611) all_184_0_217 = 0
% 12.23/3.52 |
% 12.23/3.52 | Equations (611) can reduce 609 to:
% 12.23/3.52 | (69) $false
% 12.23/3.52 |
% 12.23/3.52 |-The branch is then unsatisfiable
% 12.23/3.52 |-Branch two:
% 12.23/3.52 | (297) iext(uri_rdf_type, uri_ex_s, uri_owl_Thing) = all_0_0_0
% 12.23/3.52 | (298) all_0_0_0 = all_0_6_6
% 12.23/3.52 |
% 12.23/3.52 | Combining equations (208,298) yields a new equation:
% 12.23/3.52 | (291) all_0_0_0 = all_0_7_7
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (29), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (360) ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_2_2)
% 12.23/3.52 |
% 12.23/3.52 | From (155) and (360) follows:
% 12.23/3.52 | (617) ~ (iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_5_5)
% 12.23/3.52 |
% 12.23/3.52 | Using (210) and (617) yields:
% 12.23/3.52 | (303) ~ (all_0_5_5 = all_0_7_7)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (34), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.52 | (66) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4)
% 12.23/3.52 |
% 12.23/3.52 | From (209) and (66) follows:
% 12.23/3.52 | (218) ~ (iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_7_7)
% 12.23/3.52 |
% 12.23/3.52 | Using (55) and (218) yields:
% 12.23/3.52 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.52 |
% 12.23/3.52 +-Applying beta-rule and splitting (45), into two cases.
% 12.23/3.52 |-Branch one:
% 12.23/3.53 | (262) all_0_1_1 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (262,454) yields a new equation:
% 12.23/3.53 | (190) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (190) can reduce 189 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (254) ~ (all_0_1_1 = 0)
% 12.23/3.53 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (265) with all_104_0_218 yields:
% 12.23/3.53 | (627) ~ (all_104_0_218 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = all_104_0_218
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (627) yields:
% 12.23/3.53 | (628) ~ (all_104_0_218 = 0)
% 12.23/3.53 | (629) icext(uri_rdfs_Resource, uri_ex_o) = all_104_0_218
% 12.23/3.53 |
% 12.23/3.53 | Equations (454) can reduce 254 to:
% 12.23/3.53 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (52), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (90) all_0_6_6 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (90,208) yields a new equation:
% 12.23/3.53 | (190) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (190) can reduce 189 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (89) ~ (all_0_6_6 = 0)
% 12.23/3.53 | (93) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_s) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Equations (208) can reduce 89 to:
% 12.23/3.53 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (47), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (68) all_0_4_4 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (209,68) yields a new equation:
% 12.23/3.53 | (231) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Simplifying 231 yields:
% 12.23/3.53 | (190) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (190) can reduce 189 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (67) ~ (all_0_4_4 = 0)
% 12.23/3.53 | (71) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_p) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Equations (209) can reduce 67 to:
% 12.23/3.53 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (43), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (255) all_0_0_0 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (255,291) yields a new equation:
% 12.23/3.53 | (190) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (190) can reduce 189 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (253) ~ (all_0_0_0 = 0)
% 12.23/3.53 | (258) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_Thing, uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (258) with all_119_0_221 yields:
% 12.23/3.53 | (649) ~ (all_119_0_221 = 0) & icext(uri_owl_Thing, uri_ex_o) = all_119_0_221
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (649) yields:
% 12.23/3.53 | (650) ~ (all_119_0_221 = 0)
% 12.23/3.53 | (651) icext(uri_owl_Thing, uri_ex_o) = all_119_0_221
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (14) with all_119_0_221, uri_ex_o and discharging atoms icext(uri_owl_Thing, uri_ex_o) = all_119_0_221, yields:
% 12.23/3.53 | (652) all_119_0_221 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (10) with all_104_0_218, uri_ex_o and discharging atoms icext(uri_rdfs_Resource, uri_ex_o) = all_104_0_218, yields:
% 12.23/3.53 | (653) all_104_0_218 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (652), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (654) all_119_0_221 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (654) can reduce 650 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (650) ~ (all_119_0_221 = 0)
% 12.23/3.53 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (274) with all_137_0_223 yields:
% 12.23/3.53 | (658) ~ (all_137_0_223 = 0) & ir(uri_ex_o) = all_137_0_223
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (658) yields:
% 12.23/3.53 | (659) ~ (all_137_0_223 = 0)
% 12.23/3.53 | (660) ir(uri_ex_o) = all_137_0_223
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (653), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (661) all_104_0_218 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (661) can reduce 628 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (628) ~ (all_104_0_218 = 0)
% 12.23/3.53 | (274) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_o) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (274) with all_152_0_226 yields:
% 12.23/3.53 | (665) ~ (all_152_0_226 = 0) & ir(uri_ex_o) = all_152_0_226
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (665) yields:
% 12.23/3.53 | (666) ~ (all_152_0_226 = 0)
% 12.23/3.53 | (667) ir(uri_ex_o) = all_152_0_226
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (27) with all_152_0_226, uri_ex_o and discharging atoms ir(uri_ex_o) = all_152_0_226, yields:
% 12.23/3.53 | (668) all_152_0_226 = 0
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (13) with uri_ex_o, all_137_0_223, all_152_0_226 and discharging atoms ir(uri_ex_o) = all_152_0_226, ir(uri_ex_o) = all_137_0_223, yields:
% 12.23/3.53 | (669) all_152_0_226 = all_137_0_223
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (668,669) yields a new equation:
% 12.23/3.53 | (670) all_137_0_223 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (670) can reduce 659 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (85) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property) = all_0_4_4
% 12.23/3.53 | (86) all_0_3_3 = all_0_4_4
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (54,86) yields a new equation:
% 12.23/3.53 | (68) all_0_4_4 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (68,209) yields a new equation:
% 12.23/3.53 | (190) all_0_7_7 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (190) can reduce 303 to:
% 12.23/3.53 | (136) ~ (all_0_5_5 = 0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (48), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (137) all_0_5_5 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (137) can reduce 136 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (136) ~ (all_0_5_5 = 0)
% 12.23/3.53 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (46), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (115) all_0_2_2 = 0
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (155,115) yields a new equation:
% 12.23/3.53 | (328) all_0_5_5 = 0
% 12.23/3.53 |
% 12.23/3.53 | Simplifying 328 yields:
% 12.23/3.53 | (137) all_0_5_5 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (137) can reduce 136 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (114) ~ (all_0_2_2 = 0)
% 12.23/3.53 | (118) ? [v0] : ( ~ (v0 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (118) with all_124_0_229 yields:
% 12.23/3.53 | (687) ~ (all_124_0_229 = 0) & icext(uri_owl_ObjectProperty, uri_ex_p) = all_124_0_229
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (687) yields:
% 12.23/3.53 | (688) ~ (all_124_0_229 = 0)
% 12.23/3.53 | (689) icext(uri_owl_ObjectProperty, uri_ex_p) = all_124_0_229
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (15) with all_124_0_229, uri_ex_p and discharging atoms icext(uri_owl_ObjectProperty, uri_ex_p) = all_124_0_229, yields:
% 12.23/3.53 | (690) all_124_0_229 = 0 | ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 12.23/3.53 |
% 12.23/3.53 +-Applying beta-rule and splitting (690), into two cases.
% 12.23/3.53 |-Branch one:
% 12.23/3.53 | (691) all_124_0_229 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (691) can reduce 688 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (688) ~ (all_124_0_229 = 0)
% 12.23/3.53 | (126) ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 12.23/3.53 |
% 12.23/3.53 | Instantiating (126) with all_148_0_230 yields:
% 12.23/3.53 | (695) ~ (all_148_0_230 = 0) & ip(uri_ex_p) = all_148_0_230
% 12.23/3.53 |
% 12.23/3.53 | Applying alpha-rule on (695) yields:
% 12.23/3.53 | (696) ~ (all_148_0_230 = 0)
% 12.23/3.53 | (697) ip(uri_ex_p) = all_148_0_230
% 12.23/3.53 |
% 12.23/3.53 | Instantiating formula (22) with uri_ex_p, all_148_0_230, 0 and discharging atoms ip(uri_ex_p) = all_148_0_230, ip(uri_ex_p) = 0, yields:
% 12.23/3.53 | (698) all_148_0_230 = 0
% 12.23/3.53 |
% 12.23/3.53 | Equations (698) can reduce 696 to:
% 12.23/3.53 | (69) $false
% 12.23/3.53 |
% 12.23/3.53 |-The branch is then unsatisfiable
% 12.23/3.53 |-Branch two:
% 12.23/3.53 | (363) iext(uri_rdf_type, uri_ex_p, uri_owl_Thing) = all_0_2_2
% 12.23/3.53 | (364) all_0_2_2 = all_0_4_4
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (155,364) yields a new equation:
% 12.23/3.53 | (356) all_0_4_4 = all_0_5_5
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (209,356) yields a new equation:
% 12.23/3.53 | (358) all_0_5_5 = all_0_7_7
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (358,356) yields a new equation:
% 12.23/3.53 | (209) all_0_4_4 = all_0_7_7
% 12.23/3.53 |
% 12.23/3.53 | Combining equations (209,364) yields a new equation:
% 12.23/3.53 | (359) all_0_2_2 = all_0_7_7
% 12.23/3.53 |
% 12.23/3.54 +-Applying beta-rule and splitting (24), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (253) ~ (all_0_0_0 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (291) can reduce 253 to:
% 12.23/3.54 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (45), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (262) all_0_1_1 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (262,454) yields a new equation:
% 12.23/3.54 | (190) all_0_7_7 = 0
% 12.23/3.54 |
% 12.23/3.54 | Equations (190) can reduce 189 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (254) ~ (all_0_1_1 = 0)
% 12.23/3.54 | (265) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_o) = v0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (454) can reduce 254 to:
% 12.23/3.54 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (48), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (137) all_0_5_5 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (358,137) yields a new equation:
% 12.23/3.54 | (231) all_0_7_7 = 0
% 12.23/3.54 |
% 12.23/3.54 | Simplifying 231 yields:
% 12.23/3.54 | (190) all_0_7_7 = 0
% 12.23/3.54 |
% 12.23/3.54 | Equations (190) can reduce 189 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (136) ~ (all_0_5_5 = 0)
% 12.23/3.54 | (140) ? [v0] : ( ~ (v0 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = v0)
% 12.23/3.54 |
% 12.23/3.54 | Instantiating (140) with all_87_0_233 yields:
% 12.23/3.54 | (720) ~ (all_87_0_233 = 0) & icext(uri_rdfs_Resource, uri_ex_p) = all_87_0_233
% 12.23/3.54 |
% 12.23/3.54 | Applying alpha-rule on (720) yields:
% 12.23/3.54 | (721) ~ (all_87_0_233 = 0)
% 12.23/3.54 | (722) icext(uri_rdfs_Resource, uri_ex_p) = all_87_0_233
% 12.23/3.54 |
% 12.23/3.54 | Instantiating formula (10) with all_87_0_233, uri_ex_p and discharging atoms icext(uri_rdfs_Resource, uri_ex_p) = all_87_0_233, yields:
% 12.23/3.54 | (723) all_87_0_233 = 0 | ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (723), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (724) all_87_0_233 = 0
% 12.23/3.54 |
% 12.23/3.54 | Equations (724) can reduce 721 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (721) ~ (all_87_0_233 = 0)
% 12.23/3.54 | (79) ? [v0] : ( ~ (v0 = 0) & ir(uri_ex_p) = v0)
% 12.23/3.54 |
% 12.23/3.54 | Instantiating (79) with all_128_0_239 yields:
% 12.23/3.54 | (728) ~ (all_128_0_239 = 0) & ir(uri_ex_p) = all_128_0_239
% 12.23/3.54 |
% 12.23/3.54 | Applying alpha-rule on (728) yields:
% 12.23/3.54 | (729) ~ (all_128_0_239 = 0)
% 12.23/3.54 | (730) ir(uri_ex_p) = all_128_0_239
% 12.23/3.54 |
% 12.23/3.54 | Instantiating formula (27) with all_128_0_239, uri_ex_p and discharging atoms ir(uri_ex_p) = all_128_0_239, yields:
% 12.23/3.54 | (731) all_128_0_239 = 0
% 12.23/3.54 |
% 12.23/3.54 | Equations (731) can reduce 729 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (255) all_0_0_0 = 0
% 12.23/3.54 | (734) ~ (all_0_1_1 = 0) | ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (255,291) yields a new equation:
% 12.23/3.54 | (190) all_0_7_7 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (190,208) yields a new equation:
% 12.23/3.54 | (90) all_0_6_6 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (190,358) yields a new equation:
% 12.23/3.54 | (137) all_0_5_5 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (190,209) yields a new equation:
% 12.23/3.54 | (68) all_0_4_4 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (190,359) yields a new equation:
% 12.23/3.54 | (115) all_0_2_2 = 0
% 12.23/3.54 |
% 12.23/3.54 | Combining equations (190,454) yields a new equation:
% 12.23/3.54 | (262) all_0_1_1 = 0
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (734), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (254) ~ (all_0_1_1 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (262) can reduce 254 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (262) all_0_1_1 = 0
% 12.23/3.54 | (744) ~ (all_0_2_2 = 0) | ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (744), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (114) ~ (all_0_2_2 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (115) can reduce 114 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (115) all_0_2_2 = 0
% 12.23/3.54 | (748) ~ (all_0_3_3 = 0) | ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (748), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (749) ~ (all_0_3_3 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (54) can reduce 749 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (54) all_0_3_3 = 0
% 12.23/3.54 | (752) ~ (all_0_4_4 = 0) | ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (752), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (67) ~ (all_0_4_4 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (68) can reduce 67 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (68) all_0_4_4 = 0
% 12.23/3.54 | (756) ~ (all_0_5_5 = 0) | ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (756), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (136) ~ (all_0_5_5 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (137) can reduce 136 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (137) all_0_5_5 = 0
% 12.23/3.54 | (760) ~ (all_0_6_6 = 0) | ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 +-Applying beta-rule and splitting (760), into two cases.
% 12.23/3.54 |-Branch one:
% 12.23/3.54 | (89) ~ (all_0_6_6 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (90) can reduce 89 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (90) all_0_6_6 = 0
% 12.23/3.54 | (189) ~ (all_0_7_7 = 0)
% 12.23/3.54 |
% 12.23/3.54 | Equations (190) can reduce 189 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 |-Branch two:
% 12.23/3.54 | (749) ~ (all_0_3_3 = 0)
% 12.23/3.54 | (126) ? [v0] : ( ~ (v0 = 0) & ip(uri_ex_p) = v0)
% 12.23/3.54 |
% 12.23/3.54 | Instantiating (126) with all_13_0_244 yields:
% 12.23/3.54 | (768) ~ (all_13_0_244 = 0) & ip(uri_ex_p) = all_13_0_244
% 12.23/3.54 |
% 12.23/3.54 | Applying alpha-rule on (768) yields:
% 12.23/3.54 | (769) ~ (all_13_0_244 = 0)
% 12.23/3.54 | (770) ip(uri_ex_p) = all_13_0_244
% 12.23/3.54 |
% 12.23/3.54 | Instantiating formula (22) with uri_ex_p, 0, all_13_0_244 and discharging atoms ip(uri_ex_p) = all_13_0_244, ip(uri_ex_p) = 0, yields:
% 12.23/3.54 | (771) all_13_0_244 = 0
% 12.23/3.54 |
% 12.23/3.54 | Equations (771) can reduce 769 to:
% 12.23/3.54 | (69) $false
% 12.23/3.54 |
% 12.23/3.54 |-The branch is then unsatisfiable
% 12.23/3.54 % SZS output end Proof for theBenchmark
% 12.23/3.54
% 12.23/3.54 2938ms
%------------------------------------------------------------------------------