TSTP Solution File: SWB026+2 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWB026+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 18:59:43 EDT 2022
% Result : Theorem 2.92s 1.40s
% Output : Proof 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB026+2 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n021.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 1 04:16:45 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.63/0.61 ____ _
% 0.63/0.61 ___ / __ \_____(_)___ ________ __________
% 0.63/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.61
% 0.63/0.61 A Theorem Prover for First-Order Logic
% 0.63/0.61 (ePrincess v.1.0)
% 0.63/0.61
% 0.63/0.61 (c) Philipp Rümmer, 2009-2015
% 0.63/0.61 (c) Peter Backeman, 2014-2015
% 0.63/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.61 Bug reports to peter@backeman.se
% 0.63/0.61
% 0.63/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.61
% 0.63/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.49/0.96 Prover 0: Preprocessing ...
% 1.69/1.08 Prover 0: Constructing countermodel ...
% 2.92/1.40 Prover 0: proved (734ms)
% 2.92/1.40
% 2.92/1.40 No countermodel exists, formula is valid
% 2.92/1.40 % SZS status Theorem for theBenchmark
% 2.92/1.40
% 2.92/1.40 Generating proof ... found it (size 17)
% 3.58/1.56
% 3.58/1.56 % SZS output start Proof for theBenchmark
% 3.58/1.56 Assumed formulas after preprocessing and simplification:
% 3.58/1.56 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (iext(uri_rdfs_range, uri_ex_p, v1) & iext(uri_owl_oneOf, v1, v3) & iext(uri_owl_oneOf, v0, v2) & iext(uri_rdf_rest, v3, uri_rdf_nil) & iext(uri_rdf_rest, v2, uri_rdf_nil) & iext(uri_rdf_first, v3, uri_ex_u) & iext(uri_rdf_first, v2, uri_ex_w) & iext(uri_rdfs_domain, uri_ex_p, v0) & iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) & ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ icext(v4, v7) | ~ iext(uri_owl_oneOf, v4, v5) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_first, v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ icext(uri_owl_InverseFunctionalProperty, v4) | ~ iext(v4, v6, v7) | ~ iext(v4, v5, v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ iext(v4, v6, v7) | ~ iext(uri_rdfs_domain, v4, v5) | icext(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ ic(v4) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_first, v5, v6) | iext(uri_owl_oneOf, v4, v5) | ? [v7] : (( ~ (v7 = v6) | ~ icext(v4, v6)) & (v7 = v6 | icext(v4, v7)))) & ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_oneOf, v4, v5) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_first, v5, v6) | ic(v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ iext(uri_owl_oneOf, v4, v5) | ~ iext(uri_rdf_rest, v5, uri_rdf_nil) | ~ iext(uri_rdf_first, v5, v6) | icext(v4, v6)) & ! [v4] : ! [v5] : ( ~ icext(v5, v4) | iext(uri_rdf_type, v4, v5)) & ! [v4] : ! [v5] : ( ~ iext(uri_rdf_type, v4, v5) | icext(v5, v4)) & ! [v4] : ( ~ icext(uri_owl_InverseFunctionalProperty, v4) | ip(v4)) & ! [v4] : ( ~ ip(v4) | icext(uri_owl_InverseFunctionalProperty, v4) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = v5) & iext(v4, v6, v7) & iext(v4, v5, v7))) & ! [v4] : ( ~ ip(v4) | iext(uri_rdf_type, v4, uri_rdf_Property)) & ! [v4] : ( ~ iext(uri_rdf_type, v4, uri_rdf_Property) | ip(v4)))
% 3.58/1.57 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.58/1.57 | (1) iext(uri_rdfs_range, uri_ex_p, all_0_2_2) & iext(uri_owl_oneOf, all_0_2_2, all_0_0_0) & iext(uri_owl_oneOf, all_0_3_3, all_0_1_1) & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) & iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil) & iext(uri_rdf_first, all_0_0_0, uri_ex_u) & iext(uri_rdf_first, all_0_1_1, uri_ex_w) & iext(uri_rdfs_domain, uri_ex_p, all_0_3_3) & iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property) & ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ icext(v0, v3) | ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ icext(uri_owl_InverseFunctionalProperty, v0) | ~ iext(v0, v2, v3) | ~ iext(v0, v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_rdfs_domain, v0, v1) | icext(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ ic(v0) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_oneOf, v0, v1) | ? [v3] : (( ~ (v3 = v2) | ~ icext(v0, v2)) & (v3 = v2 | icext(v0, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | ic(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | icext(v0, v2)) & ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1)) & ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0)) & ! [v0] : ( ~ icext(uri_owl_InverseFunctionalProperty, v0) | ip(v0)) & ! [v0] : ( ~ ip(v0) | icext(uri_owl_InverseFunctionalProperty, v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = v1) & iext(v0, v2, v3) & iext(v0, v1, v3))) & ! [v0] : ( ~ ip(v0) | iext(uri_rdf_type, v0, uri_rdf_Property)) & ! [v0] : ( ~ iext(uri_rdf_type, v0, uri_rdf_Property) | ip(v0))
% 3.58/1.58 |
% 3.58/1.58 | Applying alpha-rule on (1) yields:
% 3.58/1.58 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | icext(v0, v2))
% 3.58/1.58 | (3) ! [v0] : ( ~ icext(uri_owl_InverseFunctionalProperty, v0) | ip(v0))
% 3.58/1.58 | (4) ! [v0] : ( ~ iext(uri_rdf_type, v0, uri_rdf_Property) | ip(v0))
% 3.58/1.58 | (5) ! [v0] : ( ~ ip(v0) | iext(uri_rdf_type, v0, uri_rdf_Property))
% 3.58/1.58 | (6) iext(uri_rdf_first, all_0_1_1, uri_ex_w)
% 3.58/1.58 | (7) iext(uri_rdfs_domain, uri_ex_p, all_0_3_3)
% 3.58/1.58 | (8) iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil)
% 3.58/1.58 | (9) ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty)
% 3.58/1.58 | (10) iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property)
% 3.58/1.58 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | ic(v0))
% 3.58/1.58 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ iext(v0, v2, v3) | ~ iext(uri_rdfs_domain, v0, v1) | icext(v1, v2))
% 3.58/1.59 | (13) iext(uri_rdf_first, all_0_0_0, uri_ex_u)
% 3.58/1.59 | (14) ! [v0] : ( ~ ip(v0) | icext(uri_owl_InverseFunctionalProperty, v0) | ? [v1] : ? [v2] : ? [v3] : ( ~ (v2 = v1) & iext(v0, v2, v3) & iext(v0, v1, v3)))
% 3.58/1.59 | (15) iext(uri_rdfs_range, uri_ex_p, all_0_2_2)
% 3.58/1.59 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ icext(uri_owl_InverseFunctionalProperty, v0) | ~ iext(v0, v2, v3) | ~ iext(v0, v1, v3))
% 3.58/1.59 | (17) iext(uri_owl_oneOf, all_0_2_2, all_0_0_0)
% 3.58/1.59 | (18) ! [v0] : ! [v1] : ( ~ iext(uri_rdf_type, v0, v1) | icext(v1, v0))
% 3.58/1.59 | (19) ! [v0] : ! [v1] : ( ~ icext(v1, v0) | iext(uri_rdf_type, v0, v1))
% 3.58/1.59 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ icext(v0, v3) | ~ iext(uri_owl_oneOf, v0, v1) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2))
% 3.58/1.59 | (21) iext(uri_owl_oneOf, all_0_3_3, all_0_1_1)
% 3.58/1.59 | (22) iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil)
% 3.58/1.59 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ ic(v0) | ~ iext(uri_rdf_rest, v1, uri_rdf_nil) | ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_oneOf, v0, v1) | ? [v3] : (( ~ (v3 = v2) | ~ icext(v0, v2)) & (v3 = v2 | icext(v0, v3))))
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (12) with all_0_3_3, uri_ex_p, uri_rdf_Property, uri_rdfs_domain and discharging atoms iext(uri_rdfs_domain, uri_ex_p, all_0_3_3), iext(uri_rdfs_domain, uri_rdfs_domain, uri_rdf_Property), yields:
% 3.58/1.59 | (24) icext(uri_rdf_Property, uri_ex_p)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (19) with uri_rdf_Property, uri_ex_p and discharging atoms icext(uri_rdf_Property, uri_ex_p), yields:
% 3.58/1.59 | (25) iext(uri_rdf_type, uri_ex_p, uri_rdf_Property)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (4) with uri_ex_p and discharging atoms iext(uri_rdf_type, uri_ex_p, uri_rdf_Property), yields:
% 3.58/1.59 | (26) ip(uri_ex_p)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (14) with uri_ex_p and discharging atoms ip(uri_ex_p), yields:
% 3.58/1.59 | (27) icext(uri_owl_InverseFunctionalProperty, uri_ex_p) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0, v2))
% 3.58/1.59 |
% 3.58/1.59 +-Applying beta-rule and splitting (27), into two cases.
% 3.58/1.59 |-Branch one:
% 3.58/1.59 | (28) icext(uri_owl_InverseFunctionalProperty, uri_ex_p)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (19) with uri_owl_InverseFunctionalProperty, uri_ex_p and discharging atoms icext(uri_owl_InverseFunctionalProperty, uri_ex_p), ~ iext(uri_rdf_type, uri_ex_p, uri_owl_InverseFunctionalProperty), yields:
% 3.58/1.59 | (29) $false
% 3.58/1.59 |
% 3.58/1.59 |-The branch is then unsatisfiable
% 3.58/1.59 |-Branch two:
% 3.58/1.59 | (30) ~ icext(uri_owl_InverseFunctionalProperty, uri_ex_p)
% 3.58/1.59 | (31) ? [v0] : ? [v1] : ? [v2] : ( ~ (v1 = v0) & iext(uri_ex_p, v1, v2) & iext(uri_ex_p, v0, v2))
% 3.58/1.59 |
% 3.58/1.59 | Instantiating (31) with all_59_0_4, all_59_1_5, all_59_2_6 yields:
% 3.58/1.59 | (32) ~ (all_59_1_5 = all_59_2_6) & iext(uri_ex_p, all_59_1_5, all_59_0_4) & iext(uri_ex_p, all_59_2_6, all_59_0_4)
% 3.58/1.59 |
% 3.58/1.59 | Applying alpha-rule on (32) yields:
% 3.58/1.59 | (33) ~ (all_59_1_5 = all_59_2_6)
% 3.58/1.59 | (34) iext(uri_ex_p, all_59_1_5, all_59_0_4)
% 3.58/1.59 | (35) iext(uri_ex_p, all_59_2_6, all_59_0_4)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (12) with all_59_0_4, all_59_1_5, all_0_3_3, uri_ex_p and discharging atoms iext(uri_ex_p, all_59_1_5, all_59_0_4), iext(uri_rdfs_domain, uri_ex_p, all_0_3_3), yields:
% 3.58/1.59 | (36) icext(all_0_3_3, all_59_1_5)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (12) with all_59_0_4, all_59_2_6, all_0_3_3, uri_ex_p and discharging atoms iext(uri_ex_p, all_59_2_6, all_59_0_4), iext(uri_rdfs_domain, uri_ex_p, all_0_3_3), yields:
% 3.58/1.59 | (37) icext(all_0_3_3, all_59_2_6)
% 3.58/1.59 |
% 3.58/1.59 | Instantiating formula (20) with all_59_1_5, uri_ex_w, all_0_1_1, all_0_3_3 and discharging atoms icext(all_0_3_3, all_59_1_5), iext(uri_owl_oneOf, all_0_3_3, all_0_1_1), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_first, all_0_1_1, uri_ex_w), yields:
% 3.58/1.60 | (38) all_59_1_5 = uri_ex_w
% 3.58/1.60 |
% 3.58/1.60 | Instantiating formula (20) with all_59_2_6, uri_ex_w, all_0_1_1, all_0_3_3 and discharging atoms icext(all_0_3_3, all_59_2_6), iext(uri_owl_oneOf, all_0_3_3, all_0_1_1), iext(uri_rdf_rest, all_0_1_1, uri_rdf_nil), iext(uri_rdf_first, all_0_1_1, uri_ex_w), yields:
% 3.58/1.60 | (39) all_59_2_6 = uri_ex_w
% 3.58/1.60 |
% 3.58/1.60 | Equations (38,39) can reduce 33 to:
% 3.58/1.60 | (40) $false
% 3.58/1.60 |
% 3.58/1.60 |-The branch is then unsatisfiable
% 3.58/1.60 % SZS output end Proof for theBenchmark
% 3.58/1.60
% 3.58/1.60 974ms
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