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ePrincess---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SWB022+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 18:59:41 EDT 2022

% Result   : Theorem 2.55s 1.27s
% Output   : Proof 3.79s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWB022+2 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun  1 11:32:41 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.57/0.58          ____       _                          
% 0.57/0.58    ___  / __ \_____(_)___  ________  __________
% 0.57/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.58  
% 0.57/0.58  A Theorem Prover for First-Order Logic
% 0.57/0.58  (ePrincess v.1.0)
% 0.57/0.58  
% 0.57/0.58  (c) Philipp Rümmer, 2009-2015
% 0.57/0.58  (c) Peter Backeman, 2014-2015
% 0.57/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58  Bug reports to peter@backeman.se
% 0.57/0.58  
% 0.57/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58  
% 0.57/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.93  Prover 0: Preprocessing ...
% 1.75/1.05  Prover 0: Constructing countermodel ...
% 2.55/1.26  Prover 0: proved (635ms)
% 2.55/1.27  
% 2.55/1.27  No countermodel exists, formula is valid
% 2.55/1.27  % SZS status Theorem for theBenchmark
% 2.55/1.27  
% 2.55/1.27  Generating proof ... found it (size 15)
% 3.57/1.52  
% 3.57/1.52  % SZS output start Proof for theBenchmark
% 3.57/1.52  Assumed formulas after preprocessing and simplification: 
% 3.57/1.52  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, v5) & iext(uri_owl_propertyChainAxiom, v0, v3) & iext(uri_owl_propertyChainAxiom, uri_skos_member, v1) & iext(uri_rdf_rest, v7, uri_rdf_nil) & iext(uri_rdf_rest, v6, v7) & iext(uri_rdf_rest, v5, v6) & iext(uri_rdf_rest, v4, uri_rdf_nil) & iext(uri_rdf_rest, v3, v4) & iext(uri_rdf_rest, v2, uri_rdf_nil) & iext(uri_rdf_rest, v1, v2) & iext(uri_rdf_first, v7, uri_ex_Z) & iext(uri_rdf_first, v6, uri_ex_Y) & iext(uri_rdf_first, v5, uri_ex_X) & iext(uri_rdf_first, v4, uri_rdf_rest) & iext(uri_rdf_first, v3, v0) & iext(uri_rdf_first, v2, uri_rdf_first) & iext(uri_rdf_first, v1, v0) & iext(uri_rdfs_subPropertyOf, uri_skos_memberList, v0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ iext(v12, v14, v15) |  ~ iext(v10, v13, v14) |  ~ iext(uri_owl_propertyChainAxiom, v8, v9) |  ~ iext(uri_rdf_rest, v11, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v9, v11) |  ~ iext(uri_rdf_first, v11, v12) |  ~ iext(uri_rdf_first, v9, v10) | iext(v8, v13, v15)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ ip(v12) |  ~ ip(v10) |  ~ ip(v8) |  ~ iext(uri_rdf_rest, v11, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v9, v11) |  ~ iext(uri_rdf_first, v11, v12) |  ~ iext(uri_rdf_first, v9, v10) | iext(uri_owl_propertyChainAxiom, v8, v9) |  ? [v13] :  ? [v14] :  ? [v15] : (iext(v12, v14, v15) & iext(v10, v13, v14) &  ~ iext(v8, v13, v15))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ iext(uri_owl_propertyChainAxiom, v8, v9) |  ~ iext(uri_rdf_rest, v11, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v9, v11) |  ~ iext(uri_rdf_first, v11, v12) |  ~ iext(uri_rdf_first, v9, v10) | ip(v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ iext(uri_owl_propertyChainAxiom, v8, v9) |  ~ iext(uri_rdf_rest, v11, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v9, v11) |  ~ iext(uri_rdf_first, v11, v12) |  ~ iext(uri_rdf_first, v9, v10) | ip(v10)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ iext(uri_owl_propertyChainAxiom, v8, v9) |  ~ iext(uri_rdf_rest, v11, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v9, v11) |  ~ iext(uri_rdf_first, v11, v12) |  ~ iext(uri_rdf_first, v9, v10) | ip(v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ iext(v8, v10, v11) |  ~ iext(uri_rdfs_subPropertyOf, v8, v9) | iext(v9, v10, v11)) &  ! [v8] :  ! [v9] : ( ~ iext(uri_rdfs_subPropertyOf, v8, v9) | ip(v9)) &  ! [v8] :  ! [v9] : ( ~ iext(uri_rdfs_subPropertyOf, v8, v9) | ip(v8)) & ( ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)))
% 3.79/1.54  | 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:
% 3.79/1.54  | (1) iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, all_0_2_2) & iext(uri_owl_propertyChainAxiom, all_0_7_7, all_0_4_4) & iext(uri_owl_propertyChainAxiom, uri_skos_member, all_0_6_6) & iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil) & iext(uri_rdf_rest, all_0_1_1, all_0_0_0) & iext(uri_rdf_rest, all_0_2_2, all_0_1_1) & iext(uri_rdf_rest, all_0_3_3, uri_rdf_nil) & iext(uri_rdf_rest, all_0_4_4, all_0_3_3) & iext(uri_rdf_rest, all_0_5_5, uri_rdf_nil) & iext(uri_rdf_rest, all_0_6_6, all_0_5_5) & iext(uri_rdf_first, all_0_0_0, uri_ex_Z) & iext(uri_rdf_first, all_0_1_1, uri_ex_Y) & iext(uri_rdf_first, all_0_2_2, uri_ex_X) & iext(uri_rdf_first, all_0_3_3, uri_rdf_rest) & iext(uri_rdf_first, all_0_4_4, all_0_7_7) & iext(uri_rdf_first, all_0_5_5, uri_rdf_first) & iext(uri_rdf_first, all_0_6_6, all_0_7_7) & iext(uri_rdfs_subPropertyOf, uri_skos_memberList, all_0_7_7) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ iext(v4, v6, v7) |  ~ iext(v2, v5, v6) |  ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | iext(v0, v5, v7)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ ip(v4) |  ~ ip(v2) |  ~ ip(v0) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_propertyChainAxiom, v0, v1) |  ? [v5] :  ? [v6] :  ? [v7] : (iext(v4, v6, v7) & iext(v2, v5, v6) &  ~ iext(v0, v5, v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ iext(v0, v2, v3) |  ~ iext(uri_rdfs_subPropertyOf, v0, v1) | iext(v1, v2, v3)) &  ! [v0] :  ! [v1] : ( ~ iext(uri_rdfs_subPropertyOf, v0, v1) | ip(v1)) &  ! [v0] :  ! [v1] : ( ~ iext(uri_rdfs_subPropertyOf, v0, v1) | ip(v0)) & ( ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X))
% 3.79/1.55  |
% 3.79/1.55  | Applying alpha-rule on (1) yields:
% 3.79/1.55  | (2) iext(uri_skos_memberList, uri_ex_MyOrderedCollection, all_0_2_2)
% 3.79/1.55  | (3) iext(uri_rdf_first, all_0_5_5, uri_rdf_first)
% 3.79/1.55  | (4) iext(uri_rdfs_subPropertyOf, uri_skos_memberList, all_0_7_7)
% 3.79/1.55  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v4))
% 3.79/1.55  | (6) iext(uri_owl_propertyChainAxiom, uri_skos_member, all_0_6_6)
% 3.79/1.55  | (7) iext(uri_rdf_first, all_0_3_3, uri_rdf_rest)
% 3.79/1.55  | (8) iext(uri_rdf_first, all_0_2_2, uri_ex_X)
% 3.79/1.55  | (9) iext(uri_rdf_rest, all_0_4_4, all_0_3_3)
% 3.79/1.55  | (10) iext(uri_rdf_rest, all_0_3_3, uri_rdf_nil)
% 3.79/1.55  | (11)  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)
% 3.79/1.55  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v2))
% 3.79/1.55  | (13) iext(uri_rdf_rest, all_0_2_2, all_0_1_1)
% 3.79/1.55  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | ip(v0))
% 3.79/1.55  | (15)  ! [v0] :  ! [v1] : ( ~ iext(uri_rdfs_subPropertyOf, v0, v1) | ip(v1))
% 3.79/1.55  | (16) iext(uri_rdf_first, all_0_1_1, uri_ex_Y)
% 3.79/1.55  | (17)  ! [v0] :  ! [v1] : ( ~ iext(uri_rdfs_subPropertyOf, v0, v1) | ip(v0))
% 3.79/1.55  | (18) iext(uri_rdf_first, all_0_4_4, all_0_7_7)
% 3.79/1.55  | (19) iext(uri_rdf_first, all_0_0_0, uri_ex_Z)
% 3.79/1.55  | (20) iext(uri_rdf_rest, all_0_1_1, all_0_0_0)
% 3.79/1.55  | (21) iext(uri_rdf_rest, all_0_0_0, uri_rdf_nil)
% 3.79/1.55  | (22) iext(uri_rdf_rest, all_0_6_6, all_0_5_5)
% 3.79/1.55  | (23) iext(uri_owl_propertyChainAxiom, all_0_7_7, all_0_4_4)
% 3.79/1.55  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ iext(v0, v2, v3) |  ~ iext(uri_rdfs_subPropertyOf, v0, v1) | iext(v1, v2, v3))
% 3.79/1.55  | (25) iext(uri_rdf_rest, all_0_5_5, uri_rdf_nil)
% 3.79/1.55  | (26) iext(uri_rdf_first, all_0_6_6, all_0_7_7)
% 3.79/1.55  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ ip(v4) |  ~ ip(v2) |  ~ ip(v0) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | iext(uri_owl_propertyChainAxiom, v0, v1) |  ? [v5] :  ? [v6] :  ? [v7] : (iext(v4, v6, v7) & iext(v2, v5, v6) &  ~ iext(v0, v5, v7)))
% 3.79/1.55  | (28) iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)
% 3.79/1.55  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ iext(v4, v6, v7) |  ~ iext(v2, v5, v6) |  ~ iext(uri_owl_propertyChainAxiom, v0, v1) |  ~ iext(uri_rdf_rest, v3, uri_rdf_nil) |  ~ iext(uri_rdf_rest, v1, v3) |  ~ iext(uri_rdf_first, v3, v4) |  ~ iext(uri_rdf_first, v1, v2) | iext(v0, v5, v7))
% 3.79/1.56  |
% 3.79/1.56  | Instantiating formula (24) with all_0_2_2, uri_ex_MyOrderedCollection, all_0_7_7, uri_skos_memberList and discharging atoms iext(uri_skos_memberList, uri_ex_MyOrderedCollection, all_0_2_2), iext(uri_rdfs_subPropertyOf, uri_skos_memberList, all_0_7_7), yields:
% 3.79/1.56  | (30) iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_2_2)
% 3.79/1.56  |
% 3.79/1.56  | Instantiating formula (29) with all_0_1_1, all_0_2_2, uri_ex_MyOrderedCollection, uri_rdf_rest, all_0_3_3, all_0_7_7, all_0_4_4, all_0_7_7 and discharging atoms iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_2_2), iext(uri_owl_propertyChainAxiom, all_0_7_7, all_0_4_4), iext(uri_rdf_rest, all_0_2_2, all_0_1_1), iext(uri_rdf_rest, all_0_3_3, uri_rdf_nil), iext(uri_rdf_rest, all_0_4_4, all_0_3_3), iext(uri_rdf_first, all_0_3_3, uri_rdf_rest), iext(uri_rdf_first, all_0_4_4, all_0_7_7), yields:
% 3.79/1.56  | (31) iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_1_1)
% 3.79/1.56  |
% 3.79/1.56  | Instantiating formula (29) with uri_ex_X, all_0_2_2, uri_ex_MyOrderedCollection, uri_rdf_first, all_0_5_5, all_0_7_7, all_0_6_6, uri_skos_member and discharging atoms iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_2_2), iext(uri_owl_propertyChainAxiom, uri_skos_member, all_0_6_6), iext(uri_rdf_rest, all_0_5_5, uri_rdf_nil), iext(uri_rdf_rest, all_0_6_6, all_0_5_5), iext(uri_rdf_first, all_0_2_2, uri_ex_X), iext(uri_rdf_first, all_0_5_5, uri_rdf_first), iext(uri_rdf_first, all_0_6_6, all_0_7_7), yields:
% 3.79/1.56  | (32) iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)
% 3.79/1.56  |
% 3.79/1.56  | Instantiating formula (29) with all_0_0_0, all_0_1_1, uri_ex_MyOrderedCollection, uri_rdf_rest, all_0_3_3, all_0_7_7, all_0_4_4, all_0_7_7 and discharging atoms iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_1_1), iext(uri_owl_propertyChainAxiom, all_0_7_7, all_0_4_4), iext(uri_rdf_rest, all_0_1_1, all_0_0_0), iext(uri_rdf_rest, all_0_3_3, uri_rdf_nil), iext(uri_rdf_rest, all_0_4_4, all_0_3_3), iext(uri_rdf_first, all_0_3_3, uri_rdf_rest), iext(uri_rdf_first, all_0_4_4, all_0_7_7), yields:
% 3.79/1.56  | (33) iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_0_0)
% 3.79/1.56  |
% 3.79/1.56  | Instantiating formula (29) with uri_ex_Y, all_0_1_1, uri_ex_MyOrderedCollection, uri_rdf_first, all_0_5_5, all_0_7_7, all_0_6_6, uri_skos_member and discharging atoms iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_1_1), iext(uri_owl_propertyChainAxiom, uri_skos_member, all_0_6_6), iext(uri_rdf_rest, all_0_5_5, uri_rdf_nil), iext(uri_rdf_rest, all_0_6_6, all_0_5_5), iext(uri_rdf_first, all_0_1_1, uri_ex_Y), iext(uri_rdf_first, all_0_5_5, uri_rdf_first), iext(uri_rdf_first, all_0_6_6, all_0_7_7), yields:
% 3.79/1.56  | (34) iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)
% 3.79/1.56  |
% 3.79/1.56  +-Applying beta-rule and splitting (11), into two cases.
% 3.79/1.56  |-Branch one:
% 3.79/1.56  | (35)  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)
% 3.79/1.56  |
% 3.79/1.56  	| Instantiating formula (29) with uri_ex_Z, all_0_0_0, uri_ex_MyOrderedCollection, uri_rdf_first, all_0_5_5, all_0_7_7, all_0_6_6, uri_skos_member and discharging atoms iext(all_0_7_7, uri_ex_MyOrderedCollection, all_0_0_0), iext(uri_owl_propertyChainAxiom, uri_skos_member, all_0_6_6), iext(uri_rdf_rest, all_0_5_5, uri_rdf_nil), iext(uri_rdf_rest, all_0_6_6, all_0_5_5), iext(uri_rdf_first, all_0_0_0, uri_ex_Z), iext(uri_rdf_first, all_0_5_5, uri_rdf_first), iext(uri_rdf_first, all_0_6_6, all_0_7_7),  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z), yields:
% 3.79/1.56  	| (36) $false
% 3.79/1.56  	|
% 3.79/1.56  	|-The branch is then unsatisfiable
% 3.79/1.56  |-Branch two:
% 3.79/1.56  | (37) iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)
% 3.79/1.56  | (38)  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) |  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)
% 3.79/1.56  |
% 3.79/1.56  	+-Applying beta-rule and splitting (38), into two cases.
% 3.79/1.56  	|-Branch one:
% 3.79/1.56  	| (39)  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)
% 3.79/1.56  	|
% 3.79/1.57  		| Using (34) and (39) yields:
% 3.79/1.57  		| (36) $false
% 3.79/1.57  		|
% 3.79/1.57  		|-The branch is then unsatisfiable
% 3.79/1.57  	|-Branch two:
% 3.79/1.57  	| (34) iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)
% 3.79/1.57  	| (42)  ~ iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)
% 3.79/1.57  	|
% 3.79/1.57  		| Using (32) and (42) yields:
% 3.79/1.57  		| (36) $false
% 3.79/1.57  		|
% 3.79/1.57  		|-The branch is then unsatisfiable
% 3.79/1.57  % SZS output end Proof for theBenchmark
% 3.79/1.57  
% 3.79/1.57  975ms
%------------------------------------------------------------------------------