TSTP Solution File: SWB022+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB022+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : 300s
% DateTime : Tue Sep 20 08:31:53 EDT 2022
% Result : Theorem 0.80s 0.81s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWB022+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 19:43:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.80/0.81 % SZS status Theorem
% 0.80/0.81 % SZS output start Proof
% 0.80/0.81 tff(iext_type, type, (
% 0.80/0.81 iext: ( $i * $i * $i ) > $o)).
% 0.80/0.81 tff(tptp_fun_BNODE_l33_140_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l33_140: $i)).
% 0.80/0.81 tff(uri_ex_MyOrderedCollection_type, type, (
% 0.80/0.81 uri_ex_MyOrderedCollection: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_pL_147_type, type, (
% 0.80/0.81 tptp_fun_BNODE_pL_147: $i)).
% 0.80/0.81 tff(uri_skos_member_type, type, (
% 0.80/0.81 uri_skos_member: $i)).
% 0.80/0.81 tff(uri_rdf_first_type, type, (
% 0.80/0.81 uri_rdf_first: $i)).
% 0.80/0.81 tff(ip_type, type, (
% 0.80/0.81 ip: $i > $o)).
% 0.80/0.81 tff(tptp_fun_BNODE_l11_146_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l11_146: $i)).
% 0.80/0.81 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.80/0.81 uri_owl_propertyChainAxiom: $i)).
% 0.80/0.81 tff(tptp_fun_Y2_100_type, type, (
% 0.80/0.81 tptp_fun_Y2_100: ( $i * $i * $i ) > $i)).
% 0.80/0.81 tff(tptp_fun_Y1_101_type, type, (
% 0.80/0.81 tptp_fun_Y1_101: ( $i * $i * $i ) > $i)).
% 0.80/0.81 tff(tptp_fun_Y0_102_type, type, (
% 0.80/0.81 tptp_fun_Y0_102: ( $i * $i * $i ) > $i)).
% 0.80/0.81 tff(uri_rdf_nil_type, type, (
% 0.80/0.81 uri_rdf_nil: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_l12_145_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l12_145: $i)).
% 0.80/0.81 tff(uri_rdf_rest_type, type, (
% 0.80/0.81 uri_rdf_rest: $i)).
% 0.80/0.81 tff(uri_ex_Z_type, type, (
% 0.80/0.81 uri_ex_Z: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_l32_141_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l32_141: $i)).
% 0.80/0.81 tff(uri_ex_Y_type, type, (
% 0.80/0.81 uri_ex_Y: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_l31_142_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l31_142: $i)).
% 0.80/0.81 tff(uri_ex_X_type, type, (
% 0.80/0.81 uri_ex_X: $i)).
% 0.80/0.81 tff(uri_skos_memberList_type, type, (
% 0.80/0.81 uri_skos_memberList: $i)).
% 0.80/0.81 tff(uri_skos_OrderedCollection_type, type, (
% 0.80/0.81 uri_skos_OrderedCollection: $i)).
% 0.80/0.81 tff(uri_rdf_type_type, type, (
% 0.80/0.81 uri_rdf_type: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_l22_143_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l22_143: $i)).
% 0.80/0.81 tff(tptp_fun_BNODE_l21_144_type, type, (
% 0.80/0.81 tptp_fun_BNODE_l21_144: $i)).
% 0.80/0.81 tff(uri_rdfs_subPropertyOf_type, type, (
% 0.80/0.81 uri_rdfs_subPropertyOf: $i)).
% 0.80/0.81 tff(1,plain,
% 0.80/0.81 (?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> ?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))),
% 0.80/0.81 inference(rewrite,[status(thm)],[])).
% 0.80/0.81 tff(2,plain,
% 0.80/0.81 (^[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL))), ((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12))), ((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)))), (((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first))), (((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)))), ((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil))), ((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)))), (((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21))), (((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)))), ((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL))), ((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)))), (((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22))), (((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)))), ((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest))), ((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)))), (((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil))), (((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)))), ((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection))), ((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)))), (((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31))), (((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)))), ((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X))), ((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)))), (((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32))), (((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)))), ((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y))), ((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)))), (((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33))), (((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)))), ((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z))), ((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)))), (((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> ((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)))), rewrite(((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))), (((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(3,plain,
% 0.80/0.83 (?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : ((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil)) <=> ?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[2])).
% 0.80/0.83 tff(4,axiom,(?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : ((((((((((((((((((iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11)) & iext(uri_rdf_first, BNODE_l11, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12)) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first)) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil)) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21)) & iext(uri_rdf_first, BNODE_l21, BNODE_pL)) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22)) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest)) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil)) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection)) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31)) & iext(uri_rdf_first, BNODE_l31, uri_ex_X)) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32)) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y)) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33)) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z)) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_022_List_Member_Access')).
% 0.80/0.83 tff(5,plain,
% 0.80/0.83 (?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.80/0.83 tff(6,plain,
% 0.80/0.83 (?[BNODE_pL: $i, BNODE_l11: $i, BNODE_l12: $i, BNODE_l21: $i, BNODE_l22: $i, BNODE_l31: $i, BNODE_l32: $i, BNODE_l33: $i] : (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11) & iext(uri_rdf_first, BNODE_l11, BNODE_pL) & iext(uri_rdf_rest, BNODE_l11, BNODE_l12) & iext(uri_rdf_first, BNODE_l12, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL, BNODE_l21) & iext(uri_rdf_first, BNODE_l21, BNODE_pL) & iext(uri_rdf_rest, BNODE_l21, BNODE_l22) & iext(uri_rdf_first, BNODE_l22, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31) & iext(uri_rdf_first, BNODE_l31, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31, BNODE_l32) & iext(uri_rdf_first, BNODE_l32, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32, BNODE_l33) & iext(uri_rdf_first, BNODE_l33, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33, uri_rdf_nil))),
% 0.80/0.83 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.80/0.83 tff(7,plain,(
% 0.80/0.83 iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) & iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147) & iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145) & iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) & iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147) & iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143) & iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142) & iext(uri_rdf_first, BNODE_l31!142, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141) & iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140) & iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33!140, uri_rdf_nil)),
% 0.80/0.83 inference(skolemize,[status(sab)],[6])).
% 0.80/0.83 tff(8,plain,
% 0.80/0.83 (iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(9,plain,
% 0.80/0.83 (iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(10,plain,
% 0.80/0.83 (iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(11,plain,
% 0.80/0.83 (iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)),
% 0.80/0.83 inference(and_elim,[status(thm)],[7])).
% 0.80/0.83 tff(12,plain,
% 0.80/0.83 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))))), rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))), (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(13,plain,
% 0.80/0.83 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[12])).
% 0.80/0.83 tff(14,plain,
% 0.80/0.83 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(15,plain,
% 0.80/0.83 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[14])).
% 0.80/0.83 tff(16,plain,
% 0.80/0.83 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))),
% 0.80/0.83 inference(bind,[status(th)],[])).
% 0.80/0.83 tff(17,plain,
% 0.80/0.83 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.83 inference(quant_intro,[status(thm)],[16])).
% 0.80/0.83 tff(18,plain,
% 0.80/0.83 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.84 inference(transitivity,[status(thm)],[17, 15])).
% 0.80/0.84 tff(19,plain,
% 0.80/0.84 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))), trans(monotonicity(rewrite((~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1))))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))))),
% 0.80/0.84 inference(bind,[status(th)],[])).
% 0.80/0.84 tff(20,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.84 inference(quant_intro,[status(thm)],[19])).
% 0.80/0.84 tff(21,plain,
% 0.80/0.84 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.80/0.84 inference(bind,[status(th)],[])).
% 0.80/0.84 tff(22,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.80/0.84 inference(quant_intro,[status(thm)],[21])).
% 0.80/0.84 tff(23,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.80/0.84 inference(rewrite,[status(thm)],[])).
% 0.80/0.84 tff(24,plain,
% 0.80/0.84 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))), (((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))))),
% 0.80/0.84 inference(bind,[status(th)],[])).
% 0.80/0.84 tff(25,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2))))) <=> ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.80/0.84 inference(quant_intro,[status(thm)],[24])).
% 0.80/0.84 tff(26,axiom,(![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, P2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (((ip(P) & ip(P1)) & ip(P2)) & ![Y0: $i, Y1: $i, Y2: $i] : ((iext(P1, Y0, Y1) & iext(P2, Y1, Y2)) => iext(P, Y0, Y2)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_chain_002')).
% 0.80/0.84 tff(27,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.80/0.84 tff(28,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.80/0.84 tff(29,plain,(
% 0.80/0.84 ![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))),
% 0.80/0.84 inference(skolemize,[status(sab)],[28])).
% 0.80/0.84 tff(30,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, P2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ip(P2) & ![Y0: $i, Y1: $i, Y2: $i] : ((~(iext(P1, Y0, Y1) & iext(P2, Y1, Y2))) | iext(P, Y0, Y2)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~((~(iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P)) & iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))) | iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)))))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.80/0.84 tff(31,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.80/0.84 tff(32,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.80/0.84 tff(33,plain,
% 0.80/0.84 (![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.80/0.84 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.80/0.84 tff(34,plain,
% 0.80/0.84 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))),
% 0.91/0.84 inference(rewrite,[status(thm)],[])).
% 0.91/0.84 tff(35,plain,
% 0.91/0.84 (((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))),
% 0.91/0.84 inference(rewrite,[status(thm)],[])).
% 0.91/0.84 tff(36,plain,
% 0.91/0.84 ((~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))))))),
% 0.91/0.84 inference(rewrite,[status(thm)],[])).
% 0.91/0.84 tff(37,plain,
% 0.91/0.84 (((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))),
% 0.91/0.85 inference(monotonicity,[status(thm)],[36])).
% 0.91/0.85 tff(38,plain,
% 0.91/0.85 (((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))),
% 0.91/0.85 inference(transitivity,[status(thm)],[37, 35])).
% 0.91/0.85 tff(39,plain,
% 0.91/0.85 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))))))))),
% 0.91/0.85 inference(monotonicity,[status(thm)],[38])).
% 0.91/0.85 tff(40,plain,
% 0.91/0.85 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))))),
% 0.91/0.85 inference(transitivity,[status(thm)],[39, 34])).
% 0.91/0.85 tff(41,plain,
% 0.91/0.85 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(42,plain,
% 0.91/0.85 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l11!146, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l11!146, BNODE_l12!145)) | (~iext(uri_rdf_first, BNODE_l12!145, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!145, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.91/0.85 tff(43,plain,
% 0.91/0.85 (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.91/0.85 tff(44,plain,
% 0.91/0.85 (((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146) | (~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~(iext(uri_skos_member, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_101(uri_rdf_first, BNODE_pL!147, uri_skos_member), tptp_fun_Y2_100(uri_rdf_first, BNODE_pL!147, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))),
% 0.91/0.85 inference(tautology,[status(thm)],[])).
% 0.91/0.85 tff(45,plain,
% 0.91/0.85 ((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.91/0.85 tff(46,plain,
% 0.91/0.85 (iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(47,plain,
% 0.91/0.85 ((~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))),
% 0.91/0.85 inference(tautology,[status(thm)],[])).
% 0.91/0.85 tff(48,plain,
% 0.91/0.85 ((~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!146)) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))))) | (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.91/0.85 tff(49,plain,
% 0.91/0.85 (~((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.91/0.85 tff(50,plain,
% 0.91/0.85 (((~ip(uri_rdf_first)) | (~ip(BNODE_pL!147)) | (~ip(uri_skos_member)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))),
% 0.91/0.85 inference(tautology,[status(thm)],[])).
% 0.91/0.85 tff(51,plain,
% 0.91/0.85 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.91/0.85 tff(52,plain,
% 0.91/0.85 (iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(53,assumption,(~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)), introduced(assumption)).
% 0.91/0.85 tff(54,plain,
% 0.91/0.85 (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(55,plain,
% 0.91/0.85 (^[P: $i, Q: $i] : refl(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(56,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[55])).
% 0.91/0.85 tff(57,plain,
% 0.91/0.85 (^[P: $i, Q: $i] : rewrite(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(58,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[57])).
% 0.91/0.85 tff(59,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(transitivity,[status(thm)],[58, 56])).
% 0.91/0.85 tff(60,plain,
% 0.91/0.85 (^[P: $i, Q: $i] : rewrite(((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(61,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[60])).
% 0.91/0.85 tff(62,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(63,plain,
% 0.91/0.85 (^[P: $i, Q: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i, Y: $i] : rewrite((iext(P, X, Y) => iext(Q, X, Y)) <=> ((~iext(P, X, Y)) | iext(Q, X, Y)))), (![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)) <=> ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))), (((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))) <=> ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), rewrite(((ip(P) & ip(Q)) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))) <=> (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))), (((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))) <=> (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), ((iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> (iext(uri_rdfs_subPropertyOf, P, Q) => (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))))), rewrite((iext(uri_rdfs_subPropertyOf, P, Q) => (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))), ((iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(bind,[status(th)],[])).
% 0.91/0.85 tff(64,plain,
% 0.91/0.85 (![P: $i, Q: $i] : (iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y)))) <=> ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.91/0.85 inference(quant_intro,[status(thm)],[63])).
% 0.91/0.85 tff(65,axiom,(![P: $i, Q: $i] : (iext(uri_rdfs_subPropertyOf, P, Q) => ((ip(P) & ip(Q)) & ![X: $i, Y: $i] : (iext(P, X, Y) => iext(Q, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','rdfs_subpropertyof_main')).
% 0.91/0.85 tff(66,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.91/0.85 tff(67,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.91/0.85 tff(68,plain,(
% 0.91/0.85 ![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (ip(P) & ip(Q) & ![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))),
% 0.91/0.85 inference(skolemize,[status(sab)],[67])).
% 0.91/0.85 tff(69,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.91/0.85 tff(70,plain,
% 0.91/0.85 (![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.91/0.85 tff(71,plain,
% 0.91/0.85 (((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147)) | (~((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))))))) <=> ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | (~iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147)) | (~((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))))))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(72,plain,
% 0.91/0.85 ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | ((~iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147)) | (~((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))))))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(73,plain,
% 0.91/0.85 ((~![P: $i, Q: $i] : ((~iext(uri_rdfs_subPropertyOf, P, Q)) | (~((~ip(Q)) | (~ip(P)) | (~![X: $i, Y: $i] : ((~iext(P, X, Y)) | iext(Q, X, Y))))))) | (~iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!147)) | (~((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y)))))),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.91/0.85 tff(74,plain,
% 0.91/0.85 (~((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[73, 70, 54])).
% 0.91/0.85 tff(75,plain,
% 0.91/0.85 (((~ip(BNODE_pL!147)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))),
% 0.91/0.85 inference(tautology,[status(thm)],[])).
% 0.91/0.85 tff(76,plain,
% 0.91/0.85 (![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.91/0.85 tff(77,plain,
% 0.91/0.85 (iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(78,plain,
% 0.91/0.85 (((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))) | ((~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))) | (~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142))),
% 0.91/0.85 inference(rewrite,[status(thm)],[])).
% 0.91/0.85 tff(79,plain,
% 0.91/0.85 ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))) | ((~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142))),
% 0.91/0.85 inference(quant_inst,[status(thm)],[])).
% 0.91/0.85 tff(80,plain,
% 0.91/0.85 ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!147, X, Y))) | (~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)),
% 0.91/0.85 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.91/0.85 tff(81,plain,
% 0.91/0.85 (iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)),
% 0.91/0.85 inference(unit_resolution,[status(thm)],[80, 77, 76])).
% 0.91/0.85 tff(82,plain,
% 0.91/0.85 (iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(83,plain,
% 0.91/0.85 (iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(84,plain,
% 0.91/0.85 (iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(85,plain,
% 0.91/0.85 (iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)),
% 0.91/0.85 inference(and_elim,[status(thm)],[7])).
% 0.91/0.85 tff(86,plain,
% 0.91/0.85 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(87,plain,
% 0.91/0.86 (((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(88,plain,
% 0.91/0.86 ((~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))))))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(89,plain,
% 0.91/0.86 (((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[88])).
% 0.91/0.86 tff(90,plain,
% 0.91/0.86 (((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))),
% 0.91/0.86 inference(transitivity,[status(thm)],[89, 87])).
% 0.91/0.86 tff(91,plain,
% 0.91/0.86 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))))))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[90])).
% 0.91/0.86 tff(92,plain,
% 0.91/0.86 (((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))) <=> ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))))),
% 0.91/0.86 inference(transitivity,[status(thm)],[91, 86])).
% 0.91/0.86 tff(93,plain,
% 0.91/0.86 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!147, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)))))))))))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(94,plain,
% 0.91/0.86 ((~![P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, P2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~(iext(P, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y2_100(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_102(P2, P1, P), tptp_fun_Y1_101(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_101(P2, P1, P), tptp_fun_Y2_100(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P2)) | (~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!144, BNODE_pL!147)) | (~iext(uri_rdf_first, BNODE_l22!143, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l21!144, BNODE_l22!143)) | (~iext(uri_rdf_rest, BNODE_l22!143, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))))))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.91/0.86 tff(95,plain,
% 0.91/0.86 (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[94, 33, 85, 84, 83, 82])).
% 0.91/0.86 tff(96,plain,
% 0.91/0.86 (((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144) | (~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~(iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147)) | (~iext(BNODE_pL!147, tptp_fun_Y0_102(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))) | (~iext(uri_rdf_rest, tptp_fun_Y1_101(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147), tptp_fun_Y2_100(uri_rdf_rest, BNODE_pL!147, BNODE_pL!147))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))))) | ((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))),
% 0.91/0.86 inference(tautology,[status(thm)],[])).
% 0.91/0.86 tff(97,plain,
% 0.91/0.86 ((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.91/0.86 tff(98,plain,
% 0.91/0.86 (iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)),
% 0.91/0.86 inference(and_elim,[status(thm)],[7])).
% 0.91/0.86 tff(99,plain,
% 0.91/0.86 ((~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))) | (~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))),
% 0.91/0.86 inference(tautology,[status(thm)],[])).
% 0.91/0.86 tff(100,plain,
% 0.91/0.86 ((~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!147, BNODE_l21!144)) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))))) | (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.91/0.86 tff(101,plain,
% 0.91/0.86 (~((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.91/0.86 tff(102,plain,
% 0.91/0.86 (((~ip(uri_rdf_rest)) | (~ip(BNODE_pL!147)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))),
% 0.91/0.86 inference(tautology,[status(thm)],[])).
% 0.91/0.86 tff(103,plain,
% 0.91/0.86 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.91/0.86 tff(104,plain,
% 0.91/0.86 (iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141)),
% 0.91/0.86 inference(and_elim,[status(thm)],[7])).
% 0.91/0.86 tff(105,plain,
% 0.91/0.86 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | (~iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(106,plain,
% 0.91/0.86 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(107,plain,
% 0.91/0.86 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | (~iext(uri_rdf_rest, BNODE_l31!142, BNODE_l32!141)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.91/0.86 tff(108,plain,
% 0.91/0.86 ($false),
% 0.91/0.86 inference(unit_resolution,[status(thm)],[107, 104, 103, 81, 53])).
% 0.91/0.86 tff(109,plain,(iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)), inference(lemma,lemma(discharge,[]))).
% 0.91/0.86 tff(110,plain,
% 0.91/0.86 (iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)),
% 0.91/0.86 inference(and_elim,[status(thm)],[7])).
% 0.91/0.86 tff(111,assumption,(~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)), introduced(assumption)).
% 0.91/0.86 tff(112,plain,
% 0.91/0.86 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(113,plain,
% 0.91/0.86 (((~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.91/0.86 inference(rewrite,[status(thm)],[])).
% 0.91/0.86 tff(114,plain,
% 0.91/0.86 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))))),
% 0.91/0.86 inference(monotonicity,[status(thm)],[113])).
% 0.91/0.86 tff(115,plain,
% 0.91/0.86 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.91/0.86 inference(transitivity,[status(thm)],[114, 112])).
% 0.91/0.86 tff(116,plain,
% 0.91/0.86 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y))),
% 0.91/0.86 inference(quant_inst,[status(thm)],[])).
% 0.91/0.86 tff(117,plain,
% 0.91/0.86 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(uri_rdf_first, BNODE_l32!141, uri_ex_Y)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))),
% 0.91/0.86 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.91/0.87 tff(118,plain,
% 0.91/0.87 ($false),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[117, 111, 110, 51, 109])).
% 0.91/0.87 tff(119,plain,(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)), inference(lemma,lemma(discharge,[]))).
% 0.91/0.87 tff(120,plain,
% 0.91/0.87 (iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)),
% 0.91/0.87 inference(and_elim,[status(thm)],[7])).
% 0.91/0.87 tff(121,assumption,(~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)), introduced(assumption)).
% 0.91/0.87 tff(122,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(123,plain,
% 0.91/0.87 (((~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(124,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142))))),
% 0.91/0.87 inference(monotonicity,[status(thm)],[123])).
% 0.91/0.87 tff(125,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)))),
% 0.91/0.87 inference(transitivity,[status(thm)],[124, 122])).
% 0.91/0.87 tff(126,plain,
% 0.91/0.87 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(127,plain,
% 0.91/0.87 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!142, uri_ex_X)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l31!142))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.91/0.87 tff(128,plain,
% 0.91/0.87 ($false),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[127, 121, 120, 51, 81])).
% 0.91/0.87 tff(129,plain,(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)), inference(lemma,lemma(discharge,[]))).
% 0.91/0.87 tff(130,plain,
% 0.91/0.87 ((~(~((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))))) <=> ((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(131,plain,
% 0.91/0.87 ((iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)) <=> (~((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(132,plain,
% 0.91/0.87 ((~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> (~(~((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)))))),
% 0.91/0.87 inference(monotonicity,[status(thm)],[131])).
% 0.91/0.87 tff(133,plain,
% 0.91/0.87 ((~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> ((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)))),
% 0.91/0.87 inference(transitivity,[status(thm)],[132, 130])).
% 0.91/0.87 tff(134,plain,
% 0.91/0.87 ((~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> (~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(135,plain,
% 0.91/0.87 ((~((iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> (~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(136,axiom,(~((iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_022_List_Member_Access')).
% 0.91/0.87 tff(137,plain,
% 0.91/0.87 (~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.91/0.87 tff(138,plain,
% 0.91/0.87 (~(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) & iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.91/0.87 tff(139,plain,
% 0.91/0.87 ((~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)) | (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[138, 133])).
% 0.91/0.87 tff(140,plain,
% 0.91/0.87 (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[139, 129, 119])).
% 0.91/0.87 tff(141,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(142,plain,
% 0.91/0.87 (((~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(143,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140))))),
% 0.91/0.87 inference(monotonicity,[status(thm)],[142])).
% 0.91/0.87 tff(144,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)))),
% 0.91/0.87 inference(transitivity,[status(thm)],[143, 141])).
% 0.91/0.87 tff(145,plain,
% 0.91/0.87 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | ((~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z))),
% 0.91/0.87 inference(quant_inst,[status(thm)],[])).
% 0.91/0.87 tff(146,plain,
% 0.91/0.87 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(uri_skos_member, Y0, Y2))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!140, uri_ex_Z)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140))),
% 0.91/0.87 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.91/0.87 tff(147,plain,
% 0.91/0.87 (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)),
% 0.91/0.87 inference(unit_resolution,[status(thm)],[146, 140, 52, 51])).
% 0.91/0.87 tff(148,plain,
% 0.91/0.87 (iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)),
% 0.91/0.87 inference(and_elim,[status(thm)],[7])).
% 0.91/0.87 tff(149,plain,
% 0.91/0.87 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | (~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.91/0.87 inference(rewrite,[status(thm)],[])).
% 0.91/0.87 tff(150,plain,
% 0.91/0.87 (((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140)) <=> ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(151,plain,
% 0.95/0.89 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[150])).
% 0.95/0.89 tff(152,plain,
% 0.95/0.89 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | (~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[151, 149])).
% 0.95/0.89 tff(153,plain,
% 0.95/0.89 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | ((~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(154,plain,
% 0.95/0.89 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!147, Y0, Y1)) | iext(BNODE_pL!147, Y0, Y2))) | (~iext(uri_rdf_rest, BNODE_l32!141, BNODE_l33!140)) | iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l33!140) | (~iext(BNODE_pL!147, uri_ex_MyOrderedCollection, BNODE_l32!141))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.95/0.89 tff(155,plain,
% 0.95/0.89 ($false),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[154, 148, 103, 109, 147])).
% 0.95/0.89 % SZS output end Proof
%------------------------------------------------------------------------------