TSTP Solution File: SWB022+2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB022+2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:31:53 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWB022+2 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 19:37:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(iext_type, type, (
% 0.19/0.39 iext: ( $i * $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_BNODE_l33_3_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l33_3: $i)).
% 0.19/0.39 tff(uri_ex_MyOrderedCollection_type, type, (
% 0.19/0.39 uri_ex_MyOrderedCollection: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_pL_10_type, type, (
% 0.19/0.39 tptp_fun_BNODE_pL_10: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l32_4_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l32_4: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l31_5_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l31_5: $i)).
% 0.19/0.39 tff(uri_skos_memberList_type, type, (
% 0.19/0.39 uri_skos_memberList: $i)).
% 0.19/0.39 tff(ip_type, type, (
% 0.19/0.39 ip: $i > $o)).
% 0.19/0.39 tff(uri_rdfs_subPropertyOf_type, type, (
% 0.19/0.39 uri_rdfs_subPropertyOf: $i)).
% 0.19/0.39 tff(uri_rdf_nil_type, type, (
% 0.19/0.39 uri_rdf_nil: $i)).
% 0.19/0.39 tff(uri_rdf_rest_type, type, (
% 0.19/0.39 uri_rdf_rest: $i)).
% 0.19/0.39 tff(uri_ex_Z_type, type, (
% 0.19/0.39 uri_ex_Z: $i)).
% 0.19/0.39 tff(uri_rdf_first_type, type, (
% 0.19/0.39 uri_rdf_first: $i)).
% 0.19/0.39 tff(uri_ex_Y_type, type, (
% 0.19/0.39 uri_ex_Y: $i)).
% 0.19/0.39 tff(uri_ex_X_type, type, (
% 0.19/0.39 uri_ex_X: $i)).
% 0.19/0.39 tff(uri_skos_OrderedCollection_type, type, (
% 0.19/0.39 uri_skos_OrderedCollection: $i)).
% 0.19/0.39 tff(uri_rdf_type_type, type, (
% 0.19/0.39 uri_rdf_type: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l22_6_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l22_6: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l21_7_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l21_7: $i)).
% 0.19/0.39 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.19/0.39 uri_owl_propertyChainAxiom: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l12_8_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l12_8: $i)).
% 0.19/0.39 tff(tptp_fun_BNODE_l11_9_type, type, (
% 0.19/0.39 tptp_fun_BNODE_l11_9: $i)).
% 0.19/0.39 tff(uri_skos_member_type, type, (
% 0.19/0.39 uri_skos_member: $i)).
% 0.19/0.39 tff(tptp_fun_Y2_0_type, type, (
% 0.19/0.39 tptp_fun_Y2_0: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y1_1_type, type, (
% 0.19/0.39 tptp_fun_Y1_1: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_Y0_2_type, type, (
% 0.19/0.39 tptp_fun_Y0_2: ( $i * $i * $i ) > $i)).
% 0.19/0.39 tff(1,assumption,(~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)), introduced(assumption)).
% 0.19/0.39 tff(2,assumption,(~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)), introduced(assumption)).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (?[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))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(5,plain,
% 0.19/0.43 (?[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))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.43 tff(6,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/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_022_List_Member_Access')).
% 0.19/0.43 tff(7,plain,
% 0.19/0.43 (?[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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.43 tff(8,plain,
% 0.19/0.43 (?[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))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.43 tff(9,plain,(
% 0.19/0.43 iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!10) & iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) & iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10) & iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8) & iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first) & iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil) & iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) & iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10) & iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6) & iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest) & iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil) & iext(uri_rdf_type, uri_ex_MyOrderedCollection, uri_skos_OrderedCollection) & iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5) & iext(uri_rdf_first, BNODE_l31!5, uri_ex_X) & iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4) & iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y) & iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3) & iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z) & iext(uri_rdf_rest, BNODE_l33!3, uri_rdf_nil)),
% 0.19/0.43 inference(skolemize,[status(sab)],[8])).
% 0.19/0.43 tff(10,plain,
% 0.19/0.43 (iext(uri_rdfs_subPropertyOf, uri_skos_memberList, BNODE_pL!10)),
% 0.19/0.43 inference(and_elim,[status(thm)],[9])).
% 0.19/0.43 tff(11,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(12,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.43 tff(13,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(14,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.43 tff(15,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[14, 12])).
% 0.19/0.43 tff(16,plain,
% 0.19/0.43 (^[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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(17,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.43 tff(18,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(19,plain,
% 0.19/0.43 (^[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))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(20,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.43 tff(21,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/sandbox/benchmark/theBenchmark.p','rdfs_subpropertyof_main')).
% 0.19/0.43 tff(22,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.43 tff(23,plain,
% 0.19/0.43 (![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))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.43 tff(24,plain,(
% 0.19/0.43 ![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))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[23])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 (![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))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 (((~![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!10)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, 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!10)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 ((~![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!10)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(29,plain,
% 0.19/0.44 ((~![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!10)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.44 tff(30,plain,
% 0.19/0.44 (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[29, 26, 10])).
% 0.19/0.44 tff(31,plain,
% 0.19/0.44 (((~ip(BNODE_pL!10)) | (~ip(uri_skos_memberList)) | (~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y)))) | ![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(32,plain,
% 0.19/0.44 (![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.19/0.44 tff(33,plain,
% 0.19/0.44 (iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5)),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(34,plain,
% 0.19/0.44 (((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))) | ((~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))) | (~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(35,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))) | ((~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(36,plain,
% 0.19/0.44 ((~![X: $i, Y: $i] : ((~iext(uri_skos_memberList, X, Y)) | iext(BNODE_pL!10, X, Y))) | (~iext(uri_skos_memberList, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.44 tff(37,plain,
% 0.19/0.44 (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[36, 33, 32])).
% 0.19/0.44 tff(38,plain,
% 0.19/0.44 (iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(39,plain,
% 0.19/0.44 (iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(40,plain,
% 0.19/0.44 (iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(41,plain,
% 0.19/0.44 (iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)),
% 0.19/0.44 inference(and_elim,[status(thm)],[9])).
% 0.19/0.44 tff(42,plain,
% 0.19/0.44 (^[P: $i, S1: $i, P1: $i, S2: $i, P2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(43,plain,
% 0.19/0.44 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.44 tff(44,plain,
% 0.19/0.44 (^[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(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(45,plain,
% 0.19/0.44 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.44 tff(46,plain,
% 0.19/0.44 (^[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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(47,plain,
% 0.19/0.44 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.44 tff(48,plain,
% 0.19/0.44 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[47, 45])).
% 0.19/0.44 tff(49,plain,
% 0.19/0.44 (^[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(P)) | (~ip(P1)) | (~ip(P2)) | (~![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) <=> (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))), ((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~![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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (^[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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(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(P)) | (~ip(P1)) | (~ip(P2)) | (~((~(iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (^[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)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.45 tff(56,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/sandbox/benchmark/theBenchmark.p','owl_chain_002')).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.45 tff(59,plain,(
% 0.19/0.45 ![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[58])).
% 0.19/0.45 tff(60,plain,
% 0.19/0.45 (![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_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P)) & iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))) | iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.45 tff(61,plain,
% 0.19/0.45 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.19/0.45 tff(62,plain,
% 0.19/0.45 (![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(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[61, 48])).
% 0.19/0.46 tff(63,plain,
% 0.19/0.46 (![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[62, 43])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, 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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 ((~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[66])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[67, 65])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, 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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, 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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[69, 64])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_first, BNODE_l21!7, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l21!7, BNODE_l22!6)) | (~iext(uri_rdf_first, BNODE_l22!6, uri_rdf_rest)) | (~iext(uri_rdf_rest, BNODE_l22!6, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.47 tff(73,plain,
% 0.19/0.47 (~((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[72, 63, 41, 40, 39, 38])).
% 0.19/0.47 tff(74,plain,
% 0.19/0.47 (((~(iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~(iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))) | (~iext(uri_rdf_rest, tptp_fun_Y1_1(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10), tptp_fun_Y2_0(uri_rdf_rest, BNODE_pL!10, BNODE_pL!10))))))) | (~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))))) | ((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(75,plain,
% 0.19/0.47 ((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.19/0.47 tff(76,plain,
% 0.19/0.47 (iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(77,plain,
% 0.19/0.47 ((~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))) | (~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(78,plain,
% 0.19/0.47 ((~((~iext(uri_owl_propertyChainAxiom, BNODE_pL!10, BNODE_l21!7)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))))) | (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.19/0.47 tff(79,plain,
% 0.19/0.47 (~((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.19/0.47 tff(80,plain,
% 0.19/0.47 (((~ip(BNODE_pL!10)) | (~ip(uri_rdf_rest)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2))))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.19/0.47 tff(82,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4))) <=> (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)) | (~iext(uri_rdf_rest, BNODE_l31!5, BNODE_l32!4))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[88, 82, 81, 37, 2])).
% 0.19/0.47 tff(90,plain,(iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3))) <=> (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | (iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[93])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[94, 92])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | ((~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(BNODE_pL!10, Y0, Y1)) | iext(BNODE_pL!10, Y0, Y2) | (~iext(uri_rdf_rest, Y1, Y2)))) | iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_rest, BNODE_l32!4, BNODE_l33!3))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[97, 91, 81, 90, 1])).
% 0.19/0.47 tff(99,plain,(iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)),
% 0.19/0.47 inference(and_elim,[status(thm)],[9])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, 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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 (((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 ((~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1)))))))))) <=> (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(107,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.48 tff(108,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.48 tff(109,plain,
% 0.19/0.48 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, 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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.48 tff(110,plain,
% 0.19/0.48 (((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, 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(P)) | (~ip(P1)) | (~ip(P2)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[109, 104])).
% 0.19/0.48 tff(111,plain,
% 0.19/0.48 ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | ((~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(uri_skos_member)) | (~ip(BNODE_pL!10)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(uri_skos_member, Y0, Y2) | (~iext(uri_rdf_first, Y1, Y2)) | (~iext(BNODE_pL!10, Y0, Y1)))))))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(112,plain,
% 0.19/0.48 ((~![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)) | (~(iext(P, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y2_0(P2, P1, P)) | (~iext(P1, tptp_fun_Y0_2(P2, P1, P), tptp_fun_Y1_1(P2, P1, P))) | (~iext(P2, tptp_fun_Y1_1(P2, P1, P), tptp_fun_Y2_0(P2, P1, P))))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P)) | (~ip(P1)) | (~ip(P2)) | (~![Y0: $i, Y1: $i, Y2: $i] : (iext(P, Y0, Y2) | (~iext(P2, Y1, Y2)) | (~iext(P1, Y0, Y1)))))))))))) | (~iext(uri_rdf_rest, BNODE_l11!9, BNODE_l12!8)) | (~iext(uri_rdf_first, BNODE_l11!9, BNODE_pL!10)) | (~iext(uri_rdf_first, BNODE_l12!8, uri_rdf_first)) | (~iext(uri_rdf_rest, BNODE_l12!8, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.48 tff(113,plain,
% 0.19/0.48 (~((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[112, 63, 103, 102, 101, 100])).
% 0.19/0.48 tff(114,plain,
% 0.19/0.48 (((~(iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9) | (~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~(iext(uri_skos_member, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member)) | (~iext(BNODE_pL!10, tptp_fun_Y0_2(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member))) | (~iext(uri_rdf_first, tptp_fun_Y1_1(uri_rdf_first, BNODE_pL!10, uri_skos_member), tptp_fun_Y2_0(uri_rdf_first, BNODE_pL!10, uri_skos_member))))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(115,plain,
% 0.19/0.48 ((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.19/0.48 tff(116,plain,
% 0.19/0.48 (iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)),
% 0.19/0.48 inference(and_elim,[status(thm)],[9])).
% 0.19/0.48 tff(117,plain,
% 0.19/0.48 ((~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))) | (~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(118,plain,
% 0.19/0.48 ((~((~iext(uri_owl_propertyChainAxiom, uri_skos_member, BNODE_l11!9)) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))))) | (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.19/0.48 tff(119,plain,
% 0.19/0.48 (~((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.19/0.48 tff(120,plain,
% 0.19/0.48 (((~ip(BNODE_pL!10)) | (~ip(uri_skos_member)) | (~ip(uri_rdf_first)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1))))) | ![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(121,plain,
% 0.19/0.48 (![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.19/0.48 tff(122,plain,
% 0.19/0.48 (iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)),
% 0.19/0.48 inference(and_elim,[status(thm)],[9])).
% 0.19/0.48 tff(123,plain,
% 0.19/0.48 (iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)),
% 0.19/0.48 inference(and_elim,[status(thm)],[9])).
% 0.19/0.48 tff(124,assumption,(~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)), introduced(assumption)).
% 0.19/0.48 tff(125,plain,
% 0.19/0.48 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(126,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(127,plain,
% 0.19/0.48 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[126])).
% 0.19/0.48 tff(128,plain,
% 0.19/0.48 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))),
% 0.19/0.48 inference(transitivity,[status(thm)],[127, 125])).
% 0.19/0.48 tff(129,plain,
% 0.19/0.48 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(130,plain,
% 0.19/0.48 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X) | (~iext(uri_rdf_first, BNODE_l31!5, uri_ex_X)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l31!5))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.48 tff(131,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[130, 124, 123, 121, 37])).
% 0.19/0.48 tff(132,plain,(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_X)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(133,plain,
% 0.19/0.48 (iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)),
% 0.19/0.48 inference(and_elim,[status(thm)],[9])).
% 0.19/0.48 tff(134,assumption,(~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)), introduced(assumption)).
% 0.19/0.48 tff(135,plain,
% 0.19/0.48 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(136,plain,
% 0.19/0.48 (((~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4))) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[136])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l32!4)) | (~iext(uri_rdf_first, BNODE_l32!4, uri_ex_Y))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[140, 134, 133, 121, 90])).
% 0.19/0.49 tff(142,plain,(iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Y)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 ((~(~((~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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 ((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))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 ((~(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)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 ((~(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)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[145, 143])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 ((~(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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 ((~((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)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(149,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/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_022_List_Member_Access')).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (~(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))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (~(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))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 ((~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))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[151, 146])).
% 0.19/0.49 tff(153,plain,
% 0.19/0.49 (~iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[152, 142, 132])).
% 0.19/0.49 tff(154,plain,
% 0.19/0.49 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(155,plain,
% 0.19/0.49 (((~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3))) <=> (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(156,plain,
% 0.19/0.49 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | (iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[155])).
% 0.19/0.49 tff(157,plain,
% 0.19/0.49 (((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[156, 154])).
% 0.19/0.49 tff(158,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | ((~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3)))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(159,plain,
% 0.19/0.49 ((~![Y0: $i, Y1: $i, Y2: $i] : ((~iext(uri_rdf_first, Y1, Y2)) | iext(uri_skos_member, Y0, Y2) | (~iext(BNODE_pL!10, Y0, Y1)))) | iext(uri_skos_member, uri_ex_MyOrderedCollection, uri_ex_Z) | (~iext(uri_rdf_first, BNODE_l33!3, uri_ex_Z)) | (~iext(BNODE_pL!10, uri_ex_MyOrderedCollection, BNODE_l33!3))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.49 tff(160,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[159, 153, 122, 121, 99])).
% 0.19/0.49 % SZS output end Proof
%------------------------------------------------------------------------------