%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB043+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:29:44 AM UTC 2025
% Result : Theorem 0.50s 0.68s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB043+1 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 07:55:01 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.50/0.68 % SZS status Theorem
% 0.50/0.68 % SZS output start Proof
% 0.50/0.68 tff(iext_type, type, (
% 0.50/0.68 iext: ( $i * $i * $i ) > $o)).
% 0.50/0.68 tff(uri_ex_p_type, type, (
% 0.50/0.68 uri_ex_p: $i)).
% 0.50/0.68 tff(uri_ex_p1_type, type, (
% 0.50/0.68 uri_ex_p1: $i)).
% 0.50/0.68 tff(ip_type, type, (
% 0.50/0.68 ip: $i > $o)).
% 0.50/0.68 tff(tptp_fun_X0_140_type, type, (
% 0.50/0.68 tptp_fun_X0_140: $i)).
% 0.50/0.68 tff(uri_owl_propertyChainAxiom_type, type, (
% 0.50/0.68 uri_owl_propertyChainAxiom: $i)).
% 0.50/0.68 tff(tptp_fun_Y1_98_type, type, (
% 0.50/0.68 tptp_fun_Y1_98: ( $i * $i ) > $i)).
% 0.50/0.68 tff(tptp_fun_Y0_99_type, type, (
% 0.50/0.68 tptp_fun_Y0_99: ( $i * $i ) > $i)).
% 0.50/0.68 tff(uri_rdf_nil_type, type, (
% 0.50/0.68 uri_rdf_nil: $i)).
% 0.50/0.68 tff(uri_rdf_rest_type, type, (
% 0.50/0.68 uri_rdf_rest: $i)).
% 0.50/0.68 tff(uri_rdf_first_type, type, (
% 0.50/0.68 uri_rdf_first: $i)).
% 0.50/0.68 tff(tptp_fun_Y_62_type, type, (
% 0.50/0.68 tptp_fun_Y_62: ( $i * $i ) > $i)).
% 0.50/0.68 tff(tptp_fun_X_63_type, type, (
% 0.50/0.68 tptp_fun_X_63: ( $i * $i ) > $i)).
% 0.50/0.68 tff(uri_rdfs_subPropertyOf_type, type, (
% 0.50/0.68 uri_rdfs_subPropertyOf: $i)).
% 0.50/0.68 tff(icext_type, type, (
% 0.50/0.68 icext: ( $i * $i ) > $o)).
% 0.50/0.68 tff(uri_rdf_List_type, type, (
% 0.50/0.68 uri_rdf_List: $i)).
% 0.50/0.68 tff(1,plain,
% 0.50/0.68 (?[X0: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> ?[X0: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(2,plain,
% 0.50/0.68 (^[X0: $i] : rewrite(((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil)))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(3,plain,
% 0.50/0.68 (?[X0: $i] : ((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1)) & iext(uri_rdf_rest, X0, uri_rdf_nil)) <=> ?[X0: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[2])).
% 0.50/0.68 tff(4,axiom,(?[X0: $i] : ((iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1)) & iext(uri_rdf_rest, X0, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_chain_subprop')).
% 0.50/0.68 tff(5,plain,
% 0.50/0.68 (?[X0: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.50/0.68 tff(6,plain,
% 0.50/0.68 (?[X0: $i] : (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0) & iext(uri_rdf_first, X0, uri_ex_p1) & iext(uri_rdf_rest, X0, uri_rdf_nil))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.50/0.68 tff(7,plain,(
% 0.50/0.68 iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) & iext(uri_rdf_first, X0!140, uri_ex_p1) & iext(uri_rdf_rest, X0!140, uri_rdf_nil)),
% 0.50/0.68 inference(skolemize,[status(sab)],[6])).
% 0.50/0.68 tff(8,plain,
% 0.50/0.68 (iext(uri_rdf_rest, X0!140, uri_rdf_nil)),
% 0.50/0.68 inference(and_elim,[status(thm)],[7])).
% 0.50/0.68 tff(9,plain,
% 0.50/0.68 (iext(uri_rdf_first, X0!140, uri_ex_p1)),
% 0.50/0.68 inference(and_elim,[status(thm)],[7])).
% 0.50/0.68 tff(10,plain,
% 0.50/0.68 (^[P: $i, S1: $i, P1: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(11,plain,
% 0.50/0.68 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[10])).
% 0.50/0.68 tff(12,plain,
% 0.50/0.68 (^[P: $i, S1: $i, P1: $i] : refl(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(13,plain,
% 0.50/0.68 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[12])).
% 0.50/0.68 tff(14,plain,
% 0.50/0.68 (^[P: $i, S1: $i, P1: $i] : rewrite(((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))))),
% 0.50/0.68 inference(bind,[status(th)],[])).
% 0.50/0.68 tff(15,plain,
% 0.50/0.68 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.68 inference(quant_intro,[status(thm)],[14])).
% 0.50/0.68 tff(16,plain,
% 0.50/0.68 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.68 inference(transitivity,[status(thm)],[15, 13])).
% 0.50/0.68 tff(17,plain,
% 0.50/0.68 (^[P: $i, S1: $i, P1: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) <=> ((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))), rewrite((iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) <=> (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))), rewrite((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))), ((((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) <=> (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))) <=> (((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))))), rewrite((((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil))) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))), (((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))) <=> ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(18,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[17])).
% 0.50/0.69 tff(19,plain,
% 0.50/0.69 (^[P: $i, S1: $i, P1: $i] : rewrite(((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(20,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))) <=> ![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[19])).
% 0.50/0.69 tff(21,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))) <=> ![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(22,plain,
% 0.50/0.69 (^[P: $i, S1: $i, P1: $i] : trans(monotonicity(rewrite((iext(uri_owl_propertyChainAxiom, P, S1) <=> ((ip(P) & ip(P1)) & ![Y0: $i, Y1: $i] : (iext(P1, Y0, Y1) => iext(P, Y0, Y1)))) <=> (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))), (((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((ip(P) & ip(P1)) & ![Y0: $i, Y1: $i] : (iext(P1, Y0, Y1) => iext(P, Y0, Y1))))) <=> ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))), rewrite(((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))), (((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((ip(P) & ip(P1)) & ![Y0: $i, Y1: $i] : (iext(P1, Y0, Y1) => iext(P, Y0, Y1))))) <=> ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(23,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((ip(P) & ip(P1)) & ![Y0: $i, Y1: $i] : (iext(P1, Y0, Y1) => iext(P, Y0, Y1))))) <=> ![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[22])).
% 0.50/0.69 tff(24,axiom,(![P: $i, S1: $i, P1: $i] : ((iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil)) => (iext(uri_owl_propertyChainAxiom, P, S1) <=> ((ip(P) & ip(P1)) & ![Y0: $i, Y1: $i] : (iext(P1, Y0, Y1) => iext(P, Y0, Y1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_chain_001')).
% 0.50/0.69 tff(25,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.50/0.69 tff(26,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (iext(uri_owl_propertyChainAxiom, P, S1) <=> (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.50/0.69 tff(27,plain,(
% 0.50/0.69 ![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | ((~ip(P)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))))))))),
% 0.50/0.69 inference(skolemize,[status(sab)],[26])).
% 0.50/0.69 tff(28,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~(iext(uri_rdf_first, S1, P1) & iext(uri_rdf_rest, S1, uri_rdf_nil))) | (((~iext(uri_owl_propertyChainAxiom, P, S1)) | (ip(P) & ip(P1) & ![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1)))) & (iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.50/0.69 tff(29,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.50/0.69 tff(30,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))) | (~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.50/0.69 tff(31,plain,
% 0.50/0.69 (![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.50/0.69 tff(32,plain,
% 0.50/0.69 (((~![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))) | ((~iext(uri_rdf_first, X0!140, uri_ex_p1)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))))))) <=> ((~![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))) | (~iext(uri_rdf_first, X0!140, uri_ex_p1)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))))))),
% 0.50/0.69 inference(rewrite,[status(thm)],[])).
% 0.50/0.69 tff(33,plain,
% 0.50/0.69 ((~![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))) | ((~iext(uri_rdf_first, X0!140, uri_ex_p1)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))))))),
% 0.50/0.69 inference(quant_inst,[status(thm)],[])).
% 0.50/0.69 tff(34,plain,
% 0.50/0.69 ((~![P: $i, S1: $i, P1: $i] : ((~iext(uri_rdf_first, S1, P1)) | (~iext(uri_rdf_rest, S1, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, P, S1) | (~ip(P1)) | (~ip(P)) | (~((~iext(P1, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P))) | iext(P, tptp_fun_Y0_99(P1, P), tptp_fun_Y1_98(P1, P)))))) | (~((~iext(uri_owl_propertyChainAxiom, P, S1)) | (~((~ip(P1)) | (~ip(P)) | (~![Y0: $i, Y1: $i] : ((~iext(P1, Y0, Y1)) | iext(P, Y0, Y1))))))))))) | (~iext(uri_rdf_first, X0!140, uri_ex_p1)) | (~iext(uri_rdf_rest, X0!140, uri_rdf_nil)) | (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))))))))),
% 0.50/0.69 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.50/0.69 tff(35,plain,
% 0.50/0.69 (~((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[34, 31, 9, 8])).
% 0.50/0.69 tff(36,plain,
% 0.50/0.69 (((~(iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p))) | iext(uri_ex_p, tptp_fun_Y0_99(uri_ex_p1, uri_ex_p), tptp_fun_Y1_98(uri_ex_p1, uri_ex_p)))))) | (~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(37,plain,
% 0.50/0.69 ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.50/0.69 tff(38,plain,
% 0.50/0.69 (iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)),
% 0.50/0.69 inference(and_elim,[status(thm)],[7])).
% 0.50/0.69 tff(39,plain,
% 0.50/0.69 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))))),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(40,plain,
% 0.50/0.69 ((~((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))))) | (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.50/0.69 tff(41,plain,
% 0.50/0.69 (~((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.50/0.69 tff(42,plain,
% 0.50/0.69 (((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))) | ![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))),
% 0.50/0.69 inference(tautology,[status(thm)],[])).
% 0.50/0.69 tff(43,plain,
% 0.50/0.69 (![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))),
% 0.50/0.69 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.50/0.69 tff(44,plain,
% 0.50/0.69 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(45,plain,
% 0.50/0.69 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[44])).
% 0.50/0.69 tff(46,plain,
% 0.50/0.69 (^[P1: $i, P2: $i] : refl((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(47,plain,
% 0.50/0.69 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[46])).
% 0.50/0.69 tff(48,plain,
% 0.50/0.69 (^[P1: $i, P2: $i] : rewrite((~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(49,plain,
% 0.50/0.69 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[48])).
% 0.50/0.69 tff(50,plain,
% 0.50/0.69 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.69 inference(transitivity,[status(thm)],[49, 47])).
% 0.50/0.69 tff(51,plain,
% 0.50/0.69 (^[P1: $i, P2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))), rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))), rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))), ((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))))),
% 0.50/0.69 inference(bind,[status(th)],[])).
% 0.50/0.69 tff(52,plain,
% 0.50/0.69 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) <=> ![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.69 inference(quant_intro,[status(thm)],[51])).
% 0.50/0.69 tff(53,plain,
% 0.50/0.69 (^[P1: $i, P2: $i] : rewrite((((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))) <=> (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(54,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))) <=> ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[53])).
% 0.50/0.70 tff(55,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(56,plain,
% 0.50/0.70 (^[P1: $i, P2: $i] : rewrite((iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(57,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y)))) <=> ![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[56])).
% 0.50/0.70 tff(58,axiom,(![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> ((ip(P1) & ip(P2)) & ![X: $i, Y: $i] : (iext(P1, X, Y) => iext(P2, X, Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_subpropertyof')).
% 0.50/0.70 tff(59,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.50/0.70 tff(60,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (iext(uri_rdfs_subPropertyOf, P1, P2) <=> (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.50/0.70 tff(61,plain,(
% 0.50/0.70 ![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | ((~ip(P1)) | (~ip(P2)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))))),
% 0.50/0.70 inference(skolemize,[status(sab)],[60])).
% 0.50/0.70 tff(62,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (ip(P1) & ip(P2) & ![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))) & (iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.50/0.70 tff(63,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.50/0.70 tff(64,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (~((~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y))))))) | (~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))))))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[63, 50])).
% 0.50/0.70 tff(65,plain,
% 0.50/0.70 (![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[64, 45])).
% 0.50/0.70 tff(66,plain,
% 0.50/0.70 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y))))))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(67,plain,
% 0.50/0.70 ((~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y))))))))) <=> (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(68,plain,
% 0.50/0.70 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y))))))))))),
% 0.50/0.70 inference(monotonicity,[status(thm)],[67])).
% 0.50/0.70 tff(69,plain,
% 0.50/0.70 (((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))) <=> ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y))))))))))),
% 0.50/0.70 inference(transitivity,[status(thm)],[68, 66])).
% 0.50/0.70 tff(70,plain,
% 0.50/0.70 ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(71,plain,
% 0.50/0.70 ((~![P1: $i, P2: $i] : (~((~(iext(uri_rdfs_subPropertyOf, P1, P2) | (~ip(P2)) | (~ip(P1)) | (~((~iext(P1, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1))) | iext(P2, tptp_fun_X_63(P2, P1), tptp_fun_Y_62(P2, P1)))))) | (~((~iext(uri_rdfs_subPropertyOf, P1, P2)) | (~((~ip(P2)) | (~ip(P1)) | (~![X: $i, Y: $i] : ((~iext(P1, X, Y)) | iext(P2, X, Y)))))))))) | (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.50/0.70 tff(72,plain,
% 0.50/0.70 (~((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y))))))))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.50/0.70 tff(73,plain,
% 0.50/0.70 (((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) | (~((~ip(uri_ex_p)) | (~ip(uri_ex_p1)) | (~![X: $i, Y: $i] : ((~iext(uri_ex_p1, X, Y)) | iext(uri_ex_p, X, Y)))))))) | (iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(74,plain,
% 0.50/0.70 (iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.50/0.70 tff(75,plain,
% 0.50/0.70 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(76,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[75])).
% 0.50/0.70 tff(77,plain,
% 0.50/0.70 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y))))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(78,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[77])).
% 0.50/0.70 tff(79,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y)))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(80,plain,
% 0.50/0.70 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_propertyChainAxiom, X, Y) => (ip(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y))))),
% 0.50/0.70 inference(bind,[status(th)],[])).
% 0.50/0.70 tff(81,plain,
% 0.50/0.70 (![X: $i, Y: $i] : (iext(uri_owl_propertyChainAxiom, X, Y) => (ip(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y)))),
% 0.50/0.70 inference(quant_intro,[status(thm)],[80])).
% 0.50/0.70 tff(82,axiom,(![X: $i, Y: $i] : (iext(uri_owl_propertyChainAxiom, X, Y) => (ip(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_propertychainaxiom_ext')).
% 0.50/0.70 tff(83,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.50/0.70 tff(84,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y)))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.50/0.70 tff(85,plain,(
% 0.50/0.70 ![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (ip(X) & icext(uri_rdf_List, Y)))),
% 0.50/0.70 inference(skolemize,[status(sab)],[84])).
% 0.50/0.70 tff(86,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.50/0.70 tff(87,plain,
% 0.50/0.70 (![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.50/0.70 tff(88,plain,
% 0.50/0.70 (((~![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140)))))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(89,plain,
% 0.50/0.70 ((~![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140)))))),
% 0.50/0.70 inference(quant_inst,[status(thm)],[])).
% 0.50/0.70 tff(90,plain,
% 0.50/0.70 ((~![X: $i, Y: $i] : ((~iext(uri_owl_propertyChainAxiom, X, Y)) | (~((~ip(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_propertyChainAxiom, uri_ex_p, X0!140)) | (~((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140))))),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.50/0.70 tff(91,plain,
% 0.50/0.70 (~((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140)))),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[90, 87, 38])).
% 0.50/0.70 tff(92,plain,
% 0.50/0.70 (((~ip(uri_ex_p)) | (~icext(uri_rdf_List, X0!140))) | ip(uri_ex_p)),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(93,plain,
% 0.50/0.70 (ip(uri_ex_p)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.50/0.70 tff(94,plain,
% 0.50/0.70 (((~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1)))) | ip(uri_ex_p1)),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(95,plain,
% 0.50/0.70 (ip(uri_ex_p1)),
% 0.50/0.70 inference(unit_resolution,[status(thm)],[94, 41])).
% 0.50/0.70 tff(96,plain,
% 0.50/0.70 ((~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)) <=> (~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p))),
% 0.50/0.70 inference(rewrite,[status(thm)],[])).
% 0.50/0.70 tff(97,axiom,(~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_chain_subprop')).
% 0.50/0.70 tff(98,plain,
% 0.50/0.70 (~iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p)),
% 0.50/0.70 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.50/0.70 tff(99,plain,
% 0.50/0.70 ((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))))),
% 0.50/0.70 inference(tautology,[status(thm)],[])).
% 0.50/0.70 tff(100,plain,
% 0.50/0.70 ((~(iext(uri_rdfs_subPropertyOf, uri_ex_p1, uri_ex_p) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))))) | (~ip(uri_ex_p1)) | (~ip(uri_ex_p)) | (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.50/0.72 tff(101,plain,
% 0.50/0.72 (~((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[100, 95, 93, 74])).
% 0.50/0.72 tff(102,plain,
% 0.50/0.72 (((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | (~iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(103,plain,
% 0.50/0.72 (~iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.50/0.72 tff(104,plain,
% 0.50/0.72 (((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))),
% 0.50/0.72 inference(tautology,[status(thm)],[])).
% 0.50/0.72 tff(105,plain,
% 0.50/0.72 (iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.50/0.72 tff(106,plain,
% 0.50/0.72 (((~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))) <=> ((~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))),
% 0.50/0.72 inference(rewrite,[status(thm)],[])).
% 0.50/0.72 tff(107,plain,
% 0.50/0.72 ((~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))) | ((~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1)))),
% 0.50/0.72 inference(quant_inst,[status(thm)],[])).
% 0.50/0.72 tff(108,plain,
% 0.50/0.72 ((~![Y0: $i, Y1: $i] : ((~iext(uri_ex_p1, Y0, Y1)) | iext(uri_ex_p, Y0, Y1))) | (~iext(uri_ex_p1, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))) | iext(uri_ex_p, tptp_fun_X_63(uri_ex_p, uri_ex_p1), tptp_fun_Y_62(uri_ex_p, uri_ex_p1))),
% 0.50/0.72 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.50/0.72 tff(109,plain,
% 0.50/0.72 ($false),
% 0.50/0.72 inference(unit_resolution,[status(thm)],[108, 105, 103, 43])).
% 0.50/0.72 % SZS output end Proof
% 0.50/0.73 % E exiting
%------------------------------------------------------------------------------