%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB020+2 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:29:37 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB020+2 : TPTP v9.0.0. Released v5.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:47:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(icext_type, type, (
% 0.20/0.38 icext: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: ( $i * $i ) > $i)).
% 0.20/0.38 tff(uri_ex_d_type, type, (
% 0.20/0.38 uri_ex_d: $i)).
% 0.20/0.38 tff(uri_ex_c3_type, type, (
% 0.20/0.38 uri_ex_c3: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_xc_9_type, type, (
% 0.20/0.38 tptp_fun_BNODE_xc_9: $i)).
% 0.20/0.38 tff(uri_ex_c2_type, type, (
% 0.20/0.38 uri_ex_c2: $i)).
% 0.20/0.38 tff(uri_ex_c_type, type, (
% 0.20/0.38 uri_ex_c: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_xs_10_type, type, (
% 0.20/0.38 tptp_fun_BNODE_xs_10: $i)).
% 0.20/0.38 tff(ic_type, type, (
% 0.20/0.38 ic: $i > $o)).
% 0.20/0.38 tff(iext_type, type, (
% 0.20/0.38 iext: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_BNODE_li1_5_type, type, (
% 0.20/0.38 tptp_fun_BNODE_li1_5: $i)).
% 0.20/0.38 tff(uri_owl_intersectionOf_type, type, (
% 0.20/0.38 uri_owl_intersectionOf: $i)).
% 0.20/0.38 tff(tptp_fun_X_0_type, type, (
% 0.20/0.38 tptp_fun_X_0: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(uri_rdf_nil_type, type, (
% 0.20/0.38 uri_rdf_nil: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_li2_4_type, type, (
% 0.20/0.38 tptp_fun_BNODE_li2_4: $i)).
% 0.20/0.38 tff(uri_rdf_rest_type, type, (
% 0.20/0.38 uri_rdf_rest: $i)).
% 0.20/0.38 tff(uri_owl_complementOf_type, type, (
% 0.20/0.38 uri_owl_complementOf: $i)).
% 0.20/0.38 tff(uri_rdf_first_type, type, (
% 0.20/0.38 uri_rdf_first: $i)).
% 0.20/0.38 tff(uri_rdfs_subClassOf_type, type, (
% 0.20/0.38 uri_rdfs_subClassOf: $i)).
% 0.20/0.38 tff(uri_ex_c1_type, type, (
% 0.20/0.38 uri_ex_c1: $i)).
% 0.20/0.38 tff(uri_owl_disjointWith_type, type, (
% 0.20/0.38 uri_owl_disjointWith: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_lu3_6_type, type, (
% 0.20/0.38 tptp_fun_BNODE_lu3_6: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_lu2_7_type, type, (
% 0.20/0.38 tptp_fun_BNODE_lu2_7: $i)).
% 0.20/0.38 tff(tptp_fun_BNODE_lu1_8_type, type, (
% 0.20/0.38 tptp_fun_BNODE_lu1_8: $i)).
% 0.20/0.38 tff(uri_owl_unionOf_type, type, (
% 0.20/0.38 uri_owl_unionOf: $i)).
% 0.20/0.38 tff(tptp_fun_X_1_type, type, (
% 0.20/0.38 tptp_fun_X_1: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_X_3_type, type, (
% 0.20/0.38 tptp_fun_X_3: ( $i * $i ) > $i)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)) <=> ?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $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(rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2))), ((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2))), ((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)))), (((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3))), (((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)))), ((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3))), ((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)))), (((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil))), (((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)))), ((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1))), ((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)))), (((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs))), (((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)))), ((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1))), ((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)))), (((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c))), (((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)))), ((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2))), ((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)))), (((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc))), (((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)))), ((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil))), ((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)))), (((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)) <=> ((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))), (((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)) <=> (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : ((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2)) <=> ?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.41 tff(4,axiom,(?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : ((((((((((((((iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1)) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2)) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2)) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3)) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3)) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil)) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs)) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1)) & iext(uri_rdf_first, BNODE_li1, uri_ex_c)) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2)) & iext(uri_rdf_first, BNODE_li2, BNODE_xc)) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil)) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_premise_fullish_020_Logical_Complications')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (?[BNODE_xs: $i, BNODE_xc: $i, BNODE_lu1: $i, BNODE_lu2: $i, BNODE_lu3: $i, BNODE_li1: $i, BNODE_li2: $i] : (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1) & iext(uri_rdf_first, BNODE_lu1, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1, BNODE_lu2) & iext(uri_rdf_first, BNODE_lu2, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2, BNODE_lu3) & iext(uri_rdf_first, BNODE_lu3, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs) & iext(uri_owl_intersectionOf, BNODE_xs, BNODE_li1) & iext(uri_rdf_first, BNODE_li1, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1, BNODE_li2) & iext(uri_rdf_first, BNODE_li2, BNODE_xc) & iext(uri_rdf_rest, BNODE_li2, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc, uri_ex_c2))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.20/0.41 tff(7,plain,(
% 0.20/0.41 iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) & iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7) & iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6) & iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) & iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) & iext(uri_rdf_first, BNODE_li1!5, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4) & iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9) & iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)),
% 0.20/0.41 inference(skolemize,[status(sab)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)),
% 0.20/0.41 inference(and_elim,[status(thm)],[7])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)),
% 0.20/0.41 inference(and_elim,[status(thm)],[7])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)),
% 0.20/0.41 inference(and_elim,[status(thm)],[7])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)),
% 0.20/0.41 inference(and_elim,[status(thm)],[7])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))))), rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))), (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> ((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))))), ((icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))))))), rewrite((icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (~((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))))) <=> (~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))), ((icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))), rewrite((~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))), ((icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> (~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))), ((~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))) <=> (~(~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))), rewrite((~(~(((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))), ((~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))) <=> (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))), ((((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))))), rewrite((((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) <=> (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.43 tff(26,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_intersectionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_bool_intersectionof_class_002')).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_intersectionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.43 tff(29,plain,(
% 0.20/0.43 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z)))))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_intersectionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_0(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_0(C2, C1, Z)) & icext(C2, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))))))) <=> ((~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 ((~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))))))))) <=> (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X))))))))))) <=> ((~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[37, 35])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[39, 34])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (((~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_c)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (((~icext(C1, tptp_fun_X_0(C2, C1, Z))) | (~icext(C2, tptp_fun_X_0(C2, C1, Z)))) <=> icext(Z, tptp_fun_X_0(C2, C1, Z))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~![X: $i] : (~(((~icext(C2, X)) | (~icext(C1, X))) <=> icext(Z, X)))))))))))) | (~iext(uri_rdf_rest, BNODE_li2!4, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_li2!4, BNODE_xc!9)) | (~iext(uri_rdf_rest, BNODE_li1!5, BNODE_li2!4)) | (~iext(uri_rdf_first, BNODE_li1!5, uri_ex_c)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (~((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (((~(iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~ic(BNODE_xc!9)) | (((~icext(BNODE_xc!9, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))) | (~icext(uri_ex_c, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10)))) <=> icext(BNODE_xs!10, tptp_fun_X_0(BNODE_xc!9, uri_ex_c, BNODE_xs!10))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))))) | ((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 ((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)),
% 0.20/0.44 inference(and_elim,[status(thm)],[7])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 ((~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))) | (~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 ((~((~iext(uri_owl_intersectionOf, BNODE_xs!10, BNODE_li1!5)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))))) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (((~ic(uri_ex_c)) | (~ic(BNODE_xs!10)) | (~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~ic(BNODE_xc!9))) | ![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 ((~![X: $i] : (~(((~icext(BNODE_xc!9, X)) | (~icext(uri_ex_c, X))) <=> icext(BNODE_xs!10, X)))) | (~(((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (~(((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(55,plain,
% 0.20/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.44 tff(58,plain,
% 0.20/0.44 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))), rewrite((iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))) <=> (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))), rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))), ((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) <=> (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))) <=> (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(64,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.45 tff(65,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(66,plain,
% 0.20/0.45 (^[C1: $i, C2: $i] : rewrite((iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(67,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X)))) <=> ![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.45 tff(68,axiom,(![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (icext(C1, X) => icext(C2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_rdfsext_subclassof')).
% 0.20/0.45 tff(69,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.45 tff(70,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.45 tff(71,plain,(
% 0.20/0.45 ![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[70])).
% 0.20/0.45 tff(72,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (((~iext(uri_rdfs_subClassOf, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X)))) & (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.20/0.45 tff(73,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.20/0.45 tff(74,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (~((~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))) | (~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[73, 60])).
% 0.20/0.45 tff(75,plain,
% 0.20/0.45 (![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[74, 55])).
% 0.20/0.45 tff(76,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(77,plain,
% 0.20/0.45 ((~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))))) <=> (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[78, 76])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[81, 75])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (((~(iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10) | (~ic(uri_ex_d)) | (~ic(BNODE_xs!10)) | (~((~icext(uri_ex_d, tptp_fun_X_2(BNODE_xs!10, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(BNODE_xs!10, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 ((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)),
% 0.20/0.45 inference(and_elim,[status(thm)],[7])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 ((~((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!10)) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))))) | (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (~((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (((~ic(BNODE_xs!10)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X)))) | ![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 ((~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X))))))))) <=> (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_2(C2, C1))) | icext(C2, tptp_fun_X_2(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))) | (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (~((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[96, 75])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(uri_ex_c3, X)))))))) | (iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 (iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)),
% 0.20/0.45 inference(and_elim,[status(thm)],[7])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y))) <=> ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_disjointWith, X, Y) => (ic(X) & ic(Y))) <=> ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (![X: $i, Y: $i] : (iext(uri_owl_disjointWith, X, Y) => (ic(X) & ic(Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.45 tff(108,axiom,(![X: $i, Y: $i] : (iext(uri_owl_disjointWith, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_prop_disjointwith_ext')).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.45 tff(111,plain,(
% 0.20/0.45 ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[110])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(115,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(116,plain,
% 0.20/0.46 ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.46 tff(117,plain,
% 0.20/0.46 (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[116, 113, 100])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~ic(uri_ex_c1)) | (~ic(uri_ex_d))) | ic(uri_ex_d)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (ic(uri_ex_d)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)),
% 0.20/0.46 inference(and_elim,[status(thm)],[7])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))))))), (((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))))))))), rewrite(((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))), (((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.46 tff(128,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : refl(((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(129,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(131,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))))), rewrite((~(~((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))) <=> (((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))))), rewrite((((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2))) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))), (((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))) <=> ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3))), (((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))), ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) | icext(C2, X)) | icext(C3, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) | icext(C2, X)) | icext(C3, X)))))) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))), (((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) | icext(C2, X)) | icext(C3, X)))))) <=> ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(139,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) | icext(C2, X)) | icext(C3, X)))))) <=> ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.47 tff(140,axiom,(![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, S3)) & iext(uri_rdf_first, S3, C3)) & iext(uri_rdf_rest, S3, uri_rdf_nil)) => (iext(uri_owl_unionOf, Z, S1) <=> ((((ic(Z) & ic(C1)) & ic(C2)) & ic(C3)) & ![X: $i] : (icext(Z, X) <=> ((icext(C1, X) | icext(C2, X)) | icext(C3, X))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_bool_unionof_class_003')).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.47 tff(143,plain,(
% 0.20/0.47 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z)))))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[142])).
% 0.20/0.47 tff(144,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, S3) & iext(uri_rdf_first, S3, C3) & iext(uri_rdf_rest, S3, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ic(C3) & ![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[144, 134])).
% 0.20/0.47 tff(146,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[145, 132])).
% 0.20/0.47 tff(147,plain,
% 0.20/0.47 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[146, 127])).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 (((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(150,plain,
% 0.20/0.47 ((~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 (((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[152])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))) <=> ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[153, 148])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : ((~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, S3)) | (~iext(uri_rdf_first, S3, C3)) | (~iext(uri_rdf_rest, S3, uri_rdf_nil)) | (~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_1(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_1(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_1(C3, C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C1)) | (~ic(C2)) | (~ic(C3)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!8, uri_ex_c1)) | (~iext(uri_rdf_first, BNODE_lu2!7, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu1!8, BNODE_lu2!7)) | (~iext(uri_rdf_rest, BNODE_lu3!6, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu3!6, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu2!7, BNODE_lu3!6)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 147, 125, 124, 123, 122, 121, 120])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) <=> (icext(uri_ex_c1, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c3, tptp_fun_X_1(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))) | ((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 ((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)),
% 0.20/0.48 inference(and_elim,[status(thm)],[7])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 ((~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))) | (~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 ((~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!8)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.20/0.48 tff(164,plain,
% 0.20/0.48 (((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))) | ic(uri_ex_c3)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(165,plain,
% 0.20/0.48 (ic(uri_ex_c3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.48 tff(166,plain,
% 0.20/0.48 ((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) <=> (~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(167,axiom,(~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','testcase_conclusion_fullish_020_Logical_Complications')).
% 0.20/0.48 tff(168,plain,
% 0.20/0.48 (~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.48 tff(169,plain,
% 0.20/0.48 ((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(170,plain,
% 0.20/0.48 ((~(iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))) | (~ic(uri_ex_d)) | (~ic(uri_ex_c3)) | (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.20/0.48 tff(171,plain,
% 0.20/0.48 (~((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[170, 165, 119, 99])).
% 0.20/0.48 tff(172,plain,
% 0.20/0.48 (((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(173,plain,
% 0.20/0.48 (icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.20/0.48 tff(174,plain,
% 0.20/0.48 (((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))) | ((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(175,plain,
% 0.20/0.48 ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))) | ((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(176,plain,
% 0.20/0.48 ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!10, X))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.48 tff(177,plain,
% 0.20/0.48 (icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[176, 173, 90])).
% 0.20/0.48 tff(178,plain,
% 0.20/0.48 ((((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) | (~icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(179,plain,
% 0.20/0.48 ((((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> icext(BNODE_xs!10, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.48 tff(180,plain,
% 0.20/0.48 (~((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[179, 53])).
% 0.20/0.48 tff(181,plain,
% 0.20/0.48 (((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) | icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(182,plain,
% 0.20/0.48 (icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.48 tff(183,plain,
% 0.20/0.48 (((~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))) | ![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(184,plain,
% 0.20/0.48 (![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[183, 163])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) <=> ((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 ((icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) <=> (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) <=> ((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) <=> ((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.48 tff(189,plain,
% 0.20/0.48 ((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 ((~![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[190, 184])).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (((~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[192, 180])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 ((~(icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) | (~icext(uri_ex_c, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[194, 193, 191])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (^[C1: $i, C2: $i] : refl((~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(199,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[198])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (^[C1: $i, C2: $i] : rewrite((~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[200])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[201, 199])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 (^[C1: $i, C2: $i] : trans(monotonicity(rewrite(((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) <=> ((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))), trans(monotonicity(rewrite((icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))), ((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))), rewrite((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))), ((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))), ((((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))))) <=> (((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))))), rewrite((((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) <=> (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))), ((((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))))) <=> (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))))) <=> ![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[203])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (^[C1: $i, C2: $i] : rewrite((((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))))) <=> (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))))) <=> ![C1: $i, C2: $i] : (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[205])).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (^[C1: $i, C2: $i] : rewrite((iext(uri_owl_disjointWith, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) <=> (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) <=> ![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[208])).
% 0.20/0.49 tff(210,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_eqdis_disjointwith')).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.20/0.49 tff(213,plain,(
% 0.20/0.49 ![C1: $i, C2: $i] : (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | ((~ic(C1)) | (~ic(C2)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[212])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (((~iext(uri_owl_disjointWith, C1, C2)) | (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X))))) & (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_3(C2, C1)) & icext(C2, tptp_fun_X_3(C2, C1)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[214, 204])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))) | (~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1)))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[215, 202])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[216, 197])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 ((~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))))) <=> (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[219])).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))) <=> ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_3(C2, C1))) | (~icext(C2, tptp_fun_X_3(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))) | (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[223, 217])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_3(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_3(uri_ex_c1, uri_ex_d))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))))) | ((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 ((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 ((~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))) | (~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 ((~((~iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))))) | (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[227, 100])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[228, 226])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X))))) | ![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | ((~icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))) <=> ((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | (~icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 ((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | ((~icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(234,plain,
% 0.20/0.49 ((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | (~icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (~icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[234, 173, 231])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 (((~icext(uri_ex_d, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (~icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 171])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ((~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(239,plain,
% 0.20/0.49 ((~(icext(uri_ex_c3, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[238, 237, 235])).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[239, 195])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ((icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d))) | (~icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[241, 240, 182])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)),
% 0.20/0.49 inference(and_elim,[status(thm)],[7])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[244])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[246])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[247, 245])).
% 0.20/0.49 tff(249,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[249])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 (^[Z: $i, C: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(rewrite((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), rewrite((~(icext(C, X) <=> icext(Z, X))) <=> (~(icext(C, X) <=> icext(Z, X)))), ((icext(Z, X) <=> (~icext(C, X))) <=> (~(icext(C, X) <=> icext(Z, X)))))), (![X: $i] : (icext(Z, X) <=> (~icext(C, X))) <=> ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> ((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), rewrite(((ic(Z) & ic(C)) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))), (((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))))), rewrite((iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))), ((iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[252])).
% 0.20/0.49 tff(254,axiom,(![Z: $i, C: $i] : (iext(uri_owl_complementOf, Z, C) => ((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','owl_bool_complementof_class')).
% 0.20/0.50 tff(255,plain,
% 0.20/0.50 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.20/0.50 tff(257,plain,(
% 0.20/0.50 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[256])).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[258, 248])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (~(icext(C, X) <=> icext(Z, X)))))))) | (~iext(uri_owl_complementOf, BNODE_xc!9, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.20/0.50 tff(263,plain,
% 0.20/0.50 (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[262, 259, 243])).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 (((~ic(uri_ex_c2)) | (~ic(BNODE_xc!9)) | (~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X))))) | ![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(265,plain,
% 0.20/0.50 (![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 ((~![X: $i] : (~(icext(uri_ex_c2, X) <=> icext(BNODE_xc!9, X)))) | (~(icext(uri_ex_c2, tptp_fun_X_2(uri_ex_c3, uri_ex_d)) <=> icext(BNODE_xc!9, tptp_fun_X_2(uri_ex_c3, uri_ex_d))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[266, 265, 242])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------