TSTP Solution File: SWB020+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB020+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 08:31:51 EDT 2022
% Result : Theorem 0.82s 0.78s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWB020+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 19:33:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.82/0.78 % SZS status Theorem
% 0.82/0.78 % SZS output start Proof
% 0.82/0.78 tff(icext_type, type, (
% 0.82/0.78 icext: ( $i * $i ) > $o)).
% 0.82/0.78 tff(tptp_fun_X_61_type, type, (
% 0.82/0.78 tptp_fun_X_61: ( $i * $i ) > $i)).
% 0.82/0.78 tff(uri_ex_d_type, type, (
% 0.82/0.78 uri_ex_d: $i)).
% 0.82/0.78 tff(uri_ex_c3_type, type, (
% 0.82/0.78 uri_ex_c3: $i)).
% 0.82/0.78 tff(uri_ex_c2_type, type, (
% 0.82/0.78 uri_ex_c2: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_xc_145_type, type, (
% 0.82/0.78 tptp_fun_BNODE_xc_145: $i)).
% 0.82/0.78 tff(uri_ex_c_type, type, (
% 0.82/0.78 uri_ex_c: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_xs_146_type, type, (
% 0.82/0.78 tptp_fun_BNODE_xs_146: $i)).
% 0.82/0.78 tff(ic_type, type, (
% 0.82/0.78 ic: $i > $o)).
% 0.82/0.78 tff(iext_type, type, (
% 0.82/0.78 iext: ( $i * $i * $i ) > $o)).
% 0.82/0.78 tff(tptp_fun_BNODE_li1_141_type, type, (
% 0.82/0.78 tptp_fun_BNODE_li1_141: $i)).
% 0.82/0.78 tff(uri_owl_intersectionOf_type, type, (
% 0.82/0.78 uri_owl_intersectionOf: $i)).
% 0.82/0.78 tff(tptp_fun_X_3_type, type, (
% 0.82/0.78 tptp_fun_X_3: ( $i * $i * $i ) > $i)).
% 0.82/0.78 tff(uri_rdf_nil_type, type, (
% 0.82/0.78 uri_rdf_nil: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_li2_140_type, type, (
% 0.82/0.78 tptp_fun_BNODE_li2_140: $i)).
% 0.82/0.78 tff(uri_rdf_rest_type, type, (
% 0.82/0.78 uri_rdf_rest: $i)).
% 0.82/0.78 tff(uri_owl_complementOf_type, type, (
% 0.82/0.78 uri_owl_complementOf: $i)).
% 0.82/0.78 tff(uri_rdf_first_type, type, (
% 0.82/0.78 uri_rdf_first: $i)).
% 0.82/0.78 tff(uri_rdfs_subClassOf_type, type, (
% 0.82/0.78 uri_rdfs_subClassOf: $i)).
% 0.82/0.78 tff(uri_ex_c1_type, type, (
% 0.82/0.78 uri_ex_c1: $i)).
% 0.82/0.78 tff(uri_owl_disjointWith_type, type, (
% 0.82/0.78 uri_owl_disjointWith: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_lu3_142_type, type, (
% 0.82/0.78 tptp_fun_BNODE_lu3_142: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_lu2_143_type, type, (
% 0.82/0.78 tptp_fun_BNODE_lu2_143: $i)).
% 0.82/0.78 tff(tptp_fun_BNODE_lu1_144_type, type, (
% 0.82/0.78 tptp_fun_BNODE_lu1_144: $i)).
% 0.82/0.78 tff(uri_owl_unionOf_type, type, (
% 0.82/0.78 uri_owl_unionOf: $i)).
% 0.82/0.78 tff(tptp_fun_X_7_type, type, (
% 0.82/0.78 tptp_fun_X_7: ( $i * $i * $i * $i ) > $i)).
% 0.82/0.78 tff(tptp_fun_X_66_type, type, (
% 0.82/0.78 tptp_fun_X_66: ( $i * $i ) > $i)).
% 0.82/0.78 tff(1,plain,
% 0.82/0.78 (?[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))),
% 0.82/0.79 inference(rewrite,[status(thm)],[])).
% 0.82/0.79 tff(2,plain,
% 0.82/0.79 (^[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))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(3,plain,
% 0.82/0.80 (?[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))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[2])).
% 0.82/0.80 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/sandbox/benchmark/theBenchmark.p','testcase_premise_fullish_020_Logical_Complications')).
% 0.82/0.80 tff(5,plain,
% 0.82/0.80 (?[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))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.82/0.80 tff(6,plain,
% 0.82/0.80 (?[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))),
% 0.82/0.80 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.82/0.80 tff(7,plain,(
% 0.82/0.80 iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) & iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1) & iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143) & iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2) & iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142) & iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3) & iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil) & iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) & iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146) & iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) & iext(uri_rdf_first, BNODE_li1!141, uri_ex_c) & iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140) & iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145) & iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil) & iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)),
% 0.82/0.80 inference(skolemize,[status(sab)],[6])).
% 0.82/0.80 tff(8,plain,
% 0.82/0.80 (iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)),
% 0.82/0.80 inference(and_elim,[status(thm)],[7])).
% 0.82/0.80 tff(9,plain,
% 0.82/0.80 (iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)),
% 0.82/0.80 inference(and_elim,[status(thm)],[7])).
% 0.82/0.80 tff(10,plain,
% 0.82/0.80 (iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)),
% 0.82/0.80 inference(and_elim,[status(thm)],[7])).
% 0.82/0.80 tff(11,plain,
% 0.82/0.80 (iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)),
% 0.82/0.80 inference(and_elim,[status(thm)],[7])).
% 0.82/0.80 tff(12,plain,
% 0.82/0.80 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, 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, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, 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, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, 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, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, 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, uri_rdf_nil)) | (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(13,plain,
% 0.82/0.80 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[12])).
% 0.82/0.80 tff(14,plain,
% 0.82/0.80 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(15,plain,
% 0.82/0.80 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[14])).
% 0.82/0.80 tff(16,plain,
% 0.82/0.80 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))))),
% 0.82/0.80 inference(bind,[status(th)],[])).
% 0.82/0.80 tff(17,plain,
% 0.82/0.80 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.80 inference(quant_intro,[status(thm)],[16])).
% 0.82/0.80 tff(18,plain,
% 0.82/0.80 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.80 inference(transitivity,[status(thm)],[17, 15])).
% 0.82/0.80 tff(19,plain,
% 0.82/0.80 (^[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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))), trans(monotonicity(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), rewrite(((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (~((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))), (((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))) <=> (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))))), rewrite((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))), ((iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))) <=> (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X))))))))) & (iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(20,plain,
% 0.82/0.81 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[19])).
% 0.82/0.81 tff(21,plain,
% 0.82/0.81 (^[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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(22,plain,
% 0.82/0.81 (![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[21])).
% 0.82/0.81 tff(23,plain,
% 0.82/0.81 (![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))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(24,plain,
% 0.82/0.81 (^[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))))))))),
% 0.82/0.81 inference(bind,[status(th)],[])).
% 0.82/0.81 tff(25,plain,
% 0.82/0.81 (![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))))))),
% 0.82/0.81 inference(quant_intro,[status(thm)],[24])).
% 0.82/0.81 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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_intersectionof_class_002')).
% 0.82/0.81 tff(27,plain,
% 0.82/0.81 (![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))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.82/0.81 tff(28,plain,
% 0.82/0.81 (![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))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.82/0.81 tff(29,plain,(
% 0.82/0.81 ![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_3(C2, C1, Z)) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))))),
% 0.82/0.81 inference(skolemize,[status(sab)],[28])).
% 0.82/0.81 tff(30,plain,
% 0.82/0.81 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_3(C2, C1, Z))) <=> (icext(C1, tptp_fun_X_3(C2, C1, Z)) & icext(C2, tptp_fun_X_3(C2, C1, Z)))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.82/0.81 tff(31,plain,
% 0.82/0.81 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.82/0.81 tff(32,plain,
% 0.82/0.81 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))) | (~(iext(uri_owl_intersectionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.82/0.81 tff(33,plain,
% 0.82/0.81 (![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))),
% 0.82/0.81 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.82/0.81 tff(34,plain,
% 0.82/0.81 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(35,plain,
% 0.82/0.81 (((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(36,plain,
% 0.82/0.81 ((~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))) <=> (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))),
% 0.82/0.81 inference(rewrite,[status(thm)],[])).
% 0.82/0.81 tff(37,plain,
% 0.82/0.81 (((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.81 inference(monotonicity,[status(thm)],[36])).
% 0.82/0.81 tff(38,plain,
% 0.82/0.81 (((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))) <=> ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.81 inference(transitivity,[status(thm)],[37, 35])).
% 0.82/0.81 tff(39,plain,
% 0.82/0.81 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))))),
% 0.82/0.81 inference(monotonicity,[status(thm)],[38])).
% 0.82/0.81 tff(40,plain,
% 0.82/0.81 (((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, 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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[39, 34])).
% 0.82/0.82 tff(41,plain,
% 0.82/0.82 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | ((~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(BNODE_xc!145)) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))))),
% 0.82/0.82 inference(quant_inst,[status(thm)],[])).
% 0.82/0.82 tff(42,plain,
% 0.82/0.82 ((~![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(C2)) | (~ic(C1)) | (~ic(Z)) | (icext(Z, tptp_fun_X_3(C2, C1, Z)) <=> ((~icext(C1, tptp_fun_X_3(C2, C1, Z))) | (~icext(C2, tptp_fun_X_3(C2, C1, Z))))))) | (~((~iext(uri_owl_intersectionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~((~icext(C2, X)) | (~icext(C1, X)))))))))))))) | (~iext(uri_rdf_first, BNODE_li1!141, uri_ex_c)) | (~iext(uri_rdf_rest, BNODE_li1!141, BNODE_li2!140)) | (~iext(uri_rdf_first, BNODE_li2!140, BNODE_xc!145)) | (~iext(uri_rdf_rest, BNODE_li2!140, uri_rdf_nil)) | (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.82/0.82 tff(43,plain,
% 0.82/0.82 (~((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[42, 33, 11, 10, 9, 8])).
% 0.82/0.82 tff(44,plain,
% 0.82/0.82 (((~(iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141) | (~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (icext(BNODE_xs!146, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146)) <=> ((~icext(uri_ex_c, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))) | (~icext(BNODE_xc!145, tptp_fun_X_3(BNODE_xc!145, uri_ex_c, BNODE_xs!146))))))) | (~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))))) | ((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))),
% 0.82/0.82 inference(tautology,[status(thm)],[])).
% 0.82/0.82 tff(45,plain,
% 0.82/0.82 ((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.82/0.82 tff(46,plain,
% 0.82/0.82 (iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)),
% 0.82/0.82 inference(and_elim,[status(thm)],[7])).
% 0.82/0.82 tff(47,plain,
% 0.82/0.82 ((~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))) | (~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))),
% 0.82/0.82 inference(tautology,[status(thm)],[])).
% 0.82/0.82 tff(48,plain,
% 0.82/0.82 ((~((~iext(uri_owl_intersectionOf, BNODE_xs!146, BNODE_li1!141)) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))))) | (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.82/0.82 tff(49,plain,
% 0.82/0.82 (~((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.82/0.82 tff(50,plain,
% 0.82/0.82 (((~ic(uri_ex_c)) | (~ic(BNODE_xs!146)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X))))))) | ![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))),
% 0.82/0.82 inference(tautology,[status(thm)],[])).
% 0.82/0.82 tff(51,plain,
% 0.82/0.82 (![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.82/0.82 tff(52,plain,
% 0.82/0.82 ((~![X: $i] : (icext(BNODE_xs!146, X) <=> (~((~icext(BNODE_xc!145, X)) | (~icext(uri_ex_c, X)))))) | (icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))))),
% 0.82/0.82 inference(quant_inst,[status(thm)],[])).
% 0.82/0.82 tff(53,plain,
% 0.82/0.82 (icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.82/0.82 tff(54,plain,
% 0.82/0.82 (iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146)),
% 0.82/0.82 inference(and_elim,[status(thm)],[7])).
% 0.82/0.82 tff(55,plain,
% 0.82/0.82 (^[C: $i, D: $i] : refl(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(56,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[55])).
% 0.82/0.82 tff(57,plain,
% 0.82/0.82 (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(58,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[57])).
% 0.82/0.82 tff(59,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[58, 56])).
% 0.82/0.82 tff(60,plain,
% 0.82/0.82 (^[C: $i, D: $i] : rewrite(((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(61,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[60])).
% 0.82/0.82 tff(62,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(63,plain,
% 0.82/0.82 (^[C: $i, D: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((icext(C, X) => icext(D, X)) <=> ((~icext(C, X)) | icext(D, X)))), (![X: $i] : (icext(C, X) => icext(D, X)) <=> ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> ((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), rewrite(((ic(C) & ic(D)) & ![X: $i] : ((~icext(C, X)) | icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))), (((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))) <=> (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> (iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))))), rewrite((iext(uri_rdfs_subClassOf, C, D) => (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))), ((iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(64,plain,
% 0.82/0.82 (![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X)))) <=> ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[63])).
% 0.82/0.82 tff(65,axiom,(![C: $i, D: $i] : (iext(uri_rdfs_subClassOf, C, D) => ((ic(C) & ic(D)) & ![X: $i] : (icext(C, X) => icext(D, X))))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','rdfs_subclassof_main')).
% 0.82/0.82 tff(66,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.82/0.82 tff(67,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.82/0.82 tff(68,plain,(
% 0.82/0.82 ![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (ic(C) & ic(D) & ![X: $i] : ((~icext(C, X)) | icext(D, X))))),
% 0.82/0.82 inference(skolemize,[status(sab)],[67])).
% 0.82/0.82 tff(69,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.82/0.82 tff(70,plain,
% 0.82/0.82 (![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.82/0.82 tff(71,plain,
% 0.82/0.82 (((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146)) | (~((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))))))) <=> ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146)) | (~((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(72,plain,
% 0.82/0.82 ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | ((~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146)) | (~((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))))))),
% 0.82/0.82 inference(quant_inst,[status(thm)],[])).
% 0.82/0.82 tff(73,plain,
% 0.82/0.82 ((~![C: $i, D: $i] : ((~iext(uri_rdfs_subClassOf, C, D)) | (~((~ic(D)) | (~ic(C)) | (~![X: $i] : ((~icext(C, X)) | icext(D, X))))))) | (~iext(uri_rdfs_subClassOf, uri_ex_d, BNODE_xs!146)) | (~((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X)))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.82/0.82 tff(74,plain,
% 0.82/0.82 (~((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[73, 70, 54])).
% 0.82/0.82 tff(75,plain,
% 0.82/0.82 (((~ic(BNODE_xs!146)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X)))) | ![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))),
% 0.82/0.82 inference(tautology,[status(thm)],[])).
% 0.82/0.82 tff(76,plain,
% 0.82/0.82 (![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.82/0.82 tff(77,plain,
% 0.82/0.82 (^[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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X))))))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(78,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[77])).
% 0.82/0.82 tff(79,plain,
% 0.82/0.82 (^[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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(80,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[79])).
% 0.82/0.82 tff(81,plain,
% 0.82/0.82 (^[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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(82,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[81])).
% 0.82/0.82 tff(83,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(transitivity,[status(thm)],[82, 80])).
% 0.82/0.82 tff(84,plain,
% 0.82/0.82 (^[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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))) <=> (iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(85,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[84])).
% 0.82/0.82 tff(86,plain,
% 0.82/0.82 (^[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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(87,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[86])).
% 0.82/0.82 tff(88,plain,
% 0.82/0.82 (![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))))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(89,plain,
% 0.82/0.82 (^[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)))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(90,plain,
% 0.82/0.82 (![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))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[89])).
% 0.82/0.82 tff(91,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_rdfsext_subclassof')).
% 0.82/0.82 tff(92,plain,
% 0.82/0.82 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.82/0.82 tff(93,plain,
% 0.82/0.82 (![C1: $i, C2: $i] : (iext(uri_rdfs_subClassOf, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : ((~icext(C1, X)) | icext(C2, X))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.82/0.82 tff(94,plain,(
% 0.82/0.82 ![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))))),
% 0.82/0.82 inference(skolemize,[status(sab)],[93])).
% 0.82/0.82 tff(95,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.82/0.82 tff(96,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.82/0.82 tff(97,plain,
% 0.82/0.82 (![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_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[96, 83])).
% 0.82/0.82 tff(98,plain,
% 0.82/0.82 (![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(C2, C1)))))) | (~((~iext(uri_rdfs_subClassOf, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C1, X)) | icext(C2, X)))))))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[97, 78])).
% 0.82/0.82 tff(99,plain,
% 0.82/0.82 ((~![C1: $i, C2: $i] : (~((~(iext(uri_rdfs_subClassOf, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_61(C2, C1))) | icext(C2, tptp_fun_X_61(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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(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)))))))))),
% 0.82/0.82 inference(quant_inst,[status(thm)],[])).
% 0.82/0.82 tff(100,plain,
% 0.82/0.82 (~((~(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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(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))))))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.82/0.82 tff(101,plain,
% 0.82/0.82 (((~(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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(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_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))),
% 0.82/0.82 inference(tautology,[status(thm)],[])).
% 0.82/0.82 tff(102,plain,
% 0.82/0.82 (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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.82 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.82/0.82 tff(103,plain,
% 0.82/0.82 (iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1)),
% 0.82/0.82 inference(and_elim,[status(thm)],[7])).
% 0.82/0.82 tff(104,plain,
% 0.82/0.82 (^[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))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(105,plain,
% 0.82/0.82 (![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)))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[104])).
% 0.82/0.82 tff(106,plain,
% 0.82/0.82 (^[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))))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(107,plain,
% 0.82/0.82 (![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)))))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[106])).
% 0.82/0.82 tff(108,plain,
% 0.82/0.82 (![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)))),
% 0.82/0.82 inference(rewrite,[status(thm)],[])).
% 0.82/0.82 tff(109,plain,
% 0.82/0.82 (^[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))))),
% 0.82/0.82 inference(bind,[status(th)],[])).
% 0.82/0.82 tff(110,plain,
% 0.82/0.82 (![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)))),
% 0.82/0.82 inference(quant_intro,[status(thm)],[109])).
% 0.82/0.82 tff(111,axiom,(![X: $i, Y: $i] : (iext(uri_owl_disjointWith, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax','owl_prop_disjointwith_ext')).
% 0.82/0.82 tff(112,plain,
% 0.82/0.82 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.82/0.82 tff(113,plain,
% 0.82/0.82 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.82/0.82 tff(114,plain,(
% 0.82/0.82 ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 0.82/0.82 inference(skolemize,[status(sab)],[113])).
% 0.82/0.82 tff(115,plain,
% 0.82/0.82 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.82/0.82 tff(116,plain,
% 0.82/0.82 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 0.82/0.82 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.82/0.82 tff(117,plain,
% 0.82/0.82 (((~![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)))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(118,plain,
% 0.82/0.83 ((~![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)))))),
% 0.82/0.83 inference(quant_inst,[status(thm)],[])).
% 0.82/0.83 tff(119,plain,
% 0.82/0.83 ((~![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))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.82/0.83 tff(120,plain,
% 0.82/0.83 (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)))),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[119, 116, 103])).
% 0.82/0.83 tff(121,plain,
% 0.82/0.83 (((~ic(uri_ex_c1)) | (~ic(uri_ex_d))) | ic(uri_ex_d)),
% 0.82/0.83 inference(tautology,[status(thm)],[])).
% 0.82/0.83 tff(122,plain,
% 0.82/0.83 (ic(uri_ex_d)),
% 0.82/0.83 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.82/0.83 tff(123,plain,
% 0.82/0.83 (iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(124,plain,
% 0.82/0.83 (iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(125,plain,
% 0.82/0.83 (iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(126,plain,
% 0.82/0.83 (iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(127,plain,
% 0.82/0.83 (iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(128,plain,
% 0.82/0.83 (iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)),
% 0.82/0.83 inference(and_elim,[status(thm)],[7])).
% 0.82/0.83 tff(129,plain,
% 0.82/0.83 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i, S3: $i, C3: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(130,plain,
% 0.82/0.83 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[129])).
% 0.82/0.83 tff(131,plain,
% 0.82/0.83 (^[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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z))))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(132,plain,
% 0.82/0.83 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[131])).
% 0.82/0.83 tff(133,plain,
% 0.82/0.83 (^[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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z))))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(134,plain,
% 0.82/0.83 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[133])).
% 0.82/0.83 tff(135,plain,
% 0.82/0.83 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.83 inference(transitivity,[status(thm)],[134, 132])).
% 0.82/0.83 tff(136,plain,
% 0.82/0.83 (^[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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(137,plain,
% 0.82/0.83 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[136])).
% 0.82/0.83 tff(138,plain,
% 0.82/0.83 (^[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_7(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(139,plain,
% 0.82/0.83 (![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_7(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[138])).
% 0.82/0.83 tff(140,plain,
% 0.82/0.83 (![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))))))),
% 0.82/0.83 inference(rewrite,[status(thm)],[])).
% 0.82/0.83 tff(141,plain,
% 0.82/0.83 (^[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))))))))),
% 0.82/0.83 inference(bind,[status(th)],[])).
% 0.82/0.83 tff(142,plain,
% 0.82/0.83 (![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))))))),
% 0.82/0.83 inference(quant_intro,[status(thm)],[141])).
% 0.82/0.83 tff(143,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_003')).
% 0.82/0.83 tff(144,plain,
% 0.82/0.83 (![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))))))),
% 0.82/0.83 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.82/0.83 tff(145,plain,
% 0.82/0.83 (![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))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.82/0.84 tff(146,plain,(
% 0.82/0.84 ![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_7(C3, C2, C1, Z)) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.84 inference(skolemize,[status(sab)],[145])).
% 0.82/0.84 tff(147,plain,
% 0.82/0.84 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.82/0.84 tff(148,plain,
% 0.82/0.84 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[147, 137])).
% 0.82/0.84 tff(149,plain,
% 0.82/0.84 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[148, 135])).
% 0.82/0.84 tff(150,plain,
% 0.82/0.84 (![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[149, 130])).
% 0.82/0.84 tff(151,plain,
% 0.82/0.84 (((~![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(152,plain,
% 0.82/0.84 (((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(153,plain,
% 0.82/0.84 ((~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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))))))))))),
% 0.82/0.84 inference(rewrite,[status(thm)],[])).
% 0.82/0.84 tff(154,plain,
% 0.82/0.84 (((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))))),
% 0.82/0.84 inference(monotonicity,[status(thm)],[153])).
% 0.82/0.84 tff(155,plain,
% 0.82/0.84 (((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))))),
% 0.82/0.84 inference(transitivity,[status(thm)],[154, 152])).
% 0.82/0.84 tff(156,plain,
% 0.82/0.84 (((~![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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))))))))))))),
% 0.82/0.84 inference(monotonicity,[status(thm)],[155])).
% 0.82/0.84 tff(157,plain,
% 0.82/0.84 (((~![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))))),
% 0.82/0.84 inference(transitivity,[status(thm)],[156, 151])).
% 0.82/0.84 tff(158,plain,
% 0.82/0.84 ((~![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~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)))))))))))),
% 0.82/0.84 inference(quant_inst,[status(thm)],[])).
% 0.82/0.84 tff(159,plain,
% 0.82/0.84 ((~![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(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | ((~icext(Z, tptp_fun_X_7(C3, C2, C1, Z))) <=> (icext(C3, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C2, tptp_fun_X_7(C3, C2, C1, Z)) | icext(C1, tptp_fun_X_7(C3, C2, C1, Z)))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C3)) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C3, X) | icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, BNODE_lu1!144, uri_ex_c1)) | (~iext(uri_rdf_rest, BNODE_lu1!144, BNODE_lu2!143)) | (~iext(uri_rdf_first, BNODE_lu2!143, uri_ex_c2)) | (~iext(uri_rdf_rest, BNODE_lu2!143, BNODE_lu3!142)) | (~iext(uri_rdf_first, BNODE_lu3!142, uri_ex_c3)) | (~iext(uri_rdf_rest, BNODE_lu3!142, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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))))))))))),
% 0.82/0.84 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.82/0.84 tff(160,plain,
% 0.82/0.84 (~((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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)))))))))),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[159, 150, 128, 127, 126, 125, 124, 123])).
% 0.82/0.84 tff(161,plain,
% 0.82/0.84 (((~(iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | ((~icext(uri_ex_c, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c))) <=> (icext(uri_ex_c3, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c2, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)) | icext(uri_ex_c1, tptp_fun_X_7(uri_ex_c3, uri_ex_c2, uri_ex_c1, uri_ex_c)))))) | (~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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!144)) | (~((~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)))))))),
% 0.82/0.84 inference(tautology,[status(thm)],[])).
% 0.82/0.84 tff(162,plain,
% 0.82/0.84 ((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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))))))),
% 0.82/0.84 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.82/0.84 tff(163,plain,
% 0.82/0.84 (iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)),
% 0.82/0.84 inference(and_elim,[status(thm)],[7])).
% 0.82/0.84 tff(164,plain,
% 0.82/0.84 ((~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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!144)) | (~((~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))))))),
% 0.82/0.84 inference(tautology,[status(thm)],[])).
% 0.82/0.84 tff(165,plain,
% 0.82/0.84 ((~((~iext(uri_owl_unionOf, uri_ex_c, BNODE_lu1!144)) | (~((~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))))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.82/0.85 tff(166,plain,
% 0.82/0.85 (~((~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)))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.82/0.85 tff(167,plain,
% 0.82/0.85 (((~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)),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(168,plain,
% 0.82/0.85 (ic(uri_ex_c3)),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.82/0.85 tff(169,plain,
% 0.82/0.85 ((~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)) <=> (~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(170,axiom,(~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','testcase_conclusion_fullish_020_Logical_Complications')).
% 0.82/0.85 tff(171,plain,
% 0.82/0.85 (~iext(uri_rdfs_subClassOf, uri_ex_d, uri_ex_c3)),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.82/0.85 tff(172,plain,
% 0.82/0.85 ((~(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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))) | 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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(173,plain,
% 0.82/0.85 ((~(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_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_d)) | (~((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.82/0.85 tff(174,plain,
% 0.82/0.85 (~((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[173, 168, 122, 102])).
% 0.82/0.85 tff(175,plain,
% 0.82/0.85 (((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(176,plain,
% 0.82/0.85 (icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.82/0.85 tff(177,plain,
% 0.82/0.85 (((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))) | ((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))) <=> ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))) | (~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(178,plain,
% 0.82/0.85 ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))) | ((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(179,plain,
% 0.82/0.85 ((~![X: $i] : ((~icext(uri_ex_d, X)) | icext(BNODE_xs!146, X))) | (~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.82/0.85 tff(180,plain,
% 0.82/0.85 (icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[179, 176, 76])).
% 0.82/0.85 tff(181,plain,
% 0.82/0.85 ((~(icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))))) | (~icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(182,plain,
% 0.82/0.85 ((~(icext(BNODE_xs!146, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))))) | (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.82/0.85 tff(183,plain,
% 0.82/0.85 (~((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[182, 53])).
% 0.82/0.85 tff(184,plain,
% 0.82/0.85 (((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))) | icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(185,plain,
% 0.82/0.85 (icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.82/0.85 tff(186,plain,
% 0.82/0.85 (^[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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))))) <=> (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X)))))))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(187,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))))) <=> ![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[186])).
% 0.82/0.85 tff(188,plain,
% 0.82/0.85 (^[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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(189,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[188])).
% 0.82/0.85 tff(190,plain,
% 0.82/0.85 (^[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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(191,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[190])).
% 0.82/0.85 tff(192,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(transitivity,[status(thm)],[191, 189])).
% 0.82/0.85 tff(193,plain,
% 0.82/0.85 (^[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_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1))) <=> (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))), ((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1)))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))), rewrite((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))), ((iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (icext(C1, tptp_fun_X_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1)))) <=> (iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1)) & icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(C2, C1)) & icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(194,plain,
% 0.82/0.85 (![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_66(C2, C1)) & icext(C2, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[193])).
% 0.82/0.85 tff(195,plain,
% 0.82/0.85 (^[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_66(C2, C1)) & icext(C2, tptp_fun_X_66(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_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(196,plain,
% 0.82/0.85 (![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_66(C2, C1)) & icext(C2, tptp_fun_X_66(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_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1)))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[195])).
% 0.82/0.85 tff(197,plain,
% 0.82/0.85 (![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)))))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(198,plain,
% 0.82/0.85 (^[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))))))),
% 0.82/0.85 inference(bind,[status(th)],[])).
% 0.82/0.85 tff(199,plain,
% 0.82/0.85 (![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)))))),
% 0.82/0.85 inference(quant_intro,[status(thm)],[198])).
% 0.82/0.85 tff(200,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_eqdis_disjointwith')).
% 0.82/0.85 tff(201,plain,
% 0.82/0.85 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.82/0.85 tff(202,plain,
% 0.82/0.85 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.82/0.85 tff(203,plain,(
% 0.82/0.85 ![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_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1))))))))),
% 0.82/0.85 inference(skolemize,[status(sab)],[202])).
% 0.82/0.85 tff(204,plain,
% 0.82/0.85 (![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_66(C2, C1)) & icext(C2, tptp_fun_X_66(C2, C1)))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.82/0.85 tff(205,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[204, 194])).
% 0.82/0.85 tff(206,plain,
% 0.82/0.85 (![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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1)))))))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[205, 192])).
% 0.82/0.85 tff(207,plain,
% 0.82/0.85 (![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(C2, C1))))))) | (~((~iext(uri_owl_disjointWith, C1, C2)) | (~((~ic(C2)) | (~ic(C1)) | (~![X: $i] : ((~icext(C2, X)) | (~icext(C1, X))))))))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[206, 187])).
% 0.82/0.85 tff(208,plain,
% 0.82/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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)))))))))))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(209,plain,
% 0.82/0.85 ((~((~(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_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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))))))))))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(210,plain,
% 0.82/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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)))))))))))),
% 0.82/0.85 inference(monotonicity,[status(thm)],[209])).
% 0.82/0.85 tff(211,plain,
% 0.82/0.85 (((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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)))))))))))),
% 0.82/0.85 inference(transitivity,[status(thm)],[210, 208])).
% 0.82/0.85 tff(212,plain,
% 0.82/0.85 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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))))))))))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(213,plain,
% 0.82/0.85 ((~![C1: $i, C2: $i] : (~((~(iext(uri_owl_disjointWith, C1, C2) | (~ic(C2)) | (~ic(C1)) | (~((~icext(C1, tptp_fun_X_66(C2, C1))) | (~icext(C2, tptp_fun_X_66(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_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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))))))))))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.82/0.85 tff(214,plain,
% 0.82/0.85 (~((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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)))))))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[213, 207])).
% 0.82/0.85 tff(215,plain,
% 0.82/0.85 (((~(iext(uri_owl_disjointWith, uri_ex_d, uri_ex_c1) | (~ic(uri_ex_d)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_d, tptp_fun_X_66(uri_ex_c1, uri_ex_d))) | (~icext(uri_ex_c1, tptp_fun_X_66(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)))))))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(216,plain,
% 0.82/0.85 ((~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))))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.82/0.85 tff(217,plain,
% 0.82/0.85 ((~((~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))))))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(218,plain,
% 0.82/0.85 ((~((~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))))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[217, 103])).
% 0.82/0.85 tff(219,plain,
% 0.82/0.85 (~((~ic(uri_ex_c1)) | (~ic(uri_ex_d)) | (~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[218, 216])).
% 0.82/0.85 tff(220,plain,
% 0.82/0.85 (((~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)))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(221,plain,
% 0.82/0.85 (![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.82/0.85 tff(222,plain,
% 0.82/0.85 (((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | ((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_61(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_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(rewrite,[status(thm)],[])).
% 0.82/0.85 tff(223,plain,
% 0.82/0.85 ((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | ((~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(224,plain,
% 0.82/0.85 ((~![X: $i] : ((~icext(uri_ex_c1, X)) | (~icext(uri_ex_d, X)))) | (~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.82/0.85 tff(225,plain,
% 0.82/0.85 (~icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[224, 176, 221])).
% 0.82/0.85 tff(226,plain,
% 0.82/0.85 (((~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)))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(227,plain,
% 0.82/0.85 (![X: $i] : (icext(uri_ex_c, X) <=> (icext(uri_ex_c3, X) | icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[226, 166])).
% 0.82/0.85 tff(228,plain,
% 0.82/0.85 ((~![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_61(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(quant_inst,[status(thm)],[])).
% 0.82/0.85 tff(229,plain,
% 0.82/0.85 (icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.82/0.85 tff(230,plain,
% 0.82/0.85 (((~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(231,plain,
% 0.82/0.85 (icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[230, 183])).
% 0.82/0.85 tff(232,plain,
% 0.82/0.85 ((~(icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))) | (~icext(uri_ex_c, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(233,plain,
% 0.82/0.85 (icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[232, 231, 229])).
% 0.82/0.85 tff(234,plain,
% 0.82/0.85 (((~icext(uri_ex_d, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(235,plain,
% 0.82/0.85 (~icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[234, 174])).
% 0.82/0.85 tff(236,plain,
% 0.82/0.85 ((~(icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(237,plain,
% 0.82/0.85 ((~(icext(uri_ex_c3, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))) | icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) | icext(uri_ex_c1, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.82/0.85 tff(238,plain,
% 0.82/0.85 (icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[237, 233, 225])).
% 0.82/0.85 tff(239,plain,
% 0.82/0.85 ((~(icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))) | (~icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d))) | (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d)))),
% 0.82/0.85 inference(tautology,[status(thm)],[])).
% 0.82/0.85 tff(240,plain,
% 0.82/0.85 (~(icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.82/0.85 inference(unit_resolution,[status(thm)],[239, 238, 185])).
% 0.82/0.85 tff(241,plain,
% 0.82/0.85 (iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)),
% 0.82/0.85 inference(and_elim,[status(thm)],[7])).
% 0.82/0.86 tff(242,plain,
% 0.82/0.86 (^[Z: $i, C: $i] : refl(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 0.82/0.86 inference(bind,[status(th)],[])).
% 0.82/0.86 tff(243,plain,
% 0.82/0.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.82/0.86 inference(quant_intro,[status(thm)],[242])).
% 0.82/0.86 tff(244,plain,
% 0.82/0.86 (^[Z: $i, C: $i] : rewrite(((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 0.82/0.86 inference(bind,[status(th)],[])).
% 0.82/0.86 tff(245,plain,
% 0.82/0.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.82/0.86 inference(quant_intro,[status(thm)],[244])).
% 0.82/0.86 tff(246,plain,
% 0.82/0.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))) <=> ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.82/0.86 inference(transitivity,[status(thm)],[245, 243])).
% 0.82/0.86 tff(247,plain,
% 0.82/0.86 (^[Z: $i, C: $i] : rewrite(((~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(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))))),
% 0.82/0.86 inference(bind,[status(th)],[])).
% 0.82/0.86 tff(248,plain,
% 0.82/0.86 (![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(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.82/0.86 inference(quant_intro,[status(thm)],[247])).
% 0.82/0.86 tff(249,plain,
% 0.82/0.86 (![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(Z, X) <=> (~icext(C, X)))))),
% 0.82/0.86 inference(rewrite,[status(thm)],[])).
% 0.82/0.86 tff(250,plain,
% 0.82/0.86 (^[Z: $i, C: $i] : trans(monotonicity(rewrite(((ic(Z) & ic(C)) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))) <=> (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(Z, X) <=> (~icext(C, X))))) <=> (iext(uri_owl_complementOf, Z, C) => (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X))))))), rewrite((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(Z, X) <=> (~icext(C, 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(Z, X) <=> (~icext(C, X)))))))),
% 0.82/0.86 inference(bind,[status(th)],[])).
% 0.82/0.86 tff(251,plain,
% 0.82/0.86 (![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(Z, X) <=> (~icext(C, X)))))),
% 0.82/0.86 inference(quant_intro,[status(thm)],[250])).
% 0.82/0.86 tff(252,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/sandbox/benchmark/Axioms/SWB001+0.ax','owl_bool_complementof_class')).
% 0.82/0.86 tff(253,plain,
% 0.82/0.86 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 0.92/0.87 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.92/0.87 tff(254,plain,
% 0.92/0.87 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 0.92/0.87 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.92/0.87 tff(255,plain,(
% 0.92/0.87 ![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (ic(Z) & ic(C) & ![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))),
% 0.92/0.87 inference(skolemize,[status(sab)],[254])).
% 0.92/0.87 tff(256,plain,
% 0.92/0.87 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.92/0.87 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.92/0.87 tff(257,plain,
% 0.92/0.87 (![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))),
% 0.92/0.87 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.92/0.87 tff(258,plain,
% 0.92/0.87 (((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))))))) <=> ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))))))),
% 0.92/0.87 inference(rewrite,[status(thm)],[])).
% 0.92/0.87 tff(259,plain,
% 0.92/0.87 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | ((~iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))))))),
% 0.92/0.87 inference(quant_inst,[status(thm)],[])).
% 0.92/0.87 tff(260,plain,
% 0.92/0.87 ((~![Z: $i, C: $i] : ((~iext(uri_owl_complementOf, Z, C)) | (~((~ic(C)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (~icext(C, X)))))))) | (~iext(uri_owl_complementOf, BNODE_xc!145, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X))))))),
% 0.92/0.87 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.92/0.87 tff(261,plain,
% 0.92/0.87 (~((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))))),
% 0.92/0.87 inference(unit_resolution,[status(thm)],[260, 257, 241])).
% 0.92/0.87 tff(262,plain,
% 0.92/0.87 (((~ic(uri_ex_c2)) | (~ic(BNODE_xc!145)) | (~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X))))) | ![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))),
% 0.92/0.87 inference(tautology,[status(thm)],[])).
% 0.92/0.87 tff(263,plain,
% 0.92/0.87 (![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))),
% 0.92/0.87 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.92/0.87 tff(264,plain,
% 0.92/0.87 ((~![X: $i] : (icext(BNODE_xc!145, X) <=> (~icext(uri_ex_c2, X)))) | (icext(BNODE_xc!145, tptp_fun_X_61(uri_ex_c3, uri_ex_d)) <=> (~icext(uri_ex_c2, tptp_fun_X_61(uri_ex_c3, uri_ex_d))))),
% 0.92/0.87 inference(quant_inst,[status(thm)],[])).
% 0.92/0.87 tff(265,plain,
% 0.92/0.87 ($false),
% 0.92/0.87 inference(unit_resolution,[status(thm)],[264, 263, 240])).
% 0.92/0.87 % SZS output end Proof
%------------------------------------------------------------------------------