%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWB059+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:29:46 AM UTC 2025
% Result : Theorem 54.13s 54.38s
% Output : Proof 54.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWB059+1 : TPTP v9.0.0. Released v5.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 07:54:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 54.13/54.38 % SZS status Theorem
% 54.13/54.38 % SZS output start Proof
% 54.13/54.38 tff(icext_type, type, (
% 54.13/54.38 icext: ( $i * $i ) > $o)).
% 54.13/54.38 tff(tptp_fun_X_64_type, type, (
% 54.13/54.38 tptp_fun_X_64: ( $i * $i * $i ) > $i)).
% 54.13/54.38 tff(uri_ex_c3_type, type, (
% 54.13/54.38 uri_ex_c3: $i)).
% 54.13/54.38 tff(uri_ex_c1_type, type, (
% 54.13/54.38 uri_ex_c1: $i)).
% 54.13/54.38 tff(uri_ex_c2_type, type, (
% 54.13/54.38 uri_ex_c2: $i)).
% 54.13/54.38 tff(iext_type, type, (
% 54.13/54.38 iext: ( $i * $i * $i ) > $o)).
% 54.13/54.38 tff(tptp_fun_X0_141_type, type, (
% 54.13/54.38 tptp_fun_X0_141: $i)).
% 54.13/54.38 tff(uri_owl_disjointUnionOf_type, type, (
% 54.13/54.38 uri_owl_disjointUnionOf: $i)).
% 54.13/54.38 tff(ic_type, type, (
% 54.13/54.38 ic: $i > $o)).
% 54.13/54.38 tff(tptp_fun_X1_140_type, type, (
% 54.13/54.38 tptp_fun_X1_140: $i)).
% 54.13/54.38 tff(uri_rdf_rest_type, type, (
% 54.13/54.38 uri_rdf_rest: $i)).
% 54.13/54.38 tff(uri_rdf_first_type, type, (
% 54.13/54.38 uri_rdf_first: $i)).
% 54.13/54.38 tff(uri_rdf_nil_type, type, (
% 54.13/54.38 uri_rdf_nil: $i)).
% 54.13/54.38 tff(uri_owl_disjointWith_type, type, (
% 54.13/54.38 uri_owl_disjointWith: $i)).
% 54.13/54.38 tff(uri_owl_unionOf_type, type, (
% 54.13/54.38 uri_owl_unionOf: $i)).
% 54.13/54.38 tff(uri_rdf_List_type, type, (
% 54.13/54.38 uri_rdf_List: $i)).
% 54.13/54.38 tff(tptp_fun_X_6_type, type, (
% 54.13/54.38 tptp_fun_X_6: ( $i * $i * $i ) > $i)).
% 54.13/54.38 tff(tptp_fun_X_66_type, type, (
% 54.13/54.38 tptp_fun_X_66: ( $i * $i ) > $i)).
% 54.13/54.38 tff(1,assumption,(~icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))), introduced(assumption)).
% 54.13/54.38 tff(2,plain,
% 54.13/54.38 (?[X0: $i, X1: $i] : (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))),
% 54.13/54.38 inference(rewrite,[status(thm)],[])).
% 54.13/54.38 tff(3,plain,
% 54.13/54.38 (^[X0: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2))), ((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> ((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))), ((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)))), (((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) <=> ((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1))), (((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1)))), ((((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) <=> ((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)))), rewrite(((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))), ((((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) <=> (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))))),
% 54.21/54.38 inference(bind,[status(th)],[])).
% 54.21/54.38 tff(4,plain,
% 54.21/54.38 (?[X0: $i, X1: $i] : (((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) <=> ?[X0: $i, X1: $i] : (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))),
% 54.21/54.38 inference(quant_intro,[status(thm)],[3])).
% 54.21/54.38 tff(5,axiom,(?[X0: $i, X1: $i] : (((((iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil)) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','premise_rdfbased_sem_eqdis_disjointunion_composite')).
% 54.21/54.38 tff(6,plain,
% 54.21/54.38 (?[X0: $i, X1: $i] : (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))),
% 54.21/54.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 54.21/54.38 tff(7,plain,
% 54.21/54.38 (?[X0: $i, X1: $i] : (iext(uri_owl_unionOf, uri_ex_c3, X0) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1))),
% 54.21/54.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 54.21/54.38 tff(8,plain,(
% 54.21/54.38 iext(uri_owl_unionOf, uri_ex_c3, X0!141) & iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) & iext(uri_rdf_first, X1!140, uri_ex_c2) & iext(uri_rdf_rest, X1!140, uri_rdf_nil) & iext(uri_rdf_first, X0!141, uri_ex_c1) & iext(uri_rdf_rest, X0!141, X1!140)),
% 54.21/54.38 inference(skolemize,[status(sab)],[7])).
% 54.21/54.38 tff(9,plain,
% 54.21/54.38 (iext(uri_rdf_rest, X0!141, X1!140)),
% 54.21/54.38 inference(and_elim,[status(thm)],[8])).
% 54.21/54.38 tff(10,plain,
% 54.21/54.38 (iext(uri_rdf_first, X0!141, uri_ex_c1)),
% 54.21/54.38 inference(and_elim,[status(thm)],[8])).
% 54.21/54.38 tff(11,plain,
% 54.21/54.38 (iext(uri_rdf_rest, X1!140, uri_rdf_nil)),
% 54.21/54.38 inference(and_elim,[status(thm)],[8])).
% 54.21/54.38 tff(12,plain,
% 54.21/54.38 (iext(uri_rdf_first, X1!140, uri_ex_c2)),
% 54.21/54.38 inference(and_elim,[status(thm)],[8])).
% 54.21/54.38 tff(13,plain,
% 54.21/54.38 (^[C: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))) <=> (~((~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, 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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ((~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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, 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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, 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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, 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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ((~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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))))),
% 54.21/54.38 inference(bind,[status(th)],[])).
% 54.21/54.38 tff(14,plain,
% 54.21/54.38 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))),
% 54.21/54.38 inference(quant_intro,[status(thm)],[13])).
% 54.21/54.38 tff(15,plain,
% 54.21/54.38 (^[C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ((~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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))))),
% 54.21/54.38 inference(bind,[status(th)],[])).
% 54.21/54.38 tff(16,plain,
% 54.21/54.38 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.21/54.38 inference(quant_intro,[status(thm)],[15])).
% 54.21/54.38 tff(17,plain,
% 54.21/54.38 (^[C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ((~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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))))),
% 54.21/54.38 inference(bind,[status(th)],[])).
% 54.21/54.38 tff(18,plain,
% 54.21/54.38 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.21/54.38 inference(quant_intro,[status(thm)],[17])).
% 54.21/54.38 tff(19,plain,
% 54.21/54.38 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.21/54.39 inference(transitivity,[status(thm)],[18, 16])).
% 54.21/54.39 tff(20,plain,
% 54.21/54.39 (^[C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) <=> ((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))) <=> (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))), ((~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))) <=> (~(~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))))), rewrite((~(~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> ((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C))))), ((~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))) <=> ((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))), (((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & ((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C))))))), rewrite(((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & ((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C))))) <=> (~((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))))), (((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))) <=> (~((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C))))))))), ((icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> (icext(C, tptp_fun_X_64(C2, C1, C)) <=> (~((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))))))), rewrite((icext(C, tptp_fun_X_64(C2, C1, C)) <=> (~((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))))) <=> (~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))), ((icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> (~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))), rewrite((~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))) <=> (~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))), ((icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> (~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))), ((~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))) <=> (~(~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))), rewrite((~(~(((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) <=> (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))), ((~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))) <=> (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))), ((iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))) <=> (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))), rewrite((iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))) <=> (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))), ((iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))) <=> (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))), ((((~iext(uri_owl_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))) <=> (((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))), rewrite((((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) <=> (~((~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))), ((((~iext(uri_owl_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))) <=> (~((~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))), (((~(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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))))) <=> (((~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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))))), 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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C)))))))) <=> ((~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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))), (((~(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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))))) <=> ((~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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))))),
% 54.21/54.39 inference(bind,[status(th)],[])).
% 54.21/54.39 tff(21,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))))) <=> ![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.21/54.39 inference(quant_intro,[status(thm)],[20])).
% 54.21/54.39 tff(22,plain,
% 54.21/54.39 (^[C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | ((~ic(C)) | (~ic(C1)) | (~ic(C2)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))))) <=> ((~(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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))))))),
% 54.21/54.39 inference(bind,[status(th)],[])).
% 54.21/54.39 tff(23,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | ((~ic(C)) | (~ic(C1)) | (~ic(C2)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))))) <=> ![C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))))),
% 54.21/54.39 inference(quant_intro,[status(thm)],[22])).
% 54.21/54.39 tff(24,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X)))))))) <=> ![C: $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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))))),
% 54.21/54.39 inference(rewrite,[status(thm)],[])).
% 54.21/54.39 tff(25,plain,
% 54.21/54.39 (^[C: $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_disjointUnionOf, C, S1) <=> (((ic(C) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(C, X) <=> ((icext(C1, X) | icext(C2, X)) & (~(icext(C1, X) & icext(C2, X))))))) <=> (iext(uri_owl_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, 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_disjointUnionOf, C, S1) <=> (((ic(C) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(C, X) <=> ((icext(C1, X) | icext(C2, 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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, 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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, 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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, 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_disjointUnionOf, C, S1) <=> (((ic(C) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(C, X) <=> ((icext(C1, X) | icext(C2, 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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))))))),
% 54.21/54.39 inference(bind,[status(th)],[])).
% 54.21/54.39 tff(26,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1) <=> (((ic(C) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(C, X) <=> ((icext(C1, X) | icext(C2, X)) & (~(icext(C1, X) & icext(C2, X)))))))) <=> ![C: $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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))))),
% 54.21/54.39 inference(quant_intro,[status(thm)],[25])).
% 54.21/54.39 tff(27,axiom,(![C: $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_disjointUnionOf, C, S1) <=> (((ic(C) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(C, X) <=> ((icext(C1, X) | icext(C2, X)) & (~(icext(C1, X) & icext(C2, X))))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_disjointunionof_002')).
% 54.21/54.39 tff(28,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))))),
% 54.21/54.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 54.21/54.39 tff(29,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1) <=> (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))))),
% 54.21/54.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 54.21/54.39 tff(30,plain,(
% 54.21/54.39 ![C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | ((~ic(C)) | (~ic(C1)) | (~ic(C2)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C)))))))))))),
% 54.21/54.39 inference(skolemize,[status(sab)],[29])).
% 54.21/54.39 tff(31,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1)) | (ic(C) & ic(C1) & ic(C2) & ![X: $i] : (icext(C, X) <=> ((icext(C2, X) | icext(C1, X)) & (~(icext(C1, X) & icext(C2, X))))))) & (iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~(icext(C, tptp_fun_X_64(C2, C1, C)) <=> ((icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C))) & (~(icext(C1, tptp_fun_X_64(C2, C1, C)) & icext(C2, tptp_fun_X_64(C2, C1, C))))))))))),
% 54.21/54.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 54.21/54.39 tff(32,plain,
% 54.21/54.39 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.23/54.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 54.23/54.39 tff(33,plain,
% 54.23/54.39 (![C: $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_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))) | (~(iext(uri_owl_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))))))),
% 54.23/54.39 inference(modus_ponens,[status(thm)],[32, 19])).
% 54.23/54.39 tff(34,plain,
% 54.23/54.39 (![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))),
% 54.23/54.39 inference(modus_ponens,[status(thm)],[33, 14])).
% 54.23/54.39 tff(35,plain,
% 54.23/54.39 (((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))) <=> ((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.39 inference(rewrite,[status(thm)],[])).
% 54.23/54.39 tff(36,plain,
% 54.23/54.39 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.39 inference(rewrite,[status(thm)],[])).
% 54.23/54.39 tff(37,plain,
% 54.23/54.39 ((~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))) <=> (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))),
% 54.23/54.40 inference(rewrite,[status(thm)],[])).
% 54.23/54.40 tff(38,plain,
% 54.23/54.40 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))) <=> ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.40 inference(monotonicity,[status(thm)],[37])).
% 54.23/54.40 tff(39,plain,
% 54.23/54.40 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.40 inference(transitivity,[status(thm)],[38, 36])).
% 54.23/54.40 tff(40,plain,
% 54.23/54.40 (((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))) <=> ((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))))),
% 54.23/54.40 inference(monotonicity,[status(thm)],[39])).
% 54.23/54.40 tff(41,plain,
% 54.23/54.40 (((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))) <=> ((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.40 inference(transitivity,[status(thm)],[40, 35])).
% 54.23/54.40 tff(42,plain,
% 54.23/54.40 ((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))))),
% 54.23/54.40 inference(quant_inst,[status(thm)],[])).
% 54.23/54.40 tff(43,plain,
% 54.23/54.40 ((~![C: $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_disjointUnionOf, C, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(C)) | (((~(icext(C2, tptp_fun_X_64(C2, C1, C)) | icext(C1, tptp_fun_X_64(C2, C1, C)))) | (~((~icext(C1, tptp_fun_X_64(C2, C1, C))) | (~icext(C2, tptp_fun_X_64(C2, C1, C)))))) <=> icext(C, tptp_fun_X_64(C2, C1, C))))) | (~((~iext(uri_owl_disjointUnionOf, C, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(C)) | (~![X: $i] : (~(((~(icext(C2, X) | icext(C1, X))) | (~((~icext(C2, X)) | (~icext(C1, X))))) <=> icext(C, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 54.23/54.40 tff(44,plain,
% 54.23/54.40 (~((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X)))))))))),
% 54.23/54.40 inference(unit_resolution,[status(thm)],[43, 34, 12, 11, 10, 9])).
% 54.23/54.40 tff(45,plain,
% 54.23/54.40 (((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~((~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (~(((~(icext(uri_ex_c2, X) | icext(uri_ex_c1, X))) | (~((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) <=> icext(uri_ex_c3, X))))))))) | ((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.23/54.40 inference(tautology,[status(thm)],[])).
% 54.23/54.40 tff(46,plain,
% 54.23/54.40 ((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.23/54.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 54.23/54.40 tff(47,plain,
% 54.23/54.40 (^[X1: $i, X0: $i] : refl(((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))))),
% 54.23/54.40 inference(bind,[status(th)],[])).
% 54.23/54.40 tff(48,plain,
% 54.23/54.40 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))) <=> ![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))),
% 54.23/54.40 inference(quant_intro,[status(thm)],[47])).
% 54.23/54.40 tff(49,plain,
% 54.23/54.40 (^[X1: $i, X0: $i] : trans(monotonicity(rewrite((iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)) <=> (~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))))), ((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))))))), rewrite((~(~((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2))))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))), ((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))) <=> ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))))),
% 54.23/54.40 inference(bind,[status(th)],[])).
% 54.23/54.40 tff(50,plain,
% 54.23/54.40 (![X1: $i, X0: $i] : (~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))) <=> ![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))),
% 54.23/54.40 inference(quant_intro,[status(thm)],[49])).
% 54.23/54.40 tff(51,plain,
% 54.23/54.40 ((~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))) <=> (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)))),
% 54.23/54.40 inference(rewrite,[status(thm)],[])).
% 54.23/54.40 tff(52,plain,
% 54.23/54.40 ((~?[X1: $i, X0: $i] : ((((iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil))) <=> (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)))),
% 54.23/54.40 inference(rewrite,[status(thm)],[])).
% 54.23/54.40 tff(53,axiom,(~?[X1: $i, X0: $i] : ((((iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1)) & iext(uri_rdf_rest, X0, X1)) & iext(uri_rdf_first, X1, uri_ex_c2)) & iext(uri_rdf_rest, X1, uri_rdf_nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conclusion_rdfbased_sem_eqdis_disjointunion_composite')).
% 54.23/54.40 tff(54,plain,
% 54.23/54.40 (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[53, 52])).
% 54.23/54.40 tff(55,plain,
% 54.23/54.40 (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[54, 51])).
% 54.23/54.40 tff(56,plain,
% 54.23/54.40 (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[55, 51])).
% 54.23/54.40 tff(57,plain,
% 54.23/54.40 (~?[X1: $i, X0: $i] : (iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[56, 51])).
% 54.23/54.40 tff(58,plain,
% 54.23/54.40 (^[X1: $i, X0: $i] : refl($oeq((~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil))), (~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)))))),
% 54.23/54.40 inference(bind,[status(th)],[])).
% 54.23/54.40 tff(59,plain,(
% 54.23/54.40 ![X1: $i, X0: $i] : (~(iext(uri_owl_disjointUnionOf, uri_ex_c3, X0) & iext(uri_rdf_first, X0, uri_ex_c1) & iext(uri_rdf_rest, X0, X1) & iext(uri_rdf_first, X1, uri_ex_c2) & iext(uri_rdf_rest, X1, uri_rdf_nil)))),
% 54.23/54.40 inference(nnf-neg,[status(sab)],[57, 58])).
% 54.23/54.40 tff(60,plain,
% 54.23/54.40 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[59, 50])).
% 54.23/54.40 tff(61,plain,
% 54.23/54.40 (![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))),
% 54.23/54.40 inference(modus_ponens,[status(thm)],[60, 48])).
% 54.23/54.40 tff(62,plain,
% 54.23/54.40 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)))),
% 54.23/54.40 inference(rewrite,[status(thm)],[])).
% 54.23/54.40 tff(63,plain,
% 54.23/54.40 (((~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)))),
% 54.23/54.41 inference(rewrite,[status(thm)],[])).
% 54.23/54.41 tff(64,plain,
% 54.23/54.41 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | ((~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141))))),
% 54.23/54.41 inference(monotonicity,[status(thm)],[63])).
% 54.23/54.41 tff(65,plain,
% 54.23/54.41 (((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | ((~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)))) <=> ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)))),
% 54.23/54.41 inference(transitivity,[status(thm)],[64, 62])).
% 54.23/54.41 tff(66,plain,
% 54.23/54.41 ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | ((~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)))),
% 54.23/54.41 inference(quant_inst,[status(thm)],[])).
% 54.23/54.41 tff(67,plain,
% 54.23/54.41 ((~![X1: $i, X0: $i] : ((~iext(uri_rdf_rest, X1, uri_rdf_nil)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0)) | (~iext(uri_rdf_first, X0, uri_ex_c1)) | (~iext(uri_rdf_rest, X0, X1)) | (~iext(uri_rdf_first, X1, uri_ex_c2)))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 54.23/54.41 tff(68,plain,
% 54.23/54.41 (~iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141)),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[67, 61, 12, 11, 10, 9])).
% 54.23/54.41 tff(69,plain,
% 54.23/54.41 (iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)),
% 54.23/54.41 inference(and_elim,[status(thm)],[8])).
% 54.23/54.41 tff(70,plain,
% 54.23/54.41 (^[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))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(71,plain,
% 54.23/54.41 (![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)))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[70])).
% 54.23/54.41 tff(72,plain,
% 54.23/54.41 (^[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))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(73,plain,
% 54.23/54.41 (![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)))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[72])).
% 54.23/54.41 tff(74,plain,
% 54.23/54.41 (![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)))),
% 54.23/54.41 inference(rewrite,[status(thm)],[])).
% 54.23/54.41 tff(75,plain,
% 54.23/54.41 (^[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))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(76,plain,
% 54.23/54.41 (![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)))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[75])).
% 54.23/54.41 tff(77,axiom,(![X: $i, Y: $i] : (iext(uri_owl_disjointWith, X, Y) => (ic(X) & ic(Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_disjointwith_ext')).
% 54.23/54.41 tff(78,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 54.23/54.41 tff(79,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 54.23/54.41 tff(80,plain,(
% 54.23/54.41 ![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (ic(X) & ic(Y)))),
% 54.23/54.41 inference(skolemize,[status(sab)],[79])).
% 54.23/54.41 tff(81,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 54.23/54.41 tff(82,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 54.23/54.41 tff(83,plain,
% 54.23/54.41 (((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)))))),
% 54.23/54.41 inference(rewrite,[status(thm)],[])).
% 54.23/54.41 tff(84,plain,
% 54.23/54.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | ((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)))))),
% 54.23/54.41 inference(quant_inst,[status(thm)],[])).
% 54.23/54.41 tff(85,plain,
% 54.23/54.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_disjointWith, X, Y)) | (~((~ic(Y)) | (~ic(X)))))) | (~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[84, 83])).
% 54.23/54.41 tff(86,plain,
% 54.23/54.41 (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[85, 82, 69])).
% 54.23/54.41 tff(87,plain,
% 54.23/54.41 (((~ic(uri_ex_c2)) | (~ic(uri_ex_c1))) | ic(uri_ex_c1)),
% 54.23/54.41 inference(tautology,[status(thm)],[])).
% 54.23/54.41 tff(88,plain,
% 54.23/54.41 (ic(uri_ex_c1)),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[87, 86])).
% 54.23/54.41 tff(89,plain,
% 54.23/54.41 (((~ic(uri_ex_c2)) | (~ic(uri_ex_c1))) | ic(uri_ex_c2)),
% 54.23/54.41 inference(tautology,[status(thm)],[])).
% 54.23/54.41 tff(90,plain,
% 54.23/54.41 (ic(uri_ex_c2)),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[89, 86])).
% 54.23/54.41 tff(91,plain,
% 54.23/54.41 (iext(uri_owl_unionOf, uri_ex_c3, X0!141)),
% 54.23/54.41 inference(and_elim,[status(thm)],[8])).
% 54.23/54.41 tff(92,plain,
% 54.23/54.41 (^[X: $i, Y: $i] : refl(((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(93,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[92])).
% 54.23/54.41 tff(94,plain,
% 54.23/54.41 (^[X: $i, Y: $i] : rewrite(((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(95,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[94])).
% 54.23/54.41 tff(96,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 54.23/54.41 inference(rewrite,[status(thm)],[])).
% 54.23/54.41 tff(97,plain,
% 54.23/54.41 (^[X: $i, Y: $i] : rewrite((iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(98,plain,
% 54.23/54.41 (![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y))) <=> ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[97])).
% 54.23/54.41 tff(99,axiom,(![X: $i, Y: $i] : (iext(uri_owl_unionOf, X, Y) => (ic(X) & icext(uri_rdf_List, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_prop_unionof_ext')).
% 54.23/54.41 tff(100,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 54.23/54.41 tff(101,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[100, 96])).
% 54.23/54.41 tff(102,plain,(
% 54.23/54.41 ![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (ic(X) & icext(uri_rdf_List, Y)))),
% 54.23/54.41 inference(skolemize,[status(sab)],[101])).
% 54.23/54.41 tff(103,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[102, 95])).
% 54.23/54.41 tff(104,plain,
% 54.23/54.41 (![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[103, 93])).
% 54.23/54.41 tff(105,plain,
% 54.23/54.41 (((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141)))))) <=> ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141)))))),
% 54.23/54.41 inference(rewrite,[status(thm)],[])).
% 54.23/54.41 tff(106,plain,
% 54.23/54.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | ((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141)))))),
% 54.23/54.41 inference(quant_inst,[status(thm)],[])).
% 54.23/54.41 tff(107,plain,
% 54.23/54.41 ((~![X: $i, Y: $i] : ((~iext(uri_owl_unionOf, X, Y)) | (~((~ic(X)) | (~icext(uri_rdf_List, Y)))))) | (~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141))))),
% 54.23/54.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 54.23/54.41 tff(108,plain,
% 54.23/54.41 (~((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141)))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[107, 104, 91])).
% 54.23/54.41 tff(109,plain,
% 54.23/54.41 (((~ic(uri_ex_c3)) | (~icext(uri_rdf_List, X0!141))) | ic(uri_ex_c3)),
% 54.23/54.41 inference(tautology,[status(thm)],[])).
% 54.23/54.41 tff(110,plain,
% 54.23/54.41 (ic(uri_ex_c3)),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[109, 108])).
% 54.23/54.41 tff(111,plain,
% 54.23/54.41 ((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.23/54.41 inference(tautology,[status(thm)],[])).
% 54.23/54.41 tff(112,plain,
% 54.23/54.41 ((~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | iext(uri_owl_disjointUnionOf, uri_ex_c3, X0!141) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[111, 110, 90, 88, 68])).
% 54.23/54.41 tff(113,plain,
% 54.23/54.41 (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[112, 46])).
% 54.23/54.41 tff(114,plain,
% 54.23/54.41 ((~(((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.23/54.41 inference(tautology,[status(thm)],[])).
% 54.23/54.41 tff(115,plain,
% 54.23/54.41 ((~((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[114, 113])).
% 54.23/54.41 tff(116,plain,
% 54.23/54.41 (~((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))),
% 54.23/54.41 inference(unit_resolution,[status(thm)],[115, 1])).
% 54.23/54.41 tff(117,plain,
% 54.23/54.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(rewrite((~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))) <=> (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, 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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, 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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, 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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, 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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(118,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[117])).
% 54.23/54.41 tff(119,plain,
% 54.23/54.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : refl(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(120,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[119])).
% 54.23/54.41 tff(121,plain,
% 54.23/54.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(122,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[121])).
% 54.23/54.41 tff(123,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.41 inference(transitivity,[status(thm)],[122, 120])).
% 54.23/54.41 tff(124,plain,
% 54.23/54.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> (~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))))), rewrite((~(~((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)))), ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) <=> ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil))))), trans(monotonicity(rewrite(((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) <=> ((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))), trans(monotonicity(rewrite((~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))) <=> (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), rewrite((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))), ((iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))) <=> (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))), rewrite((((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))), ((((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) <=> (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(125,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.41 inference(quant_intro,[status(thm)],[124])).
% 54.23/54.41 tff(126,plain,
% 54.23/54.41 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : rewrite(((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 54.23/54.41 inference(bind,[status(th)],[])).
% 54.23/54.41 tff(127,plain,
% 54.23/54.41 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(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_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 54.23/54.42 inference(quant_intro,[status(thm)],[126])).
% 54.23/54.42 tff(128,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, 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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 54.23/54.42 inference(rewrite,[status(thm)],[])).
% 54.23/54.42 tff(129,plain,
% 54.23/54.42 (^[Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> ((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite(((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))), ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) <=> (iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil)))), rewrite((iext(uri_owl_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))) <=> (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![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_unionOf, 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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![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_unionOf, 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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))))),
% 54.23/54.42 inference(bind,[status(th)],[])).
% 54.23/54.42 tff(130,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((((iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2)) & iext(uri_rdf_first, S2, C2)) & iext(uri_rdf_rest, S2, uri_rdf_nil)) => (iext(uri_owl_unionOf, 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_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 54.23/54.42 inference(quant_intro,[status(thm)],[129])).
% 54.23/54.42 tff(131,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_unionOf, Z, S1) <=> (((ic(Z) & ic(C1)) & ic(C2)) & ![X: $i] : (icext(Z, X) <=> (icext(C1, X) | icext(C2, X))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_bool_unionof_class_002')).
% 54.23/54.42 tff(132,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 54.23/54.42 tff(133,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (iext(uri_owl_unionOf, Z, S1) <=> (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[132, 128])).
% 54.23/54.42 tff(134,plain,(
% 54.23/54.42 ![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | ((~ic(Z)) | (~ic(C1)) | (~ic(C2)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z)))))))))),
% 54.23/54.42 inference(skolemize,[status(sab)],[133])).
% 54.23/54.42 tff(135,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~(iext(uri_rdf_first, S1, C1) & iext(uri_rdf_rest, S1, S2) & iext(uri_rdf_first, S2, C2) & iext(uri_rdf_rest, S2, uri_rdf_nil))) | (((~iext(uri_owl_unionOf, Z, S1)) | (ic(Z) & ic(C1) & ic(C2) & ![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X))))) & (iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[134, 127])).
% 54.23/54.42 tff(136,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[135, 125])).
% 54.23/54.42 tff(137,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))) | (~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[136, 123])).
% 54.23/54.42 tff(138,plain,
% 54.23/54.42 (![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))),
% 54.23/54.42 inference(modus_ponens,[status(thm)],[137, 118])).
% 54.23/54.42 tff(139,plain,
% 54.23/54.42 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (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] : ((~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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.23/54.42 inference(rewrite,[status(thm)],[])).
% 54.23/54.42 tff(140,plain,
% 54.23/54.42 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.23/54.42 inference(rewrite,[status(thm)],[])).
% 54.23/54.42 tff(141,plain,
% 54.23/54.42 ((~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))) <=> (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))),
% 54.23/54.42 inference(rewrite,[status(thm)],[])).
% 54.23/54.42 tff(142,plain,
% 54.23/54.42 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.23/54.42 inference(monotonicity,[status(thm)],[141])).
% 54.23/54.42 tff(143,plain,
% 54.23/54.42 (((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))) <=> ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.23/54.42 inference(transitivity,[status(thm)],[142, 140])).
% 54.23/54.42 tff(144,plain,
% 54.23/54.42 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (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] : ((~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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))))),
% 54.23/54.42 inference(monotonicity,[status(thm)],[143])).
% 54.23/54.42 tff(145,plain,
% 54.23/54.42 (((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (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] : ((~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_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.26/54.42 inference(transitivity,[status(thm)],[144, 139])).
% 54.26/54.42 tff(146,plain,
% 54.26/54.42 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | ((~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~ic(uri_ex_c3)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))))),
% 54.26/54.42 inference(quant_inst,[status(thm)],[])).
% 54.26/54.42 tff(147,plain,
% 54.26/54.42 ((~![Z: $i, S1: $i, C1: $i, S2: $i, C2: $i] : ((~iext(uri_rdf_first, S1, C1)) | (~iext(uri_rdf_rest, S1, S2)) | (~iext(uri_rdf_first, S2, C2)) | (~iext(uri_rdf_rest, S2, uri_rdf_nil)) | (~((~(iext(uri_owl_unionOf, Z, S1) | (~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~(icext(Z, tptp_fun_X_6(C2, C1, Z)) <=> (icext(C2, tptp_fun_X_6(C2, C1, Z)) | icext(C1, tptp_fun_X_6(C2, C1, Z))))))) | (~((~iext(uri_owl_unionOf, Z, S1)) | (~((~ic(C2)) | (~ic(C1)) | (~ic(Z)) | (~![X: $i] : (icext(Z, X) <=> (icext(C2, X) | icext(C1, X)))))))))))) | (~iext(uri_rdf_first, X1!140, uri_ex_c2)) | (~iext(uri_rdf_rest, X1!140, uri_rdf_nil)) | (~iext(uri_rdf_first, X0!141, uri_ex_c1)) | (~iext(uri_rdf_rest, X0!141, X1!140)) | (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))))),
% 54.26/54.42 inference(modus_ponens,[status(thm)],[146, 145])).
% 54.26/54.42 tff(148,plain,
% 54.26/54.42 (~((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[147, 138, 12, 11, 10, 9])).
% 54.26/54.43 tff(149,plain,
% 54.26/54.43 (((~(iext(uri_owl_unionOf, uri_ex_c3, X0!141) | (~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~(icext(uri_ex_c3, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c1, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c2, tptp_fun_X_6(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))))) | ((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(150,plain,
% 54.26/54.43 ((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[149, 148])).
% 54.26/54.43 tff(151,plain,
% 54.26/54.43 ((~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))) | (~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(152,plain,
% 54.26/54.43 ((~((~iext(uri_owl_unionOf, uri_ex_c3, X0!141)) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))))) | (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[151, 91])).
% 54.26/54.43 tff(153,plain,
% 54.26/54.43 (~((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[152, 150])).
% 54.26/54.43 tff(154,plain,
% 54.26/54.43 (((~ic(uri_ex_c3)) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X))))) | ![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(155,plain,
% 54.26/54.43 (![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[154, 153])).
% 54.26/54.43 tff(156,plain,
% 54.26/54.43 ((~![X: $i] : (icext(uri_ex_c3, X) <=> (icext(uri_ex_c2, X) | icext(uri_ex_c1, X)))) | (icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.43 inference(quant_inst,[status(thm)],[])).
% 54.26/54.43 tff(157,plain,
% 54.26/54.43 (icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[156, 155])).
% 54.26/54.43 tff(158,plain,
% 54.26/54.43 ((~(icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | (~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(159,plain,
% 54.26/54.43 (icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | (~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[158, 157])).
% 54.26/54.43 tff(160,plain,
% 54.26/54.43 (~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[159, 1])).
% 54.26/54.43 tff(161,plain,
% 54.26/54.43 (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) | (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(162,plain,
% 54.26/54.43 ($false),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[161, 160, 116])).
% 54.26/54.43 tff(163,plain,(icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))), inference(lemma,lemma(discharge,[]))).
% 54.26/54.43 tff(164,plain,
% 54.26/54.43 ((~(((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) <=> icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | ((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) | (~icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(165,plain,
% 54.26/54.43 (((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))) | (~icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[164, 113])).
% 54.26/54.43 tff(166,plain,
% 54.26/54.43 ((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[165, 163])).
% 54.26/54.43 tff(167,plain,
% 54.26/54.43 ((~(icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) <=> (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) | (~icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(168,plain,
% 54.26/54.43 ((~icext(uri_ex_c3, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[167, 157])).
% 54.26/54.43 tff(169,plain,
% 54.26/54.43 (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[168, 163])).
% 54.26/54.43 tff(170,plain,
% 54.26/54.43 ((~((~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))))) | (~(icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(171,plain,
% 54.26/54.43 (~((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[170, 169, 166])).
% 54.26/54.43 tff(172,plain,
% 54.26/54.43 (((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(173,plain,
% 54.26/54.43 (icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[172, 171])).
% 54.26/54.43 tff(174,plain,
% 54.26/54.43 (((~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))) | icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(175,plain,
% 54.26/54.43 (icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[174, 171])).
% 54.26/54.43 tff(176,plain,
% 54.26/54.43 (^[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)))))))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(177,plain,
% 54.26/54.43 (![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))))))))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[176])).
% 54.26/54.43 tff(178,plain,
% 54.26/54.43 (^[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))))))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(179,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[178])).
% 54.26/54.43 tff(180,plain,
% 54.26/54.43 (^[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))))))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(181,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[180])).
% 54.26/54.43 tff(182,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(transitivity,[status(thm)],[181, 179])).
% 54.26/54.43 tff(183,plain,
% 54.26/54.43 (^[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)))))))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(184,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[183])).
% 54.26/54.43 tff(185,plain,
% 54.26/54.43 (^[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))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(186,plain,
% 54.26/54.43 (![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)))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[185])).
% 54.26/54.43 tff(187,plain,
% 54.26/54.43 (![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)))))),
% 54.26/54.43 inference(rewrite,[status(thm)],[])).
% 54.26/54.43 tff(188,plain,
% 54.26/54.43 (^[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))))))),
% 54.26/54.43 inference(bind,[status(th)],[])).
% 54.26/54.43 tff(189,plain,
% 54.26/54.43 (![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)))))),
% 54.26/54.43 inference(quant_intro,[status(thm)],[188])).
% 54.26/54.43 tff(190,axiom,(![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> ((ic(C1) & ic(C2)) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWB001+0.ax','owl_eqdis_disjointwith')).
% 54.26/54.43 tff(191,plain,
% 54.26/54.43 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[190, 189])).
% 54.26/54.43 tff(192,plain,
% 54.26/54.43 (![C1: $i, C2: $i] : (iext(uri_owl_disjointWith, C1, C2) <=> (ic(C1) & ic(C2) & ![X: $i] : (~(icext(C1, X) & icext(C2, X)))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[191, 187])).
% 54.26/54.43 tff(193,plain,(
% 54.26/54.43 ![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))))))),
% 54.26/54.43 inference(skolemize,[status(sab)],[192])).
% 54.26/54.43 tff(194,plain,
% 54.26/54.43 (![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)))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[193, 186])).
% 54.26/54.43 tff(195,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[194, 184])).
% 54.26/54.43 tff(196,plain,
% 54.26/54.43 (![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)))))))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[195, 182])).
% 54.26/54.43 tff(197,plain,
% 54.26/54.43 (![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))))))))))),
% 54.26/54.43 inference(modus_ponens,[status(thm)],[196, 177])).
% 54.26/54.43 tff(198,plain,
% 54.26/54.43 ((~![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_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))))))))),
% 54.26/54.43 inference(quant_inst,[status(thm)],[])).
% 54.26/54.43 tff(199,plain,
% 54.26/54.43 (~((~(iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))))))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[198, 197])).
% 54.26/54.43 tff(200,plain,
% 54.26/54.43 (((~(iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2) | (~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~((~icext(uri_ex_c1, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))) | (~icext(uri_ex_c2, tptp_fun_X_66(uri_ex_c2, uri_ex_c1))))))) | (~((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))))))) | ((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))))))),
% 54.26/54.43 inference(tautology,[status(thm)],[])).
% 54.26/54.43 tff(201,plain,
% 54.26/54.43 ((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))))),
% 54.26/54.43 inference(unit_resolution,[status(thm)],[200, 199])).
% 54.26/54.43 tff(202,plain,
% 54.26/54.43 ((~((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))))))) | (~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))))),
% 54.26/54.49 inference(tautology,[status(thm)],[])).
% 54.26/54.49 tff(203,plain,
% 54.26/54.49 ((~((~iext(uri_owl_disjointWith, uri_ex_c1, uri_ex_c2)) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))))))) | (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))))),
% 54.26/54.49 inference(unit_resolution,[status(thm)],[202, 69])).
% 54.26/54.49 tff(204,plain,
% 54.26/54.49 (~((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))))),
% 54.26/54.49 inference(unit_resolution,[status(thm)],[203, 201])).
% 54.26/54.49 tff(205,plain,
% 54.26/54.49 (((~ic(uri_ex_c2)) | (~ic(uri_ex_c1)) | (~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X))))) | ![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))),
% 54.26/54.49 inference(tautology,[status(thm)],[])).
% 54.26/54.49 tff(206,plain,
% 54.26/54.49 (![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))),
% 54.26/54.49 inference(unit_resolution,[status(thm)],[205, 204])).
% 54.26/54.49 tff(207,plain,
% 54.26/54.49 (((~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))) | ((~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))) <=> ((~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.49 inference(rewrite,[status(thm)],[])).
% 54.26/54.49 tff(208,plain,
% 54.26/54.49 ((~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))) | ((~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))))),
% 54.26/54.49 inference(quant_inst,[status(thm)],[])).
% 54.26/54.49 tff(209,plain,
% 54.26/54.49 ((~![X: $i] : ((~icext(uri_ex_c2, X)) | (~icext(uri_ex_c1, X)))) | (~icext(uri_ex_c2, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3))) | (~icext(uri_ex_c1, tptp_fun_X_64(uri_ex_c2, uri_ex_c1, uri_ex_c3)))),
% 54.26/54.49 inference(modus_ponens,[status(thm)],[208, 207])).
% 54.26/54.49 tff(210,plain,
% 54.26/54.49 ($false),
% 54.26/54.49 inference(unit_resolution,[status(thm)],[209, 206, 175, 173])).
% 54.26/54.49 % SZS output end Proof
% 54.34/54.52 % E exiting
%------------------------------------------------------------------------------