Theorem. (t40_ordinal2)
∀r2_hidden : setsetprop, ∀esk28_2 : setsetset, ∀esk4_3 : setsetsetset, ∀k10_xtuple_0 : setset, ∀esk5_2 : setsetset, ∀esk6_2 : setsetset, ∀k10_ordinal2 : setsetset, ∀m1_subset_1 : setsetprop, ∀k1_zfmisc_1 : setset, ∀esk31_1 : setset, ∀k3_ordinal2 : setset, ∀v4_funct_1 : setprop, ∀esk26_1 : setset, ∀esk22_1 : setset, ∀v2_funct_1 : setprop, ∀esk27_0 : set, ∀esk19_0 : set, ∀esk14_0 : set, ∀esk7_1 : setset, ∀esk17_0 : set, ∀esk15_0 : set, ∀esk9_0 : set, ∀esk13_0 : set, ∀esk10_0 : set, ∀o_0_0_xboole_0 : set, ∀esk8_0 : set, ∀esk21_0 : set, ∀esk11_0 : set, ∀esk18_1 : setset, ∀esk16_0 : set, ∀esk24_0 : set, ∀esk23_0 : set, ∀esk20_1 : setset, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀v2_ordinal1 : setprop, ∀v2_funcop_1 : setprop, ∀esk12_1 : setset, ∀esk25_1 : setset, ∀v3_funct_1 : setprop, ∀v6_ordinal1 : setprop, ∀v1_zfmisc_1 : setprop, ∀r2_xboole_0 : setsetprop, ∀r1_tarski : setsetprop, ∀v1_funcop_1 : setprop, ∀v7_ordinal1 : setprop, ∀v1_subset_1 : setsetprop, ∀v1_ordinal1 : setprop, ∀v1_xboole_0 : setprop, ∀esk29_2 : setsetset, ∀r1_ordinal1 : setsetprop, ∀k2_xboole_0 : setsetset, ∀k1_tarski : setset, ∀esk30_1 : setset, ∀k11_ordinal2 : setsetset, ∀k4_ordinal2 : setset, ∀k3_tarski : setset, ∀esk32_3 : setsetsetset, ∀k1_funct_1 : setsetset, ∀v1_relat_1 : setprop, ∀v4_ordinal1 : setprop, ∀v1_ordinal2 : setprop, ∀v5_ordinal1 : setprop, ∀v1_funct_1 : setprop, ∀v3_ordinal1 : setprop, ∀k9_xtuple_0 : setset, ∀k1_xboole_0 : set, (∀X1 X3 X2, (X2 = k1_xboole_0False)((k11_ordinal2 X2 X3) = (k3_tarski (k4_ordinal2 X1))False)(k9_xtuple_0 X1) = X2(k1_funct_1 X1 (esk32_3 X2 X3 X1)) = (k11_ordinal2 (esk32_3 X2 X3 X1) X3)v3_ordinal1 X3v3_ordinal1 X2v1_funct_1 X1v1_relat_1 X1v5_ordinal1 X1v1_ordinal2 X1v4_ordinal1 X2False)(∀X2 X1 X3, (r2_hidden (k11_ordinal2 X1 X2) (k11_ordinal2 X3 X2)False)v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X1 X3r2_hidden (k11_ordinal2 X1 X2) (k11_ordinal2 (esk28_2 X2 X1) X2)False)(∀X1 X3 X2 X4, (r2_hidden (k11_ordinal2 X3 X2) (k11_ordinal2 X4 X2)False)(r2_hidden (k11_ordinal2 X3 X2) (k11_ordinal2 X1 X2)False)v3_ordinal1 X4v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X3 X4r2_hidden X3 X1r2_hidden X1 (esk28_2 X2 X3)False)(∀X3 X2 X1, (X1 = k1_xboole_0False)((k11_ordinal2 X1 X2) = (k3_tarski (k4_ordinal2 X3))False)(r2_hidden (esk32_3 X1 X2 X3) X1False)(k9_xtuple_0 X3) = X1v3_ordinal1 X2v3_ordinal1 X1v1_funct_1 X3v1_relat_1 X3v5_ordinal1 X3v1_ordinal2 X3v4_ordinal1 X1False)(∀X3 X2 X1, (X1 = k1_xboole_0False)((k11_ordinal2 X1 X2) = (k3_tarski (k4_ordinal2 X3))False)(v3_ordinal1 (esk32_3 X1 X2 X3)False)(k9_xtuple_0 X3) = X1v3_ordinal1 X2v3_ordinal1 X1v1_funct_1 X3v1_relat_1 X3v5_ordinal1 X3v1_ordinal2 X3v4_ordinal1 X1False)(∀X3 X2 X1, (r2_hidden (esk4_3 X1 X2 X3) (k9_xtuple_0 X1)False)X2 = (k10_xtuple_0 X1)v1_funct_1 X1v1_relat_1 X1r2_hidden X3 X2False)(∀X1 X3 X2, ((k1_funct_1 X2 (esk4_3 X2 X3 X1)) = X1False)X3 = (k10_xtuple_0 X2)v1_funct_1 X2v1_relat_1 X2r2_hidden X1 X3False)(∀X3 X2 X1, (X2 = (k10_xtuple_0 X1)False)(esk5_2 X1 X2) = (k1_funct_1 X1 X3)v1_funct_1 X1v1_relat_1 X1r2_hidden X3 (k9_xtuple_0 X1)r2_hidden (esk5_2 X1 X2) X2False)(∀X1, (v4_ordinal1 X1False)v3_ordinal1 X1r2_hidden (k2_xboole_0 (esk30_1 X1) (k1_tarski (esk30_1 X1))) X1False)(∀X3 X2 X1, (r2_hidden X1 (esk28_2 X2 X1)False)(r2_hidden (k11_ordinal2 X1 X2) (k11_ordinal2 X3 X2)False)v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X1 X3False)(∀X3 X2 X1, (v3_ordinal1 (esk28_2 X1 X2)False)(r2_hidden (k11_ordinal2 X2 X1) (k11_ordinal2 X3 X1)False)v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X2 X3False)(∀X2 X1, (X2 = (k10_xtuple_0 X1)False)((k1_funct_1 X1 (esk6_2 X1 X2)) = (esk5_2 X1 X2)False)(r2_hidden (esk5_2 X1 X2) X2False)v1_funct_1 X1v1_relat_1 X1False)(∀X1 X2, (r1_ordinal1 X1 X2False)v3_ordinal1 X2v3_ordinal1 X1r2_hidden X1 (k2_xboole_0 X2 (k1_tarski X2))False)(∀X2 X1 X3, (r2_hidden (k10_ordinal2 X3 X1) (k10_ordinal2 X3 X2)False)v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X1 X2False)(∀X2 X1, (X2 = (k10_xtuple_0 X1)False)(r2_hidden (esk5_2 X1 X2) X2False)(r2_hidden (esk6_2 X1 X2) (k9_xtuple_0 X1)False)v1_funct_1 X1v1_relat_1 X1False)(∀X2 X1, ((k11_ordinal2 (k2_xboole_0 X1 (k1_tarski X1)) X2) = (k10_ordinal2 (k11_ordinal2 X1 X2) X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1 X3, ((k1_funct_1 (esk29_2 X3 X2) X1) = (k11_ordinal2 X1 X3)False)v3_ordinal1 X3v3_ordinal1 X2v3_ordinal1 X1r2_hidden X1 X2False)(∀X1 X2, (r2_hidden (k2_xboole_0 X2 (k1_tarski X2)) X1False)v3_ordinal1 X2v3_ordinal1 X1v4_ordinal1 X1r2_hidden X2 X1False)(∀X2 X1 X3 X4, (r2_hidden X3 X4False)X4 = (k10_xtuple_0 X2)X3 = (k1_funct_1 X2 X1)v1_funct_1 X2v1_relat_1 X2r2_hidden X1 (k9_xtuple_0 X2)False)(∀X1 X2, (r2_hidden X1 (k2_xboole_0 X2 (k1_tarski X2))False)v3_ordinal1 X2v3_ordinal1 X1r1_ordinal1 X1 X2False)(∀X1, v3_ordinal1 X1v1_xboole_0 (k2_xboole_0 X1 (k1_tarski X1))False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X3 X2 X1, (r2_hidden X2 X1False)v1_ordinal1 X1r2_hidden X3 X1r2_hidden X2 X3False)(∀X2 X1, (v3_ordinal1 (k1_funct_1 X1 X2)False)v3_ordinal1 X2v1_funct_1 X1v1_relat_1 X1v5_ordinal1 X1v1_ordinal2 X1False)(∀X2 X1, v1_xboole_0 X1v1_subset_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1, (v7_ordinal1 (k2_xboole_0 X1 (k1_tarski X1))False)v3_ordinal1 X1v7_ordinal1 X1False)(∀X1 X2, X2 = (k2_xboole_0 X1 (k1_tarski X1))v3_ordinal1 X2v3_ordinal1 X1v4_ordinal1 X2False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X1 X2)False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X2 X1)False)(∀X2 X1, (v1_relat_1 (k1_funct_1 X1 X2)False)v1_funct_1 X1v1_relat_1 X1v1_funcop_1 X1False)(∀X2 X1, (v1_funct_1 (k1_funct_1 X1 X2)False)v1_funct_1 X1v1_relat_1 X1v1_funcop_1 X1False)(∀X1 X2, (r1_tarski X1 X2False)v3_ordinal1 X2v3_ordinal1 X1r1_ordinal1 X1 X2False)(∀X1 X2, (r1_ordinal1 X1 X2False)v3_ordinal1 X2v3_ordinal1 X1r1_tarski X1 X2False)(∀X1 X2, (r2_hidden X1 X2False)v3_ordinal1 X2v1_ordinal1 X1r2_xboole_0 X1 X2False)(∀X1, ((k2_xboole_0 (esk31_1 X1) (k1_tarski (esk31_1 X1))) = X1False)(v4_ordinal1 X1False)v3_ordinal1 X1False)(∀X1 X2, (v1_funct_1 X2False)v1_funct_1 X1v1_relat_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (r2_hidden X1 (k3_ordinal2 X2)False)v3_ordinal1 X1r2_hidden X1 X2False)(∀X1, (v3_ordinal1 (k2_xboole_0 X1 (k1_tarski X1))False)v3_ordinal1 X1False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, ((k9_xtuple_0 (esk29_2 X1 X2)) = X2False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, r2_xboole_0 X2 X1r2_xboole_0 X1 X2False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X2 X1, (v1_ordinal2 (esk29_2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (v5_ordinal1 (esk29_2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (v1_relat_1 (esk29_2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (v1_funct_1 (esk29_2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (v3_ordinal1 (k11_ordinal2 X1 X2)False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X1 X2, (v4_funct_1 X2False)v4_funct_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v1_zfmisc_1 X2False)v1_zfmisc_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v6_ordinal1 X2False)v6_ordinal1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (r1_ordinal1 X2 X1False)(r1_ordinal1 X1 X2False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, (r1_tarski X1 (k3_tarski X2)False)r2_hidden X1 X2False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (X1 = X2False)(r2_xboole_0 X1 X2False)r1_tarski X1 X2False)(∀X2 X1, (r1_tarski X1 X2False)r2_xboole_0 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, ((k3_ordinal2 (k10_xtuple_0 X1)) = (k4_ordinal2 X1)False)v1_funct_1 X1v1_relat_1 X1v5_ordinal1 X1False)(∀X1, (v1_zfmisc_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 (k9_xtuple_0 X1)False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 (k10_xtuple_0 X1)False)(∀X2 X1, (v1_relat_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X2 X1, (v1_funct_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X1 X2, (v3_ordinal1 X2False)v3_ordinal1 X1m1_subset_1 X2 X1False)(∀X1 X2, (v3_ordinal1 X2False)v3_ordinal1 X1m1_subset_1 X2 X1False)(∀X1, (v4_ordinal1 X1False)(r2_hidden (esk30_1 X1) X1False)v3_ordinal1 X1False)(∀X1, (v1_zfmisc_1 (k10_xtuple_0 X1)False)v1_funct_1 X1v1_relat_1 X1v3_funct_1 X1False)(∀X1, (v3_ordinal1 (k4_ordinal2 X1)False)v1_funct_1 X1v1_relat_1 X1v5_ordinal1 X1False)(∀X1, (v3_ordinal1 (k9_xtuple_0 X1)False)v1_funct_1 X1v1_relat_1 X1v5_ordinal1 X1False)(∀X1, (v1_zfmisc_1 X1False)(m1_subset_1 (esk26_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk25_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X2 X1, (r1_ordinal1 X1 X1False)v3_ordinal1 X2v3_ordinal1 X1False)(∀X2 X1, X1 = X2r2_xboole_0 X1 X2False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v2_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v2_funcop_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_funcop_1 X1False)(∀X1, (v1_funcop_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk22_1 X1) X1False)False)(∀X1, (v4_funct_1 (k1_tarski X1)False)v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v4_ordinal1 X1False)(v3_ordinal1 (esk31_1 X1)False)v3_ordinal1 X1False)(∀X1, (v4_ordinal1 X1False)(v3_ordinal1 (esk30_1 X1)False)v3_ordinal1 X1False)(∀X1, (v1_zfmisc_1 X1False)v1_zfmisc_1 (esk26_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk25_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk12_1 X1)False)(∀X1, ((k10_ordinal2 X1 k1_xboole_0) = X1False)v3_ordinal1 X1False)(∀X1, (v3_ordinal1 X1False)v1_ordinal1 X1v2_ordinal1 X1False)(∀X1, (v3_ordinal1 (k3_tarski X1)False)v3_ordinal1 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_zfmisc_1 (esk25_1 X1)False)False)(∀X1, (v4_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v7_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v5_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v2_ordinal1 X1False)v3_ordinal1 X1False)(∀X1, (v1_ordinal1 X1False)v3_ordinal1 X1False)(∀X1, (v1_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v6_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (v3_ordinal1 X1False)v7_ordinal1 X1False)(∀X1, (v3_ordinal1 X1False)v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(r2_hidden (k11_ordinal2 esk2_0 esk1_0) (k11_ordinal2 esk3_0 esk1_0)False)(∀X1, v1_xboole_0 (k2_xboole_0 X1 (k1_tarski X1))False)(∀X1, v1_subset_1 (esk20_1 X1) X1False)(∀X1, r2_xboole_0 X1 X1False)(∀X1, v1_xboole_0 (k1_tarski X1)False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v3_funct_1 esk23_0False)(v1_xboole_0 esk27_0False)(v1_xboole_0 esk24_0False)(v1_xboole_0 esk19_0False)(v1_xboole_0 esk16_0False)(v1_xboole_0 esk14_0False)(esk1_0 = k1_xboole_0False)(∀X1, (r2_hidden X1 (k2_xboole_0 X1 (k1_tarski X1))False)False)(∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1)False)False)(∀X1, (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk7_1 X1) X1False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1False)False)((r2_hidden esk2_0 esk3_0False)False)(∀X1, (v1_xboole_0 (esk18_1 X1)False)False)(∀X1, (v3_ordinal1 (k3_ordinal2 X1)False)False)((v4_ordinal1 esk11_0False)False)((v1_ordinal2 esk17_0False)False)((v4_funct_1 esk27_0False)False)((v7_ordinal1 esk24_0False)False)((v7_ordinal1 esk21_0False)False)((v5_ordinal1 esk17_0False)False)((v3_funct_1 esk14_0False)False)((v2_funct_1 esk15_0False)False)((v1_funcop_1 esk8_0False)False)((v1_relat_1 esk23_0False)False)((v1_relat_1 esk17_0False)False)((v1_relat_1 esk15_0False)False)((v1_relat_1 esk14_0False)False)((v1_relat_1 esk9_0False)False)((v1_relat_1 esk8_0False)False)((v2_ordinal1 esk16_0False)False)((v2_ordinal1 esk11_0False)False)((v1_ordinal1 esk16_0False)False)((v1_ordinal1 esk11_0False)False)((v1_funct_1 esk23_0False)False)((v1_funct_1 esk17_0False)False)((v1_funct_1 esk15_0False)False)((v1_funct_1 esk14_0False)False)((v1_funct_1 esk9_0False)False)((v1_funct_1 esk8_0False)False)((v1_xboole_0 esk13_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((v1_xboole_0 k1_xboole_0False)False)((v3_ordinal1 esk16_0False)False)((v3_ordinal1 esk11_0False)False)((v3_ordinal1 esk10_0False)False)((v3_ordinal1 esk3_0False)False)((v3_ordinal1 esk2_0False)False)((v3_ordinal1 esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.