Theorem. (
t40_ordinal3)
∀r2_hidden : set → set → prop, ∀esk3_3 : set → set → set → set, ∀k10_xtuple_0 : set → set, ∀k10_ordinal2 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀k1_tarski : set → set, ∀esk7_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m2_subset_1 : set → set → set → prop, ∀esk10_2 : set → set → set, ∀esk5_2 : set → set → set, ∀r1_ordinal1 : set → set → prop, ∀esk20_2 : set → set → set, ∀k3_ordinal2 : set → set, ∀v7_ordinal1 : set → prop, ∀esk16_0 : set, ∀np__1 : set, ∀np__0 : set, ∀esk9_1 : set → set, ∀v2_xxreal_0 : set → prop, ∀esk12_0 : set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk13_0 : set, ∀esk17_0 : set, ∀esk15_0 : set, ∀k5_numbers : set, ∀k1_numbers : set, ∀esk14_0 : set, ∀esk18_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀v2_ordinal1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀r1_tarski : set → set → prop, ∀esk19_2 : set → set → set, ∀esk8_2 : set → set → set, ∀esk21_1 : set → set, ∀esk6_3 : set → set → set → set, ∀esk4_2 : set → set → set, ∀k11_ordinal2 : set → set → set, ∀k4_ordinal2 : set → set, ∀k3_tarski : set → set, ∀esk22_3 : set → set → set → set, ∀k1_funct_1 : set → set → set, ∀v5_ordinal1 : set → prop, ∀v1_ordinal2 : set → prop, ∀v1_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀v4_ordinal1 : set → prop, ∀v3_ordinal1 : set → prop, ∀k9_xtuple_0 : set → set, ∀k1_xboole_0 : set, (∀X1 X3 X2, (X2 = k1_xboole_0 → False) → ((k11_ordinal2 X2 X3) = (k3_tarski (k4_ordinal2 X1)) → False) → (k9_xtuple_0 X1) = X2 → (k1_funct_1 X1 (esk22_3 X2 X3 X1)) = (k11_ordinal2 (esk22_3 X2 X3 X1) X3) → v3_ordinal1 X3 → v3_ordinal1 X2 → v4_ordinal1 X2 → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → v1_ordinal2 X1 → False) → (∀X3 X2 X1, (X1 = k1_xboole_0 → False) → ((k11_ordinal2 X1 X2) = (k3_tarski (k4_ordinal2 X3)) → False) → (r2_hidden (esk22_3 X1 X2 X3) X1 → False) → (k9_xtuple_0 X3) = X1 → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → v5_ordinal1 X3 → v1_relat_1 X3 → v1_funct_1 X3 → v1_ordinal2 X3 → False) → (∀X3 X2 X1, (X1 = k1_xboole_0 → False) → ((k11_ordinal2 X1 X2) = (k3_tarski (k4_ordinal2 X3)) → False) → (v3_ordinal1 (esk22_3 X1 X2 X3) → False) → (k9_xtuple_0 X3) = X1 → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → v5_ordinal1 X3 → v1_relat_1 X3 → v1_funct_1 X3 → v1_ordinal2 X3 → False) → (∀X3 X2 X1, (r2_hidden (esk3_3 X1 X2 X3) (k9_xtuple_0 X1) → False) → X2 = (k10_xtuple_0 X1) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X3 X2 → False) → (∀X1 X3 X2, ((k1_funct_1 X2 (esk3_3 X2 X3 X1)) = X1 → False) → X3 = (k10_xtuple_0 X2) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 X3 → False) → (∀X2 X1, ((k2_xboole_0 (k10_ordinal2 X1 X2) (k1_tarski (k10_ordinal2 X1 X2))) = (k10_ordinal2 X1 (k2_xboole_0 X2 (k1_tarski X2))) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X3 X2 X1, (X2 = (k10_xtuple_0 X1) → False) → (esk4_2 X1 X2) = (k1_funct_1 X1 X3) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X3 (k9_xtuple_0 X1) → r2_hidden (esk4_2 X1 X2) X2 → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk7_2 X1 X2) X3 → r2_hidden (esk7_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk6_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk6_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X1, (v4_ordinal1 X1 → False) → v3_ordinal1 X1 → r2_hidden (k2_xboole_0 (esk21_1 X1) (k1_tarski (esk21_1 X1))) X1 → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 X3 X1 → False) → m2_subset_1 X3 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 X1 X3 → False) → m2_subset_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk10_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m2_subset_1 X1 X3 X2 → False) → m1_subset_1 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (X2 = (k10_xtuple_0 X1) → False) → ((k1_funct_1 X1 (esk5_2 X1 X2)) = (esk4_2 X1 X2) → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → (r2_hidden (esk7_2 X1 X2) (esk8_2 X1 X2) → False) → False) → (∀X1 X2, (r2_hidden X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_ordinal1 (k2_xboole_0 X1 (k1_tarski X1)) X2 → False) → (∀X1 X2, (r1_ordinal1 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 (k2_xboole_0 X2 (k1_tarski X2)) → False) → (∀X2 X1 X3, (r1_ordinal1 (k10_ordinal2 X3 X1) (k10_ordinal2 X3 X2) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_ordinal1 X1 X2 → False) → (∀X2 X1, (X2 = (k10_xtuple_0 X1) → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → (r2_hidden (esk5_2 X1 X2) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1, ((k11_ordinal2 (k2_xboole_0 X1 (k1_tarski X1)) X2) = (k10_ordinal2 (k11_ordinal2 X1 X2) X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1 X3, ((k1_funct_1 (esk19_2 X2 X3) X1) = (k11_ordinal2 X1 X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (r2_hidden (k2_xboole_0 X2 (k1_tarski X2)) X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X1 → r2_hidden X2 X1 → False) → (∀X2 X1 X3 X4, (r2_hidden X3 X4 → False) → X4 = (k10_xtuple_0 X2) → X3 = (k1_funct_1 X2 X1) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → False) → (∀X1 X2, (r1_ordinal1 (k2_xboole_0 X1 (k1_tarski X1)) X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (r2_hidden X1 (k2_xboole_0 X2 (k1_tarski X2)) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_ordinal1 X1 X2 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → (r2_hidden (esk8_2 X1 X2) X1 → False) → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v1_ordinal1 X1 → r2_hidden X2 X3 → r1_tarski X1 X2 → False) → (∀X2 X1, (r2_hidden (esk20_2 X1 X2) X2 → False) → v3_ordinal1 X1 → r2_hidden X1 (k3_ordinal2 X2) → False) → (∀X2 X1, (r1_ordinal1 X1 (esk20_2 X1 X2) → False) → v3_ordinal1 X1 → r2_hidden X1 (k3_ordinal2 X2) → False) → (∀X1, v3_ordinal1 X1 → v1_xboole_0 (k2_xboole_0 X1 (k1_tarski X1)) → False) → (∀X2 X1, (v3_ordinal1 (esk20_2 X1 X2) → False) → v3_ordinal1 X1 → r2_hidden X1 (k3_ordinal2 X2) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → r2_hidden X1 X2 → False) → (∀X2 X1, (v3_ordinal1 (k1_funct_1 X1 X2) → False) → v3_ordinal1 X2 → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → v1_ordinal2 X1 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1, (v7_ordinal1 (k2_xboole_0 X1 (k1_tarski X1)) → False) → v3_ordinal1 X1 → v7_ordinal1 X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X1 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X2 X1) → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_ordinal1 X1 X2 → False) → (∀X1 X2, (r1_ordinal1 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_tarski X1 X2 → False) → (∀X2 X1, (r2_hidden X1 (k3_ordinal2 X2) → False) → v3_ordinal1 X1 → r2_hidden X1 X2 → False) → (∀X1, (v3_ordinal1 (k2_xboole_0 X1 (k1_tarski X1)) → False) → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, ((k9_xtuple_0 (esk19_2 X1 X2)) = X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v1_ordinal2 (esk19_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v1_funct_1 (esk19_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v1_relat_1 (esk19_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v7_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v5_ordinal1 (esk19_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k2_xboole_0 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (r1_ordinal1 X2 X1 → False) → (r1_ordinal1 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, ((k3_ordinal2 (k10_xtuple_0 X1)) = (k4_ordinal2 X1) → False) → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v4_ordinal1 X1 → False) → (r2_hidden (esk21_1 X1) X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 (k4_ordinal2 X1) → False) → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v3_ordinal1 (k9_xtuple_0 X1) → False) → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_ordinal1 X1 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1, (v4_ordinal1 X1 → False) → (v3_ordinal1 (esk21_1 X1) → False) → v3_ordinal1 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → (r2_hidden k1_xboole_0 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, ((k10_ordinal2 X1 k1_xboole_0) = X1 → False) → v3_ordinal1 X1 → False) → (∀X1, ((k11_ordinal2 k1_xboole_0 X1) = k1_xboole_0 → False) → v3_ordinal1 X1 → False) → (∀X1, ((k11_ordinal2 X1 k1_xboole_0) = k1_xboole_0 → False) → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 (k3_tarski X1) → False) → v3_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, v1_xboole_0 (k2_xboole_0 X1 (k1_tarski X1)) → False) → (v4_ordinal1 (k11_ordinal2 esk1_0 esk2_0) → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 np__1 → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__0 k1_numbers k5_numbers → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk9_1 X1) X1 → False) → False) → (((k2_xboole_0 np__0 (k1_tarski np__0)) = np__1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → ((m1_subset_1 np__1 k5_numbers → False) → False) → ((m1_subset_1 np__1 k1_numbers → False) → False) → ((m1_subset_1 np__0 k5_numbers → False) → False) → ((m1_subset_1 np__0 k1_numbers → False) → False) → (∀X1, (v3_ordinal1 (k3_ordinal2 X1) → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v1_ordinal2 esk15_0 → False) → False) → ((v1_funct_1 esk15_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v7_ordinal1 esk18_0 → False) → False) → ((v7_ordinal1 esk17_0 → False) → False) → ((v5_ordinal1 esk15_0 → False) → False) → ((v1_xboole_0 esk13_0 → False) → False) → ((v1_xboole_0 np__0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_ordinal1 esk14_0 → False) → False) → ((v2_ordinal1 esk12_0 → False) → False) → ((v1_ordinal1 esk14_0 → False) → False) → ((v1_ordinal1 esk12_0 → False) → False) → ((v4_ordinal1 esk12_0 → False) → False) → ((v4_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 esk14_0 → False) → False) → ((v3_ordinal1 esk12_0 → False) → False) → ((v3_ordinal1 esk11_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v3_ordinal1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False