Theorem. (
t7_ordinal4)
∀esk26_3 : set → 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, ∀esk6_2 : set → set → set, ∀esk1_0 : set, ∀esk3_0 : set, ∀v5_ordinal1 : set → prop, ∀v1_ordinal2 : set → prop, ∀v1_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀k2_xboole_0 : set → set → set, ∀v4_funct_1 : set → prop, ∀v1_zfmisc_1 : set → prop, ∀v1_finset_1 : set → prop, ∀esk17_1 : set → set, ∀esk22_1 : set → set, ∀np__1 : set, ∀v2_funct_1 : set → prop, ∀v2_ordinal1 : set → prop, ∀esk2_0 : set, ∀esk20_0 : set, ∀esk21_0 : set, ∀esk13_0 : set, ∀k1_numbers : set, ∀k5_numbers : set, ∀esk12_0 : set, ∀esk7_0 : set, ∀o_0_0_xboole_0 : set, ∀esk9_0 : set, ∀esk14_0 : set, ∀esk8_0 : set, ∀esk10_0 : set, ∀esk18_0 : set, ∀esk11_0 : set, ∀v2_xxreal_0 : set → prop, ∀esk5_1 : set → set, ∀esk15_0 : set, ∀esk24_0 : set, ∀esk16_0 : set, ∀v7_ordinal1 : set → prop, ∀v3_funct_1 : set → prop, ∀esk19_1 : set → set, ∀esk23_1 : set → set, ∀v6_ordinal1 : set → prop, ∀v1_card_1 : set → prop, ∀v3_card_1 : set → set → prop, ∀v1_ordinal1 : set → prop, ∀r1_tarski : set → set → prop, ∀esk4_0 : set, ∀esk25_2 : set → set → set, ∀esk29_2 : set → set → set, ∀esk30_3 : set → set → set → set, ∀esk28_2 : set → set → set, ∀k1_funct_1 : set → set → set, ∀r2_hidden : set → set → prop, ∀r1_ordinal2 : set → set → prop, ∀r1_ordinal1 : set → set → prop, ∀esk27_4 : set → set → set → set → set, ∀k9_xtuple_0 : set → set, ∀epred1_2 : set → set → prop, ∀v3_ordinal1 : set → prop, ∀k1_xboole_0 : set, (∀X3 X1 X2 X5 X4, (X4 = k1_xboole_0 → False) → (r2_hidden (k1_funct_1 X1 X2) X3 → False) → v3_ordinal1 X5 → v3_ordinal1 X3 → v3_ordinal1 X2 → r1_ordinal2 X4 X1 → r2_hidden X5 X4 → r2_hidden X4 X3 → epred1_2 X1 X4 → r2_hidden X2 (k9_xtuple_0 X1) → r1_ordinal1 (esk27_4 X4 X1 X5 X3) X2 → False) → (∀X1 X3 X2 X5 X4, (X4 = k1_xboole_0 → False) → (r2_hidden X1 (k1_funct_1 X2 X3) → False) → v3_ordinal1 X5 → v3_ordinal1 X3 → v3_ordinal1 X1 → r1_ordinal2 X4 X2 → r2_hidden X4 X5 → r2_hidden X1 X4 → epred1_2 X2 X4 → r2_hidden X3 (k9_xtuple_0 X2) → r1_ordinal1 (esk27_4 X4 X2 X1 X5) X3 → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → v3_ordinal1 X3 → epred1_2 X2 X1 → r2_hidden X3 (k9_xtuple_0 X2) → r2_hidden (esk28_2 X1 X2) (k1_funct_1 X2 (esk30_3 X1 X2 X3)) → r2_hidden (k1_funct_1 X2 (esk30_3 X1 X2 X3)) (esk29_2 X1 X2) → False) → (∀X4 X2 X3 X1, (X1 = k1_xboole_0 → False) → (r2_hidden (esk27_4 X1 X2 X3 X4) (k9_xtuple_0 X2) → False) → v3_ordinal1 X4 → v3_ordinal1 X3 → r1_ordinal2 X1 X2 → r2_hidden X3 X1 → r2_hidden X1 X4 → epred1_2 X2 X1 → False) → (∀X4 X2 X3 X1, (X1 = k1_xboole_0 → False) → (v3_ordinal1 (esk27_4 X1 X2 X3 X4) → False) → v3_ordinal1 X4 → v3_ordinal1 X3 → r1_ordinal2 X1 X2 → r2_hidden X3 X1 → r2_hidden X1 X4 → epred1_2 X2 X1 → False) → (∀X3 X2 X1, (r1_ordinal2 X2 X1 → False) → X2 = k1_xboole_0 → (k1_funct_1 X1 (esk26_3 X2 X1 X3)) = k1_xboole_0 → v3_ordinal1 X3 → epred1_2 X1 X2 → r2_hidden X3 (k9_xtuple_0 X1) → False) → (∀X3 X1 X2, (r1_ordinal2 X1 X2 → False) → (r2_hidden (esk26_3 X1 X2 X3) (k9_xtuple_0 X2) → False) → X1 = k1_xboole_0 → v3_ordinal1 X3 → epred1_2 X2 X1 → r2_hidden X3 (k9_xtuple_0 X2) → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (r2_hidden (esk30_3 X1 X2 X3) (k9_xtuple_0 X2) → False) → v3_ordinal1 X3 → epred1_2 X2 X1 → r2_hidden X3 (k9_xtuple_0 X2) → False) → (∀X1 X2 X3, (r1_ordinal2 X2 X3 → False) → (r1_ordinal1 X1 (esk26_3 X2 X3 X1) → False) → X2 = k1_xboole_0 → v3_ordinal1 X1 → epred1_2 X3 X2 → r2_hidden X1 (k9_xtuple_0 X3) → False) → (∀X3 X1 X2, (X2 = k1_xboole_0 → False) → (r1_ordinal2 X2 X3 → False) → (r1_ordinal1 X1 (esk30_3 X2 X3 X1) → False) → v3_ordinal1 X1 → epred1_2 X3 X2 → r2_hidden X1 (k9_xtuple_0 X3) → False) → (∀X3 X1 X2, (r1_ordinal2 X1 X2 → False) → (v3_ordinal1 (esk26_3 X1 X2 X3) → False) → X1 = k1_xboole_0 → v3_ordinal1 X3 → epred1_2 X2 X1 → r2_hidden X3 (k9_xtuple_0 X2) → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (v3_ordinal1 (esk30_3 X1 X2 X3) → False) → v3_ordinal1 X3 → epred1_2 X2 X1 → r2_hidden X3 (k9_xtuple_0 X2) → False) → (∀X2 X1 X3, ((k1_funct_1 X3 X1) = k1_xboole_0 → False) → X2 = k1_xboole_0 → v3_ordinal1 X1 → r1_ordinal2 X2 X3 → epred1_2 X3 X2 → r2_hidden X1 (k9_xtuple_0 X3) → r1_ordinal1 (esk25_2 X2 X3) 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 (esk6_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) → (∀X1, (r1_ordinal1 (k1_funct_1 esk3_0 X1) (k1_funct_1 esk1_0 X1) → False) → v3_ordinal1 X1 → r2_hidden X1 (k9_xtuple_0 esk1_0) → False) → (∀X1, (r1_ordinal1 (k1_funct_1 esk1_0 X1) (k1_funct_1 esk4_0 X1) → False) → v3_ordinal1 X1 → r2_hidden X1 (k9_xtuple_0 esk1_0) → False) → (∀X2 X1, (r2_hidden (esk25_2 X1 X2) (k9_xtuple_0 X2) → False) → X1 = k1_xboole_0 → r1_ordinal2 X1 X2 → epred1_2 X2 X1 → 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, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (r2_hidden (esk28_2 X1 X2) X1 → False) → epred1_2 X2 X1 → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (r2_hidden X1 (esk29_2 X1 X2) → False) → epred1_2 X2 X1 → False) → (∀X2 X1, (v3_ordinal1 (esk25_2 X1 X2) → False) → X1 = k1_xboole_0 → r1_ordinal2 X1 X2 → epred1_2 X2 X1 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (v3_ordinal1 (esk29_2 X1 X2) → False) → epred1_2 X2 X1 → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (r1_ordinal2 X1 X2 → False) → (v3_ordinal1 (esk28_2 X1 X2) → False) → epred1_2 X2 X1 → False) → (∀X2 X1, (v3_ordinal1 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v5_ordinal1 X1 → v1_funct_1 X1 → v1_ordinal2 X1 → v3_ordinal1 X2 → False) → (∀X1 X2, (v3_card_1 (k9_xtuple_0 X2) X1 → False) → v1_relat_1 X2 → v1_funct_1 X2 → v1_card_1 X1 → v3_card_1 X2 X1 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1 X3, (r1_tarski X1 X3 → False) → r1_tarski X2 X3 → r1_tarski X1 X2 → 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) → (∀X1 X2, (v1_funct_1 X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (epred1_2 X2 X1 → False) → v1_relat_1 X2 → v5_ordinal1 X2 → v1_funct_1 X2 → v1_ordinal2 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = X2 → False) → ((k2_xboole_0 X1 X2) = X1 → 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) → (∀X1 X2, (v4_funct_1 X2 → False) → v4_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 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, (v1_zfmisc_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 (k9_xtuple_0 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) → (∀X2 X1, (v1_funct_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_relat_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X1, (v3_ordinal1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v5_ordinal1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → 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, (v3_card_1 (esk22_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v3_card_1 (esk19_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, v1_xboole_0 X1 → v3_card_1 X1 np__1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v3_card_1 X1 np__1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v3_card_1 X1 k1_xboole_0 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_card_1 X1 np__1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_card_1 (esk23_1 X1) np__1 → False) → False) → (∀X1, (X1 = k1_xboole_0 → False) → r1_tarski X1 k1_xboole_0 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (esk17_1 X1) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (k1_zfmisc_1 X1) → False) → (∀X1, (v3_card_1 X1 k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v3_ordinal1 X1 → v1_finset_1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X1, (v1_funct_1 (esk22_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (v1_relat_1 (esk22_1 X1) → False) → v1_card_1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v7_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, (v1_card_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v1_xboole_0 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_card_1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_ordinal2 esk2_0 esk1_0 → False) → (v1_finset_1 esk16_0 → False) → (v3_funct_1 esk20_0 → False) → (v1_xboole_0 esk24_0 → False) → (v1_xboole_0 esk21_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 np__1 → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk5_1 X1) X1 → 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) → ((r1_ordinal2 esk2_0 esk4_0 → False) → False) → ((r1_ordinal2 esk2_0 esk3_0 → False) → False) → (((k9_xtuple_0 esk4_0) = (k9_xtuple_0 esk1_0) → False) → False) → (((k9_xtuple_0 esk3_0) = (k9_xtuple_0 esk1_0) → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v4_funct_1 esk24_0 → False) → False) → ((v1_finset_1 esk11_0 → False) → False) → ((v7_ordinal1 esk21_0 → False) → False) → ((v7_ordinal1 esk18_0 → False) → False) → ((v2_funct_1 esk12_0 → False) → False) → ((v2_ordinal1 esk13_0 → False) → False) → ((v2_ordinal1 esk11_0 → False) → False) → ((v1_ordinal1 esk13_0 → False) → False) → ((v1_ordinal1 esk11_0 → False) → False) → ((v1_card_1 esk11_0 → False) → False) → ((v1_card_1 esk7_0 → False) → False) → ((v1_xboole_0 esk10_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v3_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk11_0 → False) → False) → ((v3_ordinal1 esk9_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v1_ordinal2 esk14_0 → False) → False) → ((v1_ordinal2 esk4_0 → False) → False) → ((v1_ordinal2 esk3_0 → False) → False) → ((v1_ordinal2 esk1_0 → False) → False) → ((v1_funct_1 esk20_0 → False) → False) → ((v1_funct_1 esk14_0 → False) → False) → ((v1_funct_1 esk12_0 → False) → False) → ((v1_funct_1 esk8_0 → False) → False) → ((v1_funct_1 esk4_0 → False) → False) → ((v1_funct_1 esk3_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v5_ordinal1 esk14_0 → False) → False) → ((v5_ordinal1 esk4_0 → False) → False) → ((v5_ordinal1 esk3_0 → False) → False) → ((v5_ordinal1 esk1_0 → False) → False) → ((v1_relat_1 esk20_0 → False) → False) → ((v1_relat_1 esk14_0 → False) → False) → ((v1_relat_1 esk12_0 → False) → False) → ((v1_relat_1 esk8_0 → False) → False) → ((v1_relat_1 esk4_0 → False) → False) → ((v1_relat_1 esk3_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False