Theorem. (
t10_card_1)
∀esk1_0 : set, ∀k9_xtuple_0 : set → set, ∀v1_funct_1 : set → prop, ∀esk2_0 : set, ∀r1_ordinal1 : set → set → prop, ∀k1_card_1 : set → set, ∀v2_funct_1 : set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀r2_hidden : set → set → prop, ∀v1_finset_1 : set → prop, ∀esk4_2 : set → set → set, ∀v3_ordinal1 : set → prop, ∀v4_funct_1 : set → prop, ∀v1_zfmisc_1 : set → prop, ∀k2_funct_1 : set → set, ∀v3_funct_1 : set → prop, ∀v5_ordinal1 : set → prop, ∀esk29_1 : set → set, ∀esk27_1 : set → set, ∀esk14_1 : set → set, ∀v2_funcop_1 : set → prop, ∀v2_finset_1 : set → prop, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀esk22_1 : set → set, ∀esk25_0 : set, ∀esk32_0 : set, ∀esk30_0 : set, ∀esk21_0 : set, ∀esk17_0 : set, ∀esk13_0 : set, ∀esk18_1 : set → set, ∀esk23_0 : set, ∀esk12_0 : set, ∀esk10_0 : set, ∀esk16_0 : set, ∀esk9_0 : set, ∀esk6_0 : set, ∀o_0_0_xboole_0 : set, ∀esk8_0 : set, ∀esk5_1 : set → set, ∀esk7_0 : set, ∀esk15_0 : set, ∀esk19_0 : set, ∀esk26_0 : set, ∀esk31_0 : set, ∀esk20_0 : set, ∀k1_xboole_0 : set, ∀v7_ordinal1 : set → prop, ∀esk11_1 : set → set, ∀esk24_1 : set → set, ∀esk28_1 : set → set, ∀esk3_0 : set, ∀r2_tarski : set → set → prop, ∀v6_ordinal1 : set → prop, ∀v5_finset_1 : set → prop, ∀v1_card_1 : set → prop, ∀r2_wellord2 : set → set → prop, ∀v1_subset_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀v1_funcop_1 : set → prop, ∀r1_tarski : set → set → prop, ∀k3_relat_1 : set → set → set, ∀k10_xtuple_0 : set → set, ∀v1_relat_1 : set → prop, (∀X2 X1, (r1_tarski (k10_xtuple_0 (k3_relat_1 X1 X2)) (k10_xtuple_0 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1, (k9_xtuple_0 X1) = esk1_0 → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → r1_tarski (k10_xtuple_0 X1) esk2_0 → r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → (∀X1 X2, ((k9_xtuple_0 (k3_relat_1 X1 X2)) = (k9_xtuple_0 X1) → False) → v1_relat_1 X2 → v1_relat_1 X1 → r1_tarski (k10_xtuple_0 X1) (k9_xtuple_0 X2) → False) → (∀X1 X2, (v2_funct_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v2_funct_1 X2 → v2_funct_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v2_funct_1 X2 → v2_funct_1 X1 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v1_funcop_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → False) → (∀X1 X2, (v1_finset_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_finset_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_finset_1 X1 → False) → (∀X2 X1, v1_xboole_0 X1 → v1_subset_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 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, (r2_wellord2 X1 X3 → False) → r2_wellord2 X2 X3 → r2_wellord2 X1 X2 → False) → (∀X1 X2, (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, ((k10_xtuple_0 (esk4_2 X1 X2)) = X2 → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, ((k9_xtuple_0 (esk4_2 X1 X2)) = X1 → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, (v2_funct_1 (esk4_2 X1 X2) → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, (v1_funct_1 (esk4_2 X1 X2) → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, (v1_relat_1 (esk4_2 X1 X2) → False) → r2_wellord2 X1 X2 → False) → (∀X1 X2 X3, (r2_wellord2 X2 X3 → False) → (k9_xtuple_0 X1) = X2 → (k10_xtuple_0 X1) = X3 → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 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) → (∀X2 X1, (r1_ordinal1 (k1_card_1 X2) X1 → False) → v1_card_1 X1 → r1_tarski X2 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) → (∀X1 X2, (v4_funct_1 X2 → False) → v4_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v5_finset_1 X2 → False) → v5_finset_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_zfmisc_1 X2 → False) → v1_zfmisc_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_finset_1 X2 → False) → v1_finset_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 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, (r2_tarski X1 X2 → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, (r2_wellord2 X1 X2 → False) → r2_tarski X1 X2 → False) → (∀X2 X1, (r2_wellord2 X2 X1 → False) → r2_wellord2 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → ((r1_tarski (k10_xtuple_0 esk3_0) esk2_0 → False) → (r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → False) → (∀X1, ((k9_xtuple_0 (k2_funct_1 X1)) = (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → False) → (∀X1, ((k10_xtuple_0 (k2_funct_1 X1)) = (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 (k10_xtuple_0 X1) → 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, (X2 = (k1_card_1 X1) → False) → v1_card_1 X2 → r2_wellord2 X1 X2 → False) → (∀X1 X2, (v1_finset_1 X2 → False) → v5_finset_1 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, (v1_zfmisc_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v3_funct_1 X1 → False) → (∀X1, (v3_ordinal1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v5_ordinal1 X1 → False) → (∀X1, (v2_funct_1 (k2_funct_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → False) → (∀X1, (v1_funct_1 (k2_funct_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → False) → (∀X1, (v1_relat_1 (k2_funct_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk29_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk28_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk24_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk11_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X2 X1, (r2_wellord2 X2 X1 → False) → X1 = (k1_card_1 X2) → v1_card_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, (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_funcop_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_funcop_1 X1 → False) → (∀X1, (v1_funcop_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_xboole_0 X1 → False) → (v1_subset_1 (esk24_1 X1) X1 → False) → False) → (∀X1, (v5_finset_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v2_finset_1 X1 → False) → (∀X1, (v1_finset_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_finset_1 X1 → False) → (∀X1, (v1_finset_1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_finset_1 X1 → False) → (∀X1, (v1_funct_1 (k2_funct_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_relat_1 (k2_funct_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → ((v2_funct_1 esk3_0 → False) → (r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → False) → ((v1_funct_1 esk3_0 → False) → (r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → False) → ((v1_relat_1 esk3_0 → False) → (r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → False) → (((k9_xtuple_0 esk3_0) = esk1_0 → False) → (r1_ordinal1 (k1_card_1 esk1_0) (k1_card_1 esk2_0) → False) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk29_1 X1) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk28_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk27_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk14_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk11_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k1_card_1 X1) → False) → (∀X1, (v2_finset_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X1, (v5_finset_1 (k1_zfmisc_1 X1) → False) → v1_finset_1 X1 → False) → (∀X1, (v1_finset_1 (k1_zfmisc_1 X1) → False) → v1_finset_1 X1 → False) → (∀X1, (v1_xboole_0 (k10_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 (k9_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 (k1_card_1 X1) → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_card_1 (k1_card_1 X1) → False) → v1_xboole_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (v1_finset_1 (esk29_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_zfmisc_1 (esk27_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_finset_1 (esk14_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_card_1 (k1_card_1 X1) → False) → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_finset_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_1 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_finset_1 X1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_finset_1 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, (v3_ordinal1 X1 → False) → v1_card_1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, v1_subset_1 (esk22_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v3_funct_1 esk25_0 → False) → (v1_zfmisc_1 esk20_0 → False) → (v1_xboole_0 esk32_0 → False) → (v1_xboole_0 esk31_0 → False) → (v1_xboole_0 esk30_0 → False) → (v1_xboole_0 esk26_0 → False) → (v1_xboole_0 esk21_0 → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk17_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 esk7_0 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk22_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 (esk5_1 X1) X1 → False) → False) → (∀X1, ((k1_card_1 (k1_card_1 X1)) = (k1_card_1 X1) → False) → False) → (∀X1, (r2_wellord2 X1 X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, (v1_xboole_0 (esk18_1 X1) → False) → False) → (∀X1, (v1_card_1 (k1_card_1 X1) → False) → False) → ((v2_finset_1 esk32_0 → False) → False) → ((v4_funct_1 esk30_0 → False) → False) → ((v7_ordinal1 esk26_0 → False) → False) → ((v7_ordinal1 esk23_0 → False) → False) → ((v5_finset_1 esk31_0 → False) → False) → ((v3_funct_1 esk15_0 → False) → False) → ((v1_funcop_1 esk8_0 → False) → False) → ((v1_zfmisc_1 esk13_0 → False) → False) → ((v2_ordinal1 esk17_0 → False) → False) → ((v1_ordinal1 esk17_0 → False) → False) → ((v1_finset_1 esk31_0 → False) → False) → ((v1_finset_1 esk21_0 → False) → False) → ((v1_finset_1 esk7_0 → False) → False) → ((v1_xboole_0 esk12_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v3_ordinal1 esk17_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((v1_card_1 esk6_0 → False) → False) → ((v2_funct_1 esk16_0 → False) → False) → ((v1_funct_1 esk32_0 → False) → False) → ((v1_funct_1 esk25_0 → False) → False) → ((v1_funct_1 esk21_0 → False) → False) → ((v1_funct_1 esk16_0 → False) → False) → ((v1_funct_1 esk15_0 → False) → False) → ((v1_funct_1 esk9_0 → False) → False) → ((v1_funct_1 esk8_0 → False) → False) → ((v1_relat_1 esk32_0 → False) → False) → ((v1_relat_1 esk25_0 → False) → False) → ((v1_relat_1 esk21_0 → False) → False) → ((v1_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v1_relat_1 esk9_0 → False) → False) → ((v1_relat_1 esk8_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False