Theorem. (
l46_zf_fund1)
∀v1_relat_1 : set → prop, ∀esk5_2 : set → set → set, ∀esk4_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, ∀esk9_2 : set → set → set, ∀v2_relat_1 : set → prop, ∀v1_finset_1 : set → prop, ∀v2_finset_1 : set → prop, ∀r1_tarski : set → set → prop, ∀v5_finset_1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v5_ordinal1 : set → prop, ∀esk35_1 : set → set, ∀esk18_1 : set → set, ∀esk30_1 : set → set, ∀v3_funct_1 : set → prop, ∀v7_ordinal1 : set → prop, ∀k4_ordinal1 : set, ∀k1_xboole_0 : set, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀esk23_0 : set, ∀esk38_0 : set, ∀esk36_0 : set, ∀esk27_0 : set, ∀esk20_0 : set, ∀esk11_0 : set, ∀v1_xtuple_0 : set → prop, ∀esk8_1 : set → set, ∀v2_xxreal_0 : set → prop, ∀esk22_0 : set, ∀v2_card_1 : set → prop, ∀esk25_0 : set, ∀esk19_0 : set, ∀esk13_0 : set, ∀o_0_0_xboole_0 : set, ∀esk12_0 : set, ∀esk10_0 : set, ∀esk17_0 : set, ∀esk15_0 : set, ∀esk28_0 : set, ∀esk21_0 : set, ∀esk29_0 : set, ∀esk16_0 : set, ∀k5_numbers : set, ∀esk14_0 : set, ∀esk24_0 : set, ∀esk32_0 : set, ∀esk37_0 : set, ∀esk31_0 : set, ∀v1_xcmplx_0 : set → prop, ∀v1_xxreal_0 : set → prop, ∀k1_numbers : set, ∀v1_xreal_0 : set → prop, ∀v2_funct_1 : set → prop, ∀np__1 : set, ∀esk33_1 : set → set, ∀esk34_1 : set → set, ∀esk26_1 : set → set, ∀v3_ordinal1 : set → prop, ∀v1_zfmisc_1 : set → prop, ∀v3_relat_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v1_card_1 : set → prop, ∀v3_card_1 : set → set → prop, ∀esk6_1 : set → set, ∀v1_funct_1 : set → prop, ∀esk7_3 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀k1_funct_1 : set → set → set, ∀k1_tarski : set → set, ∀k2_tarski : set → set → set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀k9_xtuple_0 : set → set, ((k2_tarski esk1_0 esk2_0) = (k9_xtuple_0 esk3_0) → (k2_tarski (k2_tarski (k2_tarski esk1_0 (k1_funct_1 esk3_0 esk1_0)) (k1_tarski esk1_0)) (k2_tarski (k2_tarski esk2_0 (k1_funct_1 esk3_0 esk2_0)) (k1_tarski esk2_0))) = esk3_0 → False) → (((k2_tarski esk1_0 esk2_0) = (k9_xtuple_0 esk3_0) → False) → ((k2_tarski (k2_tarski (k2_tarski esk1_0 (k1_funct_1 esk3_0 esk1_0)) (k1_tarski esk1_0)) (k2_tarski (k2_tarski esk2_0 (k1_funct_1 esk3_0 esk2_0)) (k1_tarski esk2_0))) = esk3_0 → False) → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → (esk7_3 X1 X2 X3) = X1 → r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → (esk7_3 X1 X2 X3) = X2 → r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → ((esk7_3 X1 X2 X3) = X2 → False) → ((esk7_3 X1 X2 X3) = X1 → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → False) → (∀X2 X1, ((k2_tarski (k2_tarski (esk4_2 X1 X2) (esk5_2 X1 X2)) (k1_tarski (esk4_2 X1 X2))) = X2 → False) → v1_relat_1 X1 → r2_hidden X2 X1 → False) → (∀X3 X1 X2, (r2_hidden X1 (k9_xtuple_0 X2) → False) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X2 → False) → (∀X1 X3 X2, (X1 = (k1_funct_1 X2 X3) → False) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) X2 → False) → (∀X3 X1 X2, (r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X2 → False) → X3 = (k1_funct_1 X2 X1) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) = (k2_tarski (k2_tarski X2 X4) (k1_tarski X2)) → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) = (k2_tarski (k2_tarski X4 X2) (k1_tarski X4)) → 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 (esk9_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, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_relat_1 X1 → v1_xboole_0 (k1_funct_1 X1 X2) → m1_subset_1 X2 (k9_xtuple_0 X1) → False) → (∀X3 X2 X1, (v1_relat_1 X1 → False) → (esk6_1 X1) = (k2_tarski (k2_tarski X2 X3) (k1_tarski X2)) → 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, (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) → (∀X1 X2, (v4_funct_1 (k2_tarski X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (v1_finset_1 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_finset_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v3_relat_1 X1 → 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) → (∀X3 X2 X1 X4, (X1 = X4 → False) → (X1 = X3 → False) → X2 = (k2_tarski X3 X4) → r2_hidden X1 X2 → 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, (v5_finset_1 (k2_tarski X1 X2) → False) → v1_finset_1 X2 → v1_finset_1 X1 → 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_finset_1 X2 → False) → v1_finset_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) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k2_tarski X2 X4) → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k2_tarski X4 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, (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, (v3_ordinal1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v5_ordinal1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk26_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk35_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk34_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k9_xtuple_0 X1) → False) → (∀X1, (v3_card_1 (esk33_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v3_card_1 (esk30_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_relat_1 X1 → False) → (r2_hidden (esk6_1 X1) X1 → False) → False) → (∀X1, (v4_funct_1 (k1_tarski X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_finset_1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_finset_1 X1 → False) → (∀X1, (v1_zfmisc_1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v1_finset_1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → 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 (esk34_1 X1) np__1 → False) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (esk26_1 X1) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (k1_zfmisc_1 X1) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk35_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk18_1 X1) → False) → (∀X1, (v3_card_1 X1 k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_finset_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v2_relat_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_relat_1 X1 → 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, (v5_finset_1 (k1_tarski X1) → False) → v1_finset_1 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 (k9_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_funct_1 (esk33_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (v1_relat_1 (esk33_1 X1) → False) → v1_card_1 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 (esk35_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_finset_1 (esk18_1 X1) → False) → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_finset_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → v7_ordinal1 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) → v7_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_card_1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 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, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (v3_funct_1 esk31_0 → False) → (v1_finset_1 esk23_0 → False) → (v1_finset_1 k4_ordinal1 → False) → (v1_xboole_0 esk38_0 → False) → (v1_xboole_0 esk37_0 → False) → (v1_xboole_0 esk36_0 → False) → (v1_xboole_0 esk32_0 → False) → (v1_xboole_0 esk27_0 → False) → (v1_xboole_0 esk24_0 → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 k4_ordinal1 → False) → (v1_xboole_0 np__1 → False) → (∀X1 X2 X3 X4, (v1_relat_1 (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_tarski (k2_tarski X3 X4) (k1_tarski X3))) → False) → False) → (∀X1 X2, (v1_funct_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) → False) → False) → (∀X1 X2, (v1_relat_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) → False) → False) → (∀X2 X1, (v1_xtuple_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) → False) → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → (∀X1 X2, (v1_finset_1 (k2_tarski X1 X2) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → (∀X1, (v3_card_1 (k1_tarski X1) np__1 → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((m1_subset_1 k1_xboole_0 k4_ordinal1 → False) → False) → ((m1_subset_1 np__1 k5_numbers → False) → False) → ((m1_subset_1 np__1 k1_numbers → False) → False) → (∀X1, (v1_finset_1 (k1_tarski X1) → False) → False) → ((v2_xxreal_0 esk22_0 → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v2_card_1 k4_ordinal1 → False) → False) → ((v1_xtuple_0 esk16_0 → False) → False) → ((v2_finset_1 esk38_0 → False) → False) → ((v4_funct_1 esk36_0 → False) → False) → ((v5_finset_1 esk37_0 → False) → False) → ((v1_xxreal_0 esk29_0 → False) → False) → ((v1_xxreal_0 esk22_0 → False) → False) → ((v2_relat_1 esk27_0 → False) → False) → ((v2_relat_1 esk25_0 → False) → False) → ((v2_relat_1 esk21_0 → False) → False) → ((v1_xcmplx_0 esk29_0 → False) → False) → ((v1_xcmplx_0 esk22_0 → False) → False) → ((v7_ordinal1 esk32_0 → False) → False) → ((v7_ordinal1 esk28_0 → False) → False) → ((v2_funct_1 esk19_0 → False) → False) → ((v1_xreal_0 esk29_0 → False) → False) → ((v1_xreal_0 esk22_0 → False) → False) → ((v1_xreal_0 esk15_0 → False) → False) → ((v2_ordinal1 esk20_0 → False) → False) → ((v2_ordinal1 esk17_0 → False) → False) → ((v1_ordinal1 esk20_0 → False) → False) → ((v1_ordinal1 esk17_0 → False) → False) → ((v1_finset_1 esk37_0 → False) → False) → ((v1_finset_1 esk24_0 → False) → False) → ((