Theorem. (
t42_ordinal3)
∀esk4_3 : set → set → set → set, ∀k9_xtuple_0 : set → set, ∀v1_relat_1 : set → prop, ∀v1_funct_1 : set → prop, ∀k10_xtuple_0 : set → set, ∀esk5_2 : set → set → set, ∀k1_xboole_0 : set, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk17_2 : set → set → set, ∀k3_ordinal2 : set → set, ∀esk7_2 : set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_ordinal2 : set → prop, ∀v5_ordinal1 : set → prop, ∀k4_ordinal2 : set → set, ∀esk16_0 : set, ∀esk12_0 : set, ∀esk8_1 : set → set, ∀esk15_0 : set, ∀o_0_0_xboole_0 : set, ∀esk13_0 : set, ∀esk9_0 : set, ∀esk10_0 : set, ∀esk11_0 : set, ∀esk14_0 : set, ∀v7_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v1_xboole_0 : set → prop, ∀v1_ordinal1 : set → prop, ∀r1_tarski : set → set → prop, ∀r1_ordinal1 : set → set → prop, ∀esk6_2 : set → set → set, ∀k1_funct_1 : set → set → set, ∀v3_ordinal1 : set → prop, ∀v4_ordinal1 : set → prop, ∀esk18_3 : set → set → set → set, ∀k11_ordinal2 : set → set → set, ∀r2_hidden : set → set → prop, (∀X2 X1 X3, (r2_hidden X1 (k11_ordinal2 (esk18_3 X1 X2 X3) X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X2 → r2_hidden X1 (k11_ordinal2 X2 X3) → False) → (∀X2 X1 X3, (r2_hidden (esk18_3 X1 X2 X3) X2 → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X2 → r2_hidden X1 (k11_ordinal2 X2 X3) → False) → (∀X2 X1 X3, (v3_ordinal1 (esk18_3 X1 X2 X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → v4_ordinal1 X2 → r2_hidden X1 (k11_ordinal2 X2 X3) → False) → (∀X3 X2 X1, (r2_hidden (esk4_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 (esk4_3 X2 X3 X1)) = X1 → False) → X3 = (k10_xtuple_0 X2) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 X3 → False) → (∀X3 X2 X1, (X2 = (k10_xtuple_0 X1) → False) → (esk5_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 (esk5_2 X1 X2) X2 → False) → (∀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) X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X3 X2 X1, (X1 = k1_xboole_0 → False) → (r2_hidden (k11_ordinal2 X2 X1) (k11_ordinal2 X3 X1) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X2 X3 → False) → (∀X2 X1 X3, (r1_ordinal1 (k11_ordinal2 X1 X3) (k11_ordinal2 X2 X3) → 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 (esk5_2 X1 X2) X2 → False) → (r2_hidden (esk6_2 X1 X2) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 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) → (∀X2 X1, ((k1_funct_1 esk2_0 X1) = (k11_ordinal2 X2 esk3_0) → False) → X2 = (k1_funct_1 esk1_0 X1) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 (k9_xtuple_0 esk1_0) → 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 (esk17_2 X1 X2) X2 → False) → v3_ordinal1 X1 → r2_hidden X1 (k3_ordinal2 X2) → False) → (∀X2 X1, (r1_ordinal1 X1 (esk17_2 X1 X2) → False) → v3_ordinal1 X1 → r2_hidden X1 (k3_ordinal2 X2) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk7_2 X1 X2) X2 → False) → (∀X2 X1, (v3_ordinal1 (esk17_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, (r2_hidden X2 X1 → False) → v1_ordinal1 X1 → r2_hidden X3 X1 → r2_hidden X2 X3 → False) → (∀X2 X1, (v3_ordinal1 (k1_funct_1 X1 X2) → False) → v5_ordinal1 X1 → v1_relat_1 X1 → v1_funct_1 X1 → v1_ordinal2 X1 → v3_ordinal1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r2_hidden X3 X1 → r1_tarski X1 X2 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk7_2 X1 X2) X1 → False) → 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) → (∀X2 X1, (X1 = X2 → False) → r1_tarski X2 X1 → r1_tarski 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, (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, ((k4_ordinal2 X1) = (k3_ordinal2 (k10_xtuple_0 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, (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, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → 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, (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, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k11_ordinal2 (k4_ordinal2 esk1_0) esk3_0) = (k4_ordinal2 esk2_0) → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk12_0 → False) → (esk3_0 = k1_xboole_0 → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, (v3_ordinal1 (k3_ordinal2 X1) → False) → False) → ((v4_ordinal1 (k4_ordinal2 esk1_0) → False) → False) → (((k9_xtuple_0 esk2_0) = (k9_xtuple_0 esk1_0) → False) → False) → ((v7_ordinal1 esk16_0 → False) → False) → ((v7_ordinal1 esk15_0 → False) → False) → ((v1_xboole_0 esk11_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_ordinal1 esk12_0 → False) → False) → ((v2_ordinal1 esk10_0 → False) → False) → ((v1_ordinal1 esk12_0 → False) → False) → ((v1_ordinal1 esk10_0 → False) → False) → ((v4_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 esk12_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 esk9_0 → False) → False) → ((v3_ordinal1 esk3_0 → False) → False) → ((v1_ordinal2 esk13_0 → False) → False) → ((v1_ordinal2 esk2_0 → False) → False) → ((v1_ordinal2 esk1_0 → False) → False) → ((v1_funct_1 esk13_0 → False) → False) → ((v1_funct_1 esk2_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v1_relat_1 esk13_0 → False) → False) → ((v1_relat_1 esk2_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → ((v5_ordinal1 esk13_0 → False) → False) → ((v5_ordinal1 esk2_0 → False) → False) → ((v5_ordinal1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False