Theorem. (
t19_arytm_3)
∀k9_ordinal3 : set → set → set, ∀k6_ordinal3 : set → set → set, ∀esk3_2 : set → set → set, ∀esk4_2 : set → set → set, ∀k1_xboole_0 : set, ∀k2_arytm_3 : set → set → set, ∀v6_ordinal1 : set → prop, ∀esk18_1 : set → set, ∀esk15_0 : set, ∀k1_numbers : set, ∀k5_numbers : set, ∀esk14_1 : set → set, ∀esk12_0 : set, ∀esk10_0 : set, ∀esk17_0 : set, ∀v2_xxreal_0 : set → prop, ∀esk8_1 : set → set, ∀esk13_0 : set, ∀esk19_0 : set, ∀esk16_1 : set → set, ∀esk1_0 : set, ∀esk2_0 : set, ∀v5_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀esk11_1 : set → set, ∀r1_tarski : set → set → prop, ∀v1_subset_1 : set → set → prop, ∀esk6_2 : set → set → set, ∀esk5_2 : set → set → set, ∀r2_hidden : set → set → prop, ∀k11_ordinal2 : set → set → set, ∀r1_arytm_3 : set → set → prop, ∀np__1 : set, ∀esk9_2 : set → set → set, ∀m2_subset_1 : set → set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀v3_ordinal1 : set → prop, ∀v7_ordinal1 : set → prop, ∀r2_arytm_3 : set → set → prop, ∀esk7_3 : set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k4_ordinal1 : set, ∀k3_arytm_3 : set → set → set, (∀X1 X3 X2, (X3 = (k3_arytm_3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X3 X2 → r2_arytm_3 X3 X1 → m1_subset_1 X3 k4_ordinal1 → r2_arytm_3 (esk7_3 X1 X2 X3) X3 → False) → (∀X1 X3 X2, (X3 = (k3_arytm_3 X1 X2) → False) → (r2_arytm_3 (esk7_3 X1 X2 X3) X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X3 X2 → r2_arytm_3 X3 X1 → m1_subset_1 X3 k4_ordinal1 → False) → (∀X1 X3 X2, (X3 = (k3_arytm_3 X1 X2) → False) → (r2_arytm_3 (esk7_3 X1 X2 X3) X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X3 X2 → r2_arytm_3 X3 X1 → m1_subset_1 X3 k4_ordinal1 → False) → (∀X1 X3 X2, (X3 = (k3_arytm_3 X1 X2) → False) → (v7_ordinal1 (esk7_3 X1 X2 X3) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X3 X2 → r2_arytm_3 X3 X1 → m1_subset_1 X3 k4_ordinal1 → False) → (∀X1 X3 X2, (X3 = (k3_arytm_3 X1 X2) → False) → (v3_ordinal1 (esk7_3 X1 X2 X3) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X3 X2 → r2_arytm_3 X3 X1 → m1_subset_1 X3 k4_ordinal1 → False) → (∀X3 X2 X1 X4, (r2_arytm_3 X1 X4 → False) → X4 = (k3_arytm_3 X2 X3) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X3 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X1 X3 → r2_arytm_3 X1 X2 → m1_subset_1 X4 k4_ordinal1 → 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 X5 X4 X1 X3, (X3 = np__1 → False) → X2 = (k11_ordinal2 X3 X5) → X1 = (k11_ordinal2 X3 X4) → v3_ordinal1 X5 → v3_ordinal1 X4 → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_arytm_3 X1 X2 → False) → (∀X1 X2, (r2_arytm_3 X2 X1 → False) → (k9_ordinal3 X2 (k6_ordinal3 X1 X2)) = X1 → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (r2_hidden X1 k4_ordinal1 → False) → (v1_xboole_0 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 (k11_ordinal2 X1 X2) → False) → (∀X2 X1, (r2_hidden X1 k4_ordinal1 → False) → (v1_xboole_0 (k11_ordinal2 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 (k11_ordinal2 X2 X1) → False) → (∀X1 X2 X3, ((k11_ordinal2 (k11_ordinal2 X1 X2) X3) = (k11_ordinal2 X1 (k11_ordinal2 X2 X3)) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, ((k11_ordinal2 (esk3_2 X1 X2) (esk4_2 X1 X2)) = X1 → False) → (r1_arytm_3 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, ((k11_ordinal2 (esk3_2 X2 X1) (esk5_2 X2 X1)) = X1 → False) → (r1_arytm_3 X2 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, ((k9_ordinal3 X1 (k6_ordinal3 X2 X1)) = X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → r2_arytm_3 X1 X2 → False) → (∀X3 X1 X2, (r2_arytm_3 X1 X2 → False) → X1 = (k3_arytm_3 X2 X3) → v3_ordinal1 X3 → v3_ordinal1 X2 → v7_ordinal1 X3 → v7_ordinal1 X2 → m1_subset_1 X1 k4_ordinal1 → False) → (∀X3 X1 X2, (r2_arytm_3 X1 X2 → False) → X1 = (k3_arytm_3 X3 X2) → v3_ordinal1 X3 → v3_ordinal1 X2 → v7_ordinal1 X3 → v7_ordinal1 X2 → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1 X2, ((k11_ordinal2 X2 (esk6_2 X2 X1)) = X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_arytm_3 X2 X1 → False) → (∀X2 X1 X3, (X1 = X3 → False) → (X2 = k1_xboole_0 → False) → (k11_ordinal2 X1 X2) = (k11_ordinal2 X3 X2) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 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, (m1_subset_1 (k2_arytm_3 X1 X2) k4_ordinal1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (m1_subset_1 (k3_arytm_3 X1 X2) k4_ordinal1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (esk6_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_arytm_3 X1 X2 → 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) → (∀X1 X3 X2, (r2_arytm_3 X3 X2 → False) → X2 = (k11_ordinal2 X3 X1) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_arytm_3 X1 X2 → False) → (v3_ordinal1 (esk5_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_arytm_3 X1 X2 → False) → (v3_ordinal1 (esk4_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_arytm_3 X1 X2 → False) → (v3_ordinal1 (esk3_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (v7_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v7_ordinal1 (k6_ordinal3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (k9_ordinal3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (k6_ordinal3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 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, (X1 = k1_xboole_0 → False) → ((k6_ordinal3 (k11_ordinal2 X2 X1) X1) = X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, ((k9_ordinal3 X1 X2) = (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, ((k9_ordinal3 X1 X2) = (k9_ordinal3 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, ((k2_arytm_3 X1 X2) = (k2_arytm_3 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, ((k3_arytm_3 X1 X2) = (k3_arytm_3 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (r1_arytm_3 X2 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_arytm_3 X1 X2 → False) → (∀X2 X1, (r1_arytm_3 X1 X2 → False) → (esk3_2 X1 X2) = np__1 → v3_ordinal1 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, (v3_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k6_ordinal3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 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, (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, (X1 = np__1 → False) → (k11_ordinal2 X1 X2) = np__1 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (X1 = np__1 → False) → (k11_ordinal2 X2 X1) = np__1 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → 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, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk18_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) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (r2_arytm_3 X1 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1, ((k3_arytm_3 X1 k1_xboole_0) = X1 → False) → v3_ordinal1 X1 → v7_ordinal1 X1 → False) → (∀X1, ((k2_arytm_3 X1 k1_xboole_0) = k1_xboole_0 → False) → v3_ordinal1 X1 → v7_ordinal1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk18_1 X1) X1 → False) → False) → (∀X1, (v7_ordinal1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk11_1 X1) → False) → (∀X1, ((k11_ordinal2 np__1 X1) = X1 → False) → v3_ordinal1 X1 → False) → (∀X1, ((k11_ordinal2 X1 np__1) = X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (r1_arytm_3 np__1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, ((k11_ordinal2 k1_xboole_0 X1) = k1_xboole_0 → False) → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → 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, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (k1_xboole_0 = esk1_0 → k1_xboole_0 = esk2_0 → False) → (r1_arytm_3 (k6_ordinal3 esk1_0 (k3_arytm_3 esk1_0 esk2_0)) (k6_ordinal3 esk2_0 (k3_arytm_3 esk1_0 esk2_0)) → False) → (∀X1, v1_subset_1 (esk16_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 np__1 → False) → (v1_xboole_0 k4_ordinal1 → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → (∀X1, (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((m1_subset_1 np__1 k5_numbers → False) → False) → ((m1_subset_1 np__1 k1_numbers → False) → False) → ((m1_subset_1 k1_xboole_0 k4_ordinal1 → False) → False) → (∀X1, (v1_xboole_0 (esk14_1 X1) → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v1_xboole_0 esk12_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_ordinal1 esk13_0 → False) → False) → ((v1_ordinal1 esk13_0 → False) → False) → ((v7_ordinal1 esk19_0 → False) → False) → ((v7_ordinal1 esk17_0 → False) → False) → ((v7_ordinal1 esk2_0 → False) → False) → ((v7_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v3_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 k4_ordinal1 → False) → False) → False