Theorem. (
t46_arytm_3)
∀k1_xboole_0 : set, ∀k2_tarski : set → set → set, ∀k1_tarski : set → set, ∀k4_ordinal1 : set, ∀r1_arytm_3 : set → set → prop, ∀r2_hidden : set → set → prop, ∀a_0_0_arytm_3 : set, ∀v7_ordinal1 : set → prop, ∀esk8_1 : set → set, ∀esk7_1 : set → set, ∀esk9_1 : set → set, ∀v6_ordinal1 : set → prop, ∀esk19_1 : set → set, ∀esk20_0 : set, ∀esk14_0 : set, ∀k6_subset_1 : set → set → set, ∀esk5_1 : set → set, ∀esk13_0 : set, ∀esk11_0 : set, ∀esk18_0 : set, ∀v2_xxreal_0 : set → prop, ∀esk15_1 : set → set, ∀k5_numbers : set, ∀k1_numbers : set, ∀esk10_0 : set, ∀esk16_0 : set, ∀esk17_1 : set → set, ∀esk1_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀v5_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀esk12_1 : set → set, ∀r1_tarski : set → set → prop, ∀k2_xboole_0 : set → set → set, ∀v1_subset_1 : set → set → prop, ∀k6_ordinal3 : set → set → set, ∀k3_arytm_3 : set → set → set, ∀k4_arytm_3 : set → set → set, ∀np__1 : set, ∀a_0_1_arytm_3 : set, ∀esk21_2 : set → set → set, ∀esk6_2 : set → set → set, ∀k11_ordinal2 : set → set → set, ∀k10_ordinal2 : set → set → set, ∀v3_ordinal1 : set → prop, ∀m2_subset_1 : set → set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀k9_arytm_3 : set → set → set, ∀k9_ordinal3 : set → set → set, ∀k7_arytm_3 : set → set, ∀k6_arytm_3 : set → set, ∀k8_ordinal3 : set → set → set, ∀k8_arytm_3 : set → set → set, ∀k5_arytm_3 : set, ∀m1_subset_1 : set → set → prop, (∀X2 X1, ((k8_arytm_3 (k8_ordinal3 (k9_ordinal3 (k6_arytm_3 X1) (k7_arytm_3 X2)) (k9_ordinal3 (k6_arytm_3 X2) (k7_arytm_3 X1))) (k9_ordinal3 (k7_arytm_3 X1) (k7_arytm_3 X2))) = (k9_arytm_3 X1 X2) → False) → m1_subset_1 X2 k5_arytm_3 → m1_subset_1 X1 k5_arytm_3 → False) → (∀X3 X1 X2, (X2 = k1_xboole_0 → False) → (r2_hidden X3 a_0_0_arytm_3 → False) → X3 = (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) → r1_arytm_3 X1 X2 → m1_subset_1 X2 k4_ordinal1 → m1_subset_1 X1 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 X3, ((k10_ordinal2 (k11_ordinal2 X1 X3) (k11_ordinal2 X2 X3)) = (k11_ordinal2 (k10_ordinal2 X1 X2) X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X3 X2 X1, (X1 = k1_xboole_0 → False) → ((k8_arytm_3 (k9_ordinal3 X2 X1) (k9_ordinal3 X3 X1)) = (k8_arytm_3 X2 X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X3 → v7_ordinal1 X2 → v7_ordinal1 X1 → 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 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk21_2 X3 X2) → False) → (∀X1, ((k2_tarski (k2_tarski (esk7_1 X1) (esk8_1 X1)) (k1_tarski (esk7_1 X1))) = X1 → False) → r2_hidden X1 a_0_0_arytm_3 → False) → (∀X1 X2, (r2_hidden X2 a_0_1_arytm_3 → False) → X2 = (k2_tarski (k2_tarski X1 np__1) (k1_tarski X1)) → m1_subset_1 X1 k4_ordinal1 → 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) → (∀X1 X2, ((k9_ordinal3 (k4_arytm_3 X1 X2) (k3_arytm_3 X1 X2)) = X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1, ((k2_tarski (k2_tarski (esk9_1 X1) np__1) (k1_tarski (esk9_1 X1))) = X1 → False) → r2_hidden X1 a_0_1_arytm_3 → False) → (∀X1 X2, ((k6_ordinal3 X1 (k3_arytm_3 X1 X2)) = (k4_arytm_3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (m1_subset_1 (k9_arytm_3 X1 X2) k5_arytm_3 → False) → m1_subset_1 X2 k5_arytm_3 → m1_subset_1 X1 k5_arytm_3 → False) → (∀X1 X2, (X2 = k1_xboole_0 → False) → ((k7_arytm_3 (k8_arytm_3 X1 X2)) = (k4_arytm_3 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (X2 = k1_xboole_0 → False) → ((k6_arytm_3 (k8_arytm_3 X1 X2)) = (k4_arytm_3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_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) → (∀X2 X1, ((k9_arytm_3 X1 X2) = (k9_arytm_3 X2 X1) → False) → m1_subset_1 X2 k5_arytm_3 → m1_subset_1 X1 k5_arytm_3 → False) → (∀X1 X2, (m1_subset_1 (k4_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, (m1_subset_1 (k8_arytm_3 X1 X2) k5_arytm_3 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (r2_hidden (esk21_2 X1 X2) X2 → False) → r2_hidden 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 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 (k6_ordinal3 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (k8_ordinal3 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) → (∀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) → (∀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, ((k8_ordinal3 X1 X2) = (k10_ordinal2 X1 X2) → 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, ((k8_ordinal3 X1 X2) = (k8_ordinal3 X2 X1) → 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) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (k3_arytm_3 X1 X2) = k1_xboole_0 → v3_ordinal1 X2 → v3_ordinal1 X1 → v7_ordinal1 X2 → v7_ordinal1 X1 → 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_arytm_3 X2 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_arytm_3 X1 X2 → False) → (∀X1, (r1_arytm_3 (esk7_1 X1) (esk8_1 X1) → False) → r2_hidden X1 a_0_0_arytm_3 → 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, (v7_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_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) → (∀X2 X1, (v3_ordinal1 (k2_xboole_0 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) → (∀X1, (m1_subset_1 (esk9_1 X1) k4_ordinal1 → False) → r2_hidden X1 a_0_1_arytm_3 → False) → (∀X1, (m1_subset_1 (esk8_1 X1) k4_ordinal1 → False) → r2_hidden X1 a_0_0_arytm_3 → False) → (∀X1, (m1_subset_1 (esk7_1 X1) k4_ordinal1 → False) → r2_hidden X1 a_0_0_arytm_3 → False) → (∀X1, (m1_subset_1 (k7_arytm_3 X1) k4_ordinal1 → False) → m1_subset_1 X1 k5_arytm_3 → False) → (∀X1, (m1_subset_1 (k6_arytm_3 X1) k4_ordinal1 → False) → m1_subset_1 X1 k5_arytm_3 → 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, (v7_ordinal1 X1 → False) → v3_ordinal1 X1 → m1_subset_1 X1 k5_arytm_3 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (esk8_1 X1) = k1_xboole_0 → r2_hidden X1 a_0_0_arytm_3 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk19_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 (esk12_1 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) → ((k8_arytm_3 (k8_ordinal3 (k9_ordinal3 esk3_0 esk1_0) (k9_ordinal3 esk2_0 esk4_0)) (k9_ordinal3 esk2_0 esk1_0)) = (k9_arytm_3 (k8_arytm_3 esk3_0 esk2_0) (k8_arytm_3 esk4_0 esk1_0)) → False) → (∀X1 X2, v1_xboole_0 (k2_tarski X1 X2) → False) → (∀X1, v1_subset_1 (esk17_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 np__1 → False) → (v1_xboole_0 k4_ordinal1 → False) → (v1_xboole_0 k5_arytm_3 → False) → (esk2_0 = k1_xboole_0 → False) → (esk1_0 = k1_xboole_0 → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → (∀X1 X2, (m1_subset_1 (k6_subset_1 X1 X2) (k1_zfmisc_1 X1) → False) → False) → (((k2_xboole_0 (k6_subset_1 a_0_0_arytm_3 a_0_1_arytm_3) k4_ordinal1) = k5_arytm_3 → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 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, ((k6_subset_1 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k6_subset_1 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → ((m1_subset_1 esk10_0 k5_arytm_3 → 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 (esk15_1 X1) → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v1_xboole_0 esk13_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_ordinal1 esk14_0 → False) → False) → ((v1_ordinal1 esk14_0 → False) → False) → ((v7_ordinal1 esk20_0 → False) → False) → ((v7_ordinal1 esk18_0 → False) → False) → ((v7_ordinal1 esk4_0 → False) → False) → ((v7_ordinal1 esk3_0 → False) → False) → ((v7_ordinal1 esk2_0 → False) → False) → ((v7_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 esk14_0 → False) → False) → ((v3_ordinal1 esk11_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 esk4_0 → False) → False) → ((v3_ordinal1 esk3_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v3_ordinal1 esk1_0 → False) → False) → ((v3_ordinal1 k4_ordinal1 → False) → False) → False