Theorem. (
l18_taxonom2)
∀k2_xboole_0 : set → set → set, ∀esk8_3 : set → set → set → set, ∀esk24_3 : set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v4_taxonom2 : set → prop, ∀esk3_0 : set, ∀esk2_0 : set, ∀k5_setfam_1 : set → set → set, ∀esk1_0 : set, ∀k3_tarski : set → set, ∀esk10_2 : set → set → set, ∀esk11_2 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀v3_taxonom2 : set → prop, ∀m1_taxonom2 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀v1_subset_1 : set → set → prop, ∀esk6_1 : set → set, ∀esk7_1 : set → set, ∀esk17_1 : set → set, ∀esk21_1 : set → set, ∀esk20_0 : set, ∀esk19_1 : set → set, ∀esk16_1 : set → set, ∀esk18_0 : set, ∀esk15_1 : set → set, ∀esk22_1 : set → set, ∀k1_xboole_0 : set, ∀esk23_1 : set → set, ∀esk13_1 : set → set, ∀esk12_1 : set → set, ∀esk5_2 : set → set → set, ∀esk4_2 : set → set → set, ∀k1_tarski : set → set, ∀v3_abian : set → set → prop, ∀esk9_3 : set → set → set → set, ∀k7_subset_1 : set → set → set → set, ∀r1_tarski : set → set → prop, ∀r2_hidden : set → set → prop, ∀esk14_3 : set → set → set → set, ∀k4_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk14_3 X1 X2 X3) X2 → False) → r2_hidden (esk14_3 X1 X2 X3) X3 → r2_hidden (esk14_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X2 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk14_3 X1 X2 X3) X3 → False) → r2_hidden (esk14_3 X1 X2 X3) X2 → False) → (∀X4 X3 X1 X2, (r2_hidden X1 X2 → False) → v4_taxonom2 X2 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X3)) → r2_hidden X1 (esk24_3 X3 X2 X4) → False) → (∀X4 X3 X1 X2, (r1_tarski X1 X2 → False) → v4_taxonom2 X4 → m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X3)) → r2_hidden X1 (esk24_3 X3 X4 X2) → False) → (∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2) → False) → (r2_hidden (esk14_3 X1 X2 X3) X3 → False) → (r2_hidden (esk14_3 X1 X2 X3) X1 → False) → False) → (∀X3 X1 X4 X2, (r2_hidden X1 (esk24_3 X4 X2 X3) → False) → v4_taxonom2 X2 → r1_tarski X1 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X4)) → False) → (∀X1, (esk3_0 = X1 → False) → v4_taxonom2 X1 → r1_tarski X1 esk2_0 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0)) → r1_tarski (k5_setfam_1 esk1_0 esk3_0) (k5_setfam_1 esk1_0 X1) → False) → (∀X3 X2 X1, (m1_subset_1 (k7_subset_1 X2 X1 X3) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk10_2 X1 X2) X3 → r2_hidden (esk10_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk9_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk9_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X2 X1, ((k5_setfam_1 X2 X1) = X2 → False) → v3_abian X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk10_2 X1 X2) X2 → False) → (r2_hidden (esk10_2 X1 X2) (esk11_2 X1 X2) → False) → False) → (∀X1 X2, (v3_abian X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X3 X2 X1, ((k7_subset_1 X2 X1 X3) = (k4_xboole_0 X1 X3) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (m1_subset_1 (k5_setfam_1 X2 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X1 X3 X2, (r1_tarski X3 X2 → False) → (r1_tarski X2 X3 → False) → (r1_xboole_0 X2 X3 → False) → v3_taxonom2 X1 → r2_hidden X3 X1 → r2_hidden X2 X1 → False) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → (esk4_2 X1 X2) = X1 → r2_hidden (esk4_2 X1 X2) X2 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk10_2 X1 X2) X2 → False) → (r2_hidden (esk11_2 X1 X2) X1 → False) → False) → (∀X3 X2 X1, (r1_tarski (k2_xboole_0 X1 X3) X2 → False) → r1_tarski X3 X2 → r1_tarski X1 X2 → False) → (∀X2 X1, (v3_taxonom2 X1 → False) → m1_taxonom2 X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk5_2 X1 X2) X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X2 = (k2_xboole_0 X3 X4) → r2_hidden X1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X4 = (k4_xboole_0 X2 X3) → r2_hidden X1 X2 → False) → (∀X2 X1, (m1_taxonom2 X1 X2 → False) → v3_taxonom2 X1 → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1, ((k5_setfam_1 X2 X1) = (k3_tarski X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X4 X3 X2 X1, X3 = (k4_xboole_0 X4 X2) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X1 X2 X3, (X2 = X3 → False) → (r1_xboole_0 X2 X3 → False) → v4_taxonom2 X1 → r2_hidden X3 X1 → r2_hidden X2 X1 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → 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) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k4_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X2 X4) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X4 X2) → r2_hidden X1 X2 → False) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → ((esk4_2 X1 X2) = X1 → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r1_tarski X1 X2 → r2_hidden X3 X1 → False) → (∀X2 X1 X3, (r1_tarski X1 X3 → False) → r1_tarski X2 X3 → r1_tarski X1 X2 → 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, (m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → m1_taxonom2 X1 X2 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk5_2 X1 X2) X1 → False) → 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) → (∀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) → (∀X1, (v3_taxonom2 X1 → False) → r1_xboole_0 (esk6_1 X1) (esk7_1 X1) → False) → (∀X1, (v3_taxonom2 X1 → False) → r1_tarski (esk7_1 X1) (esk6_1 X1) → False) → (∀X1, (v3_taxonom2 X1 → False) → r1_tarski (esk6_1 X1) (esk7_1 X1) → False) → (∀X1, (v4_taxonom2 X1 → False) → r1_xboole_0 (esk12_1 X1) (esk13_1 X1) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 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, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (X1 = X3 → False) → X2 = (k1_tarski X3) → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k1_tarski X2) → False) → (∀X1, (v3_taxonom2 X1 → False) → (r2_hidden (esk7_1 X1) X1 → False) → False) → (∀X1, (v3_taxonom2 X1 → False) → (r2_hidden (esk6_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk23_1 X1) X1 → False) → False) → (∀X1, (v4_taxonom2 X1 → False) → (r2_hidden (esk13_1 X1) X1 → False) → False) → (∀X1, (v4_taxonom2 X1 → False) → (r2_hidden (esk12_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk17_1 X1) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X1, (v4_taxonom2 X1 → False) → (esk13_1 X1) = (esk12_1 X1) → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, v1_subset_1 (esk21_1 X1) X1 → False) → ((k5_setfam_1 esk1_0 esk3_0) = esk1_0 → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk20_0 → False) → (∀X1 X2, (r1_tarski (k4_xboole_0 X1 X2) X1 → False) → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0)) → False) → False) → ((v3_abian esk2_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0)) → False) → False) → (∀X1, (m1_subset_1 (esk15_1 X1) X1 → False) → False) → (∀X1, (m1_taxonom2 (esk16_1 X1) X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k4_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k4_xboole_0 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → ((r1_tarski esk3_0 esk2_0 → False) → False) → ((m1_taxonom2 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk19_1 X1) → False) → False) → (∀X1, (v4_taxonom2 (esk22_1 X1) → False) → False) → ((v1_xboole_0 esk18_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v4_taxonom2 esk3_0 → False) → False) → False