Theorem. (
t19_taxonom2)
∀k1_xboole_0 : set, ∀esk13_2 : set → set → set, ∀k5_setfam_1 : set → set → set, ∀esk14_2 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_eqrel_1 : set → set → prop, ∀r1_setfam_1 : set → set → prop, ∀esk5_0 : set, ∀esk2_0 : set, ∀k1_tarski : set → set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk6_0 : set, ∀r1_tarski : set → set → prop, ∀esk15_3 : set → set → set → set, ∀esk7_0 : set, ∀esk17_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀v1_subset_1 : set → set → prop, ∀esk20_1 : set → set, ∀v1_setfam_1 : set → prop, ∀esk22_1 : set → set, ∀esk25_1 : set → set, ∀esk23_1 : set → set, ∀esk18_1 : set → set, ∀esk21_0 : set, ∀esk4_0 : set, ∀esk19_1 : set → set, ∀esk24_0 : set, ∀esk26_1 : set → set, ∀esk27_1 : set → set, ∀esk11_2 : set → set → set, ∀esk8_2 : set → set → set, ∀esk10_2 : set → set → set, ∀esk16_2 : set → set → set, ∀k3_tarski : set → set, ∀esk9_3 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀esk12_3 : set → set → set → set, ∀k2_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk12_3 X1 X2 X3) X3 → r2_hidden (esk12_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk12_3 X1 X2 X3) X3 → r2_hidden (esk12_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk12_3 X1 X2 X3) X3 → False) → (r2_hidden (esk12_3 X1 X2 X3) X2 → False) → (r2_hidden (esk12_3 X1 X2 X3) X1 → False) → False) → (∀X1 X2, ((esk13_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → r1_xboole_0 (esk13_2 X1 X2) (esk14_2 X1 X2) → False) → (∀X3 X2 X1 X4, (X1 = X4 → False) → (r1_xboole_0 X4 X1 → False) → m1_eqrel_1 X3 X2 → r2_hidden X4 X3 → r2_hidden X1 X3 → m1_subset_1 X4 (k1_zfmisc_1 X2) → m1_subset_1 X1 (k1_zfmisc_1 X2) → m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X2)) → False) → (r1_setfam_1 esk3_0 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) → m1_eqrel_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk1_0 → r1_setfam_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk6_0 → False) → (∀X3 X2 X1, (r2_hidden (esk9_3 X1 X2 X3) X2 → False) → r2_hidden X3 X1 → r1_setfam_1 X1 X2 → False) → (∀X1 X3 X2, (r1_tarski X1 (esk9_3 X2 X3 X1) → False) → r2_hidden X1 X2 → r1_setfam_1 X2 X3 → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk16_2 X1 X2) X3 → r2_hidden (esk16_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk15_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk15_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X1 X2, ((esk13_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (m1_subset_1 (esk14_2 X1 X2) (k1_zfmisc_1 X1) → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X1 X2, ((esk13_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (k5_setfam_1 X1 X2) = X1 → (esk14_2 X1 X2) = (esk13_2 X1 X2) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X1 X2, ((esk13_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (r2_hidden (esk14_2 X1 X2) X2 → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → ((r1_setfam_1 esk3_0 esk6_0 → False) → r1_setfam_1 esk3_0 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) → m1_eqrel_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk1_0 → False) → ((r2_hidden esk7_0 esk6_0 → False) → r1_setfam_1 esk3_0 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) → m1_eqrel_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk1_0 → False) → ((m1_eqrel_1 esk6_0 esk1_0 → False) → r1_setfam_1 esk3_0 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) → m1_eqrel_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk1_0 → False) → ((r1_tarski esk2_0 esk7_0 → False) → r1_setfam_1 esk3_0 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) → m1_eqrel_1 (k2_xboole_0 esk5_0 (k1_tarski esk2_0)) esk1_0 → False) → (∀X1 X2, (m1_eqrel_1 X2 X1 → False) → (m1_subset_1 (esk13_2 X1 X2) (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, X1 = k1_xboole_0 → m1_eqrel_1 X2 X3 → r2_hidden X1 X2 → m1_subset_1 X1 (k1_zfmisc_1 X3) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X3)) → False) → (∀X1 X2, (m1_eqrel_1 X2 X1 → False) → (r2_hidden (esk13_2 X1 X2) X2 → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk16_2 X1 X2) X2 → False) → (r2_hidden (esk16_2 X1 X2) (esk17_2 X1 X2) → False) → False) → (∀X1 X3 X2, (r1_setfam_1 X3 X2 → False) → r2_hidden X1 X2 → r1_tarski (esk10_2 X3 X2) X1 → 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) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → (esk8_2 X1 X2) = X1 → r2_hidden (esk8_2 X1 X2) X2 → False) → (∀X1 X2, ((k5_setfam_1 X1 X2) = X1 → False) → m1_eqrel_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk16_2 X1 X2) X2 → False) → (r2_hidden (esk17_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, (r1_tarski X1 X2 → False) → r2_hidden (esk11_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) → (∀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) → (∀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) → (∀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) → ((esk8_2 X1 X2) = X1 → False) → (r2_hidden (esk8_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) → (∀X1, (r1_tarski X1 esk2_0 → False) → (r1_tarski esk2_0 X1 → False) → (r1_xboole_0 esk2_0 X1 → False) → r2_hidden X1 esk3_0 → 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_eqrel_1 X1 X2 → False) → (∀X1 X2, (r1_setfam_1 X1 X2 → False) → (r2_hidden (esk10_2 X1 X2) X1 → False) → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk11_2 X1 X2) X1 → False) → False) → (∀X1, (r2_hidden X1 esk5_0 → False) → r2_hidden X1 esk3_0 → r1_xboole_0 X1 esk2_0 → 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, (v1_xboole_0 X1 → False) → r1_tarski X1 X2 → r1_xboole_0 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) → (∀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, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 X2 → m1_eqrel_1 X2 X1 → False) → (∀X2 X1 X3, (X1 = X3 → False) → X2 = (k1_tarski X3) → r2_hidden X1 X2 → False) → (∀X1, (r1_xboole_0 X1 esk2_0 → False) → r2_hidden X1 esk5_0 → False) → (∀X1, (r2_hidden X1 esk3_0 → False) → r2_hidden X1 esk5_0 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (v1_setfam_1 X1 → False) → m1_eqrel_1 X1 X2 → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k1_tarski X2) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk27_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_eqrel_1 (esk26_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_eqrel_1 (esk22_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk26_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk22_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk20_1 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, (v1_xboole_0 X1 → False) → (v1_setfam_1 (esk26_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_setfam_1 (esk22_1 X1) → False) → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, v1_subset_1 (esk25_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v1_xboole_0 esk24_0 → False) → (v1_xboole_0 esk2_0 → False) → (v1_xboole_0 esk1_0 → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (k1_zfmisc_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 (esk25_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk19_1 X1) X1 → False) → False) → (∀X1, (m1_eqrel_1 (esk18_1 X1) X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_setfam_1 X1 X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → ((r2_hidden esk4_0 esk3_0 → False) → False) → ((m1_eqrel_1 esk3_0 esk1_0 → False) → False) → ((r1_tarski esk4_0 esk2_0 → False) → False) → ((r1_tarski esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk23_1 X1) → False) → False) → ((v1_xboole_0 esk21_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → False