Theorem. (
t9_partit1)
∀v1_xboole_0 : set → prop, ∀esk5_3 : set → set → set → set, ∀r1_tarski : set → set → prop, ∀m1_eqrel_1 : set → set → prop, ∀r1_partit1 : set → set → set → prop, ∀k1_xboole_0 : set, ∀esk7_2 : set → set → set, ∀k5_setfam_1 : set → set → set, ∀esk8_2 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀esk10_2 : set → set → set, ∀v1_subset_1 : set → set → prop, ∀esk26_2 : set → set → set, ∀v5_membered : set → prop, ∀v3_membered : set → prop, ∀v1_membered : set → prop, ∀v7_ordinal1 : set → prop, ∀v1_rat_1 : set → prop, ∀v1_xxreal_0 : set → prop, ∀esk16_1 : set → set, ∀v1_setfam_1 : set → prop, ∀esk24_1 : set → set, ∀v7_membered : set → prop, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk22_0 : set, ∀esk19_0 : set, ∀esk20_1 : set → set, ∀esk13_1 : set → set, ∀esk17_0 : set, ∀esk14_1 : set → set, ∀esk15_0 : set, ∀esk21_0 : set, ∀esk23_1 : set → set, ∀esk18_1 : set → set, ∀esk25_1 : set → set, ∀v1_xcmplx_0 : set → prop, ∀v1_xreal_0 : set → prop, ∀v1_int_1 : set → prop, ∀v2_membered : set → prop, ∀v4_membered : set → prop, ∀v6_membered : set → prop, ∀esk6_2 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk11_2 : set → set → set, ∀esk9_3 : set → set → set → set, ∀k9_subset_1 : set → set → set → set, ∀k3_tarski : set → set, ∀r2_hidden : set → set → prop, ∀esk12_3 : set → set → set → set, ∀k3_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk12_3 X1 X2 X3) X3 → r2_hidden (esk12_3 X1 X2 X3) X2 → r2_hidden (esk12_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk12_3 X1 X2 X3) X3 → False) → (r2_hidden (esk12_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk12_3 X1 X2 X3) X3 → False) → (r2_hidden (esk12_3 X1 X2 X3) X2 → False) → False) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (r1_tarski (esk5_3 X1 X2 X3) X2 → False) → m1_eqrel_1 X2 X1 → r1_partit1 X1 X2 X3 → False) → (∀X3 X1 X2, ((k3_tarski (esk5_3 X2 X3 X1)) = X1 → False) → (v1_xboole_0 X2 → False) → m1_eqrel_1 X3 X2 → r1_partit1 X2 X3 X1 → False) → (∀X1 X2, ((esk7_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 (esk7_2 X1 X2) (esk8_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) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (esk5_3 X1 X2 X3) = k1_xboole_0 → m1_eqrel_1 X2 X1 → r1_partit1 X1 X2 X3 → False) → (∀X3 X2 X1, (m1_subset_1 (k9_subset_1 X2 X3 X1) (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) → (∀X1 X2, ((esk7_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (m1_subset_1 (esk8_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, ((esk7_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (k5_setfam_1 X1 X2) = X1 → (esk8_2 X1 X2) = (esk7_2 X1 X2) → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X1 X2, ((esk7_2 X1 X2) = k1_xboole_0 → False) → (m1_eqrel_1 X2 X1 → False) → (r2_hidden (esk8_2 X1 X2) X2 → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X1 X3) = (k9_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1 X2, (m1_eqrel_1 X2 X1 → False) → (m1_subset_1 (esk7_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 (esk7_2 X1 X2) X2 → False) → (k5_setfam_1 X1 X2) = X1 → m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1)) → False) → (∀X4 X3 X2 X1, (X1 = k1_xboole_0 → False) → (v1_xboole_0 X4 → False) → (r1_partit1 X4 X2 X3 → False) → X3 = (k3_tarski X1) → m1_eqrel_1 X2 X4 → r1_tarski X1 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) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X1) = (k3_xboole_0 X3 X1) → 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 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) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X3) = X3 → False) → m1_subset_1 X1 (k1_zfmisc_1 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 X3 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_xboole_0 X2 X3) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk6_2 X1 X2) 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) → (∀X1 X2 X3, r1_xboole_0 X2 X3 → r2_hidden X1 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 = (k3_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X4 X2) → r2_hidden X1 X3 → False) → (∀X2 X1 X3, (r1_tarski X1 X3 → False) → r1_tarski X2 X3 → r1_tarski X1 X2 → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r2_hidden X3 X1 → 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_eqrel_1 X1 X2 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) X1 → False) → False) → (∀X1 X2, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk26_2 X1 X2) X1 → False) → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk26_2 X1 X2) X2 → 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) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v6_membered (k2_xboole_0 X1 X2) → False) → v6_membered X2 → v6_membered X1 → False) → (∀X2 X1, (v5_membered (k2_xboole_0 X1 X2) → False) → v5_membered X2 → v5_membered X1 → False) → (∀X2 X1, (v4_membered (k2_xboole_0 X1 X2) → False) → v4_membered X2 → v4_membered X1 → False) → (∀X2 X1, (v3_membered (k2_xboole_0 X1 X2) → False) → v3_membered X2 → v3_membered X1 → False) → (∀X2 X1, (v2_membered (k2_xboole_0 X1 X2) → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (v1_membered (k2_xboole_0 X1 X2) → False) → v1_membered X2 → v1_membered X1 → False) → (∀X1 X2, (v6_membered X2 → False) → v6_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v5_membered X2 → False) → v5_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v4_membered X2 → False) → v4_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v3_membered X2 → False) → v3_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v2_membered X2 → False) → v2_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_membered X2 → False) → v1_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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, (v6_membered (k3_xboole_0 X1 X2) → False) → v6_membered X1 → False) → (∀X2 X1, (v6_membered (k3_xboole_0 X2 X1) → False) → v6_membered X1 → False) → (∀X2 X1, (v5_membered (k3_xboole_0 X1 X2) → False) → v5_membered X1 → False) → (∀X2 X1, (v5_membered (k3_xboole_0 X2 X1) → False) → v5_membered X1 → False) → (∀X2 X1, (v4_membered (k3_xboole_0 X1 X2) → False) → v4_membered X1 → False) → (∀X2 X1, (v4_membered (k3_xboole_0 X2 X1) → False) → v4_membered X1 → False) → (∀X2 X1, (v3_membered (k3_xboole_0 X1 X2) → False) → v3_membered X1 → False) → (∀X2 X1, (v3_membered (k3_xboole_0 X2 X1) → False) → v3_membered X1 → False) → (∀X2 X1, (v2_membered (k3_xboole_0 X1 X2) → False) → v2_membered X1 → False) → (∀X2 X1, (v2_membered (k3_xboole_0 X2 X1) → False) → v2_membered X1 → False) → (∀X2 X1, (v1_membered (k3_xboole_0 X1 X2) → False) → v1_membered X1 → False) → (∀X2 X1, (v1_membered (k3_xboole_0 X2 X1) → False) → v1_membered X1 → 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) → (∀X1 X2, (v7_ordinal1 X2 → False) → v6_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_int_1 X2 → False) → v5_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_rat_1 X2 → False) → v4_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xreal_0 X2 → False) → v3_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xxreal_0 X2 → False) → v2_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xcmplx_0 X2 → False) → v1_membered X1 → m1_subset_1 X2 X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 X2 → m1_eqrel_1 X2 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk25_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk16_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) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk25_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_eqrel_1 (esk24_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_eqrel_1 (esk18_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk24_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk18_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk16_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 (esk24_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_setfam_1 (esk18_1 X1) → False) → False) → (∀X1, (v7_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v6_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_membered X1 → False) → v6_membered X1 → False) → (∀X1, (v4_membered X1 → False) → v5_membered X1 → False) → (∀X1, (v3_membered X1 → False) → v4_membered X1 → False) → (∀X1, (v2_membered X1 → False) → v3_membered X1 → False) → (∀X1, (v1_membered X1 → False) → v3_membered X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_partit1 esk1_0 esk2_0 (k9_subset_1 esk1_0 esk3_0 esk4_0) → False) → (∀X1, v1_subset_1 (esk23_1 X1) X1 → False) → (r1_xboole_0 esk3_0 esk4_0 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk22_0 → False) → (v1_xboole_0 esk21_0 → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk1_0 → False) → ((r1_partit1 esk1_0 esk2_0 esk4_0 → False) → False) → ((r1_partit1 esk1_0 esk2_0 esk3_0 → False) → False) → (∀X1 X2, (r1_tarski (k3_xboole_0 X1 X2) X1 → False) → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk14_1 X1) X1 → False) → False) → (∀X1, (m1_eqrel_1 (esk13_1 X1) X1 → False) → False) → ((m1_subset_1 esk4_0 (k1_zfmisc_1 esk1_0) → False) → False) → ((m1_subset_1 esk3_0 (k1_zfmisc_1 esk1_0) → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((m1_eqrel_1 esk2_0 esk1_0 → False) → False) → (∀X1, (v1_xboole_0 (esk20_1 X1) → False) → False) → ((v7_membered esk22_0 → False) → False) → ((v6_membered esk22_0 → False) → False) → ((v6_membered esk19_0 → False) → False) → ((v6_membered esk15_0 → False) → False) → ((v1_xboole_0 esk17_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → (((k3_tarski k1_xboole_0) = k1_xboole_0 → False) → False) → False