Theorem. (t17_partit1)
∀k3_xboole_0 : setsetset, ∀esk12_3 : setsetsetset, ∀k3_tarski : setset, ∀esk5_3 : setsetsetset, ∀esk9_3 : setsetsetset, ∀esk11_2 : setsetset, ∀v1_subset_1 : setsetprop, ∀v6_membered : setprop, ∀v4_membered : setprop, ∀v2_membered : setprop, ∀v7_ordinal1 : setprop, ∀v1_rat_1 : setprop, ∀v1_xxreal_0 : setprop, ∀esk17_1 : setset, ∀v1_setfam_1 : setprop, ∀esk25_1 : setset, ∀v7_membered : setprop, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk22_0 : set, ∀esk16_0 : set, ∀esk21_1 : setset, ∀o_1_0_partit1 : setset, ∀esk18_0 : set, ∀esk14_1 : setset, ∀esk15_1 : setset, ∀esk20_0 : set, ∀esk23_0 : set, ∀esk24_1 : setset, ∀esk19_1 : setset, ∀esk26_1 : setset, ∀v1_xcmplx_0 : setprop, ∀v1_xreal_0 : setprop, ∀v1_int_1 : setprop, ∀v1_membered : setprop, ∀v3_membered : setprop, ∀v5_membered : setprop, ∀esk6_2 : setsetset, ∀esk10_2 : setsetset, ∀r1_setfam_1 : setsetprop, ∀k1_zfmisc_1 : setset, ∀m1_subset_1 : setsetprop, ∀r1_xboole_0 : setsetprop, ∀esk8_2 : setsetset, ∀k5_setfam_1 : setsetset, ∀esk7_2 : setsetset, ∀k1_xboole_0 : set, ∀esk3_3 : setsetsetset, ∀r1_tarski : setsetprop, ∀esk4_4 : setsetsetsetset, ∀r1_partit1 : setsetsetprop, ∀v1_xboole_0 : setprop, ∀r2_partit1 : setsetsetsetprop, ∀esk13_4 : setsetsetsetset, ∀r2_hidden : setsetprop, ∀m1_eqrel_1 : setsetprop, ∀k3_partit1 : setsetsetset, (∀X4 X2 X3 X1, (X4 = (k3_partit1 X1 X2 X3)False)(v1_xboole_0 X1False)m1_eqrel_1 X4 X1m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r2_hidden (esk13_4 X1 X2 X3 X4) X4r2_partit1 X1 X2 X3 (esk13_4 X1 X2 X3 X4)False)(∀X4 X3 X2 X1, (X4 = (k3_partit1 X1 X2 X3)False)(v1_xboole_0 X1False)(r2_hidden (esk13_4 X1 X2 X3 X4) X4False)(r2_partit1 X1 X2 X3 (esk13_4 X1 X2 X3 X4)False)m1_eqrel_1 X4 X1m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1False)(∀X3 X4 X2 X1, (v1_xboole_0 X1False)(r2_partit1 X1 X2 X3 X4False)(r1_partit1 X1 X2 (esk4_4 X1 X2 X3 X4)False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r1_partit1 X1 X3 X4r1_partit1 X1 X2 X4False)(∀X3 X4 X2 X1, (v1_xboole_0 X1False)(r2_partit1 X1 X3 X2 X4False)(r1_partit1 X1 X2 (esk4_4 X1 X3 X2 X4)False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r1_partit1 X1 X3 X4r1_partit1 X1 X2 X4False)(∀X3 X4 X2 X1, (v1_xboole_0 X1False)(r2_partit1 X1 X2 X3 X4False)(r1_tarski (esk4_4 X1 X2 X3 X4) X4False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r1_partit1 X1 X3 X4r1_partit1 X1 X2 X4False)(∀X3 X4 X2 X1, (v1_xboole_0 X1False)(r2_partit1 X1 X2 X3 X4False)(esk4_4 X1 X2 X3 X4) = X4m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r1_partit1 X1 X3 X4r1_partit1 X1 X2 X4False)(∀X3 X4 X5 X1 X2, (X1 = X2False)(v1_xboole_0 X3False)m1_eqrel_1 X5 X3m1_eqrel_1 X4 X3r1_tarski X1 X2r1_partit1 X3 X5 X1r1_partit1 X3 X4 X1r2_partit1 X3 X4 X5 X2False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)r2_hidden (esk12_3 X1 X2 X3) X3r2_hidden (esk12_3 X1 X2 X3) X2r2_hidden (esk12_3 X1 X2 X3) X1False)(∀X5 X4 X3 X2 X1, (v1_xboole_0 X1False)(r2_hidden X4 X5False)X5 = (k3_partit1 X1 X2 X3)m1_eqrel_1 X5 X1m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r2_partit1 X1 X2 X3 X4False)(∀X2 X3 X4 X1, (v1_xboole_0 X1False)(r1_partit1 X1 X2 X3False)m1_eqrel_1 X4 X1m1_eqrel_1 X2 X1r2_partit1 X1 X2 X4 X3False)(∀X2 X3 X4 X1, (v1_xboole_0 X1False)(r1_partit1 X1 X2 X3False)m1_eqrel_1 X4 X1m1_eqrel_1 X2 X1r2_partit1 X1 X4 X2 X3False)(∀X1 X5 X4 X2 X3, (v1_xboole_0 X3False)(r2_partit1 X3 X4 X5 X1False)X2 = (k3_partit1 X3 X4 X5)m1_eqrel_1 X5 X3m1_eqrel_1 X4 X3m1_eqrel_1 X2 X3r2_hidden X1 X2False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk12_3 X1 X2 X3) X3False)(r2_hidden (esk12_3 X1 X2 X3) X1False)False)(∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk12_3 X1 X2 X3) X3False)(r2_hidden (esk12_3 X1 X2 X3) X2False)False)(∀X2 X3 X1, (v1_xboole_0 X1False)(r1_tarski (esk3_3 X1 X2 X3) X2False)m1_eqrel_1 X2 X1r1_partit1 X1 X2 X3False)(∀X3 X1 X2, ((k3_tarski (esk3_3 X2 X3 X1)) = X1False)(v1_xboole_0 X2False)m1_eqrel_1 X3 X2r1_partit1 X2 X3 X1False)(∀X1 X2, ((esk7_2 X1 X2) = k1_xboole_0False)(m1_eqrel_1 X2 X1False)(k5_setfam_1 X1 X2) = X1m1_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 = X4False)(r1_xboole_0 X4 X1False)m1_eqrel_1 X3 X2r2_hidden X4 X3r2_hidden X1 X3m1_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 X1False)(esk3_3 X1 X2 X3) = k1_xboole_0m1_eqrel_1 X2 X1r1_partit1 X1 X2 X3False)(∀X2 X3 X1, (v1_xboole_0 X1False)(m1_eqrel_1 (k3_partit1 X1 X2 X3) X1False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1False)(∀X2 X3 X1, (v1_xboole_0 X1False)(r1_setfam_1 X2 (k3_partit1 X1 X2 X3)False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1False)(∀X3 X2 X1, (r2_hidden (esk5_3 X1 X2 X3) X2False)r2_hidden X3 X1r1_setfam_1 X1 X2False)(∀X1 X3 X2, (r1_tarski X1 (esk5_3 X2 X3 X1)False)r2_hidden X1 X2r1_setfam_1 X2 X3False)(∀X2 X3 X1, ((k3_partit1 X1 X2 X3) = (k3_partit1 X1 X3 X2)False)(v1_xboole_0 X1False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1False)(∀X3 X2 X1, (X2 = (k3_tarski X1)False)r2_hidden X3 X1r2_hidden (esk10_2 X1 X2) X3r2_hidden (esk10_2 X1 X2) X2False)(∀X1 X2 X3, (r2_hidden (esk9_3 X1 X2 X3) X1False)X2 = (k3_tarski X1)r2_hidden X3 X2False)(∀X2 X3 X1, (r2_hidden X1 (esk9_3 X2 X3 X1)False)X3 = (k3_tarski X2)r2_hidden X1 X3False)(∀X1 X2, ((esk7_2 X1 X2) = k1_xboole_0False)(m1_eqrel_1 X2 X1False)(m1_subset_1 (esk8_2 X1 X2) (k1_zfmisc_1 X1)False)(k5_setfam_1 X1 X2) = X1m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X3 X4 X2 X1, (v1_xboole_0 X1False)(r1_partit1 X1 X3 X4False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r2_hidden X4 X2r1_setfam_1 X3 X2False)(∀X1 X2, ((esk7_2 X1 X2) = k1_xboole_0False)(m1_eqrel_1 X2 X1False)(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_0False)(m1_eqrel_1 X2 X1False)(r2_hidden (esk8_2 X1 X2) X2False)(k5_setfam_1 X1 X2) = X1m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X1 X2, (m1_eqrel_1 X2 X1False)(m1_subset_1 (esk7_2 X1 X2) (k1_zfmisc_1 X1)False)(k5_setfam_1 X1 X2) = X1m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X3 X2 X1, X1 = k1_xboole_0m1_eqrel_1 X2 X3r2_hidden X1 X2m1_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 X1False)(r2_hidden (esk7_2 X1 X2) X2False)(k5_setfam_1 X1 X2) = X1m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X4 X3 X2 X1, (X1 = k1_xboole_0False)(v1_xboole_0 X4False)(r1_partit1 X4 X2 X3False)X3 = (k3_tarski X1)m1_eqrel_1 X2 X4r1_tarski X1 X2False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk10_2 X1 X2) X2False)(r2_hidden (esk10_2 X1 X2) (esk11_2 X1 X2)False)False)(∀X1 X3 X2, (r1_setfam_1 X3 X2False)r2_hidden X1 X2r1_tarski (esk6_2 X3 X2) X1False)(∀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 X3, (X2 = X3False)(v1_xboole_0 X1False)m1_eqrel_1 X3 X1m1_eqrel_1 X2 X1r1_setfam_1 X3 X2r1_setfam_1 X2 X3False)(∀X1 X2, ((k5_setfam_1 X1 X2) = X1False)m1_eqrel_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk10_2 X1 X2) X2False)(r2_hidden (esk11_2 X1 X2) X1False)False)(∀X2 X3 X1 X4, (r2_hidden X1 X4False)X4 = (k3_xboole_0 X2 X3)r2_hidden X1 X3r2_hidden X1 X2False)(∀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 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)X4 = (k3_tarski X3)r2_hidden X2 X3r2_hidden X1 X2False)(∀X2 X1, v1_xboole_0 X1v1_subset_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k3_xboole_0 X2 X4)r2_hidden X1 X3False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k3_xboole_0 X4 X2)r2_hidden X1 X3False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_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 X2False)(∀X1 X2, (r1_setfam_1 X1 X2False)(r2_hidden (esk6_2 X1 X2) X1False)False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1 X2, (v6_membered X2False)v6_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v5_membered X2False)v5_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v4_membered X2False)v4_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v3_membered X2False)v3_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v2_membered X2False)v2_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v1_membered X2False)v1_membered X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (r1_tarski X1 (k3_tarski X2)False)r2_hidden X1 X2False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (v6_membered (k3_xboole_0 X1 X2)False)v6_membered X1False)(∀X2 X1, (v6_membered (k3_xboole_0 X2 X1)False)v6_membered X1False)(∀X2 X1, (v5_membered (k3_xboole_0 X1 X2)False)v5_membered X1False)(∀X2 X1, (v5_membered (k3_xboole_0 X2 X1)False)v5_membered X1False)(∀X2 X1, (v4_membered (k3_xboole_0 X1 X2)False)v4_membered X1False)(∀X2 X1, (v4_membered (k3_xboole_0 X2 X1)False)v4_membered X1False)(∀X2 X1, (v3_membered (k3_xboole_0 X1 X2)False)v3_membered X1False)(∀X2 X1, (v3_membered (k3_xboole_0 X2 X1)False)v3_membered X1False)(∀X2 X1, (v2_membered (k3_xboole_0 X1 X2)False)v2_membered X1False)(∀X2 X1, (v2_membered (k3_xboole_0 X2 X1)False)v2_membered X1False)(∀X2 X1, (v1_membered (k3_xboole_0 X1 X2)False)v1_membered X1False)(∀X2 X1, (v1_membered (k3_xboole_0 X2 X1)False)v1_membered X1False)(∀X2 X1, (r1_xboole_0 X2 X1False)r1_xboole_0 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1 X2, (r1_xboole_0 X1 X2False)(k3_xboole_0 X1 X2) = k1_xboole_0False)(∀X2 X1, ((k3_xboole_0 X1 X2) = k1_xboole_0False)r1_xboole_0 X1 X2False)(∀X1 X2, (v7_ordinal1 X2False)v6_membered X1m1_subset_1 X2 X1False)(∀X1 X2, (v1_int_1 X2False)v5_membered X1m1_subset_1 X2 X1False)(∀X1 X2, (v1_rat_1 X2False)v4_membered X1m1_subset_1 X2 X1False)(∀X1 X2, (v1_xreal_0 X2False)v3_membered X1m1_subset_1 X2 X1False)(∀X1 X2, (v1_xxreal_0 X2False)v2_membered X1m1_subset_1 X2 X1False)(∀X1 X2, (v1_xcmplx_0 X2False)v1_membered X1m1_subset_1 X2 X1False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 X2m1_eqrel_1 X2 X1False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk26_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X2 X1, (v1_setfam_1 X1False)m1_eqrel_1 X1 X2False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk26_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)(m1_eqrel_1 (esk25_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)(m1_eqrel_1 (esk19_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk25_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk19_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk17_1 X1)False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_setfam_1 (esk25_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(v1_setfam_1 (esk19_1 X1)False)False)(∀X1, (v7_membered X1False)v1_xboole_0 X1False)(∀X1, (v6_membered X1False)v1_xboole_0 X1False)(∀X1, (v5_membered X1False)v6_membered X1False)(∀X1, (v4_membered X1False)v5_membered X1False)(∀X1, (v3_membered X1False)v4_membered X1False)(∀X1, (v2_membered X1False)v3_membered X1False)(∀X1, (v1_membered X1False)v3_membered X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)((k3_partit1 esk1_0 esk2_0 esk2_0) = esk2_0False)(∀X1, v1_subset_1 (esk24_1 X1) X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk23_0False)(v1_xboole_0 esk22_0False)(v1_xboole_0 esk20_0False)(v1_xboole_0 esk16_0False)(v1_xboole_0 esk1_0False)(∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1)False)False)(∀X1, (m1_subset_1 (esk24_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk15_1 X1) X1False)False)(∀X1, (m1_subset_1 (o_1_0_partit1 X1) X1False)False)(∀X1, (m1_eqrel_1 (esk14_1 X1) X1False)False)(∀X1, ((k3_xboole_0 X1 X1) = X1False)False)(∀X1, (r1_setfam_1 X1 X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0False)False)((m1_eqrel_1 esk2_0 esk1_0False)False)(∀X1, (v1_xboole_0 (esk21_1 X1)False)False)((v7_membered esk23_0False)False)((v6_membered esk23_0False)False)((v6_membered esk20_0False)False)((v6_membered esk16_0False)False)((v1_xboole_0 esk18_0False)False)((v1_xboole_0 k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.