Theorem. (t24_connsp_3)
∀m1_connsp_3 : setsetprop, ∀esk8_3 : setsetsetset, ∀k5_setfam_1 : setsetset, ∀esk7_2 : setsetset, ∀esk4_2 : setsetset, ∀esk5_2 : setsetset, ∀esk10_3 : setsetsetset, ∀esk12_2 : setsetset, ∀v4_pre_topc : setsetprop, ∀v2_connsp_1 : setsetprop, ∀esk1_0 : set, ∀esk2_0 : set, ∀v1_subset_1 : setsetprop, ∀v7_struct_0 : setprop, ∀esk22_1 : setset, ∀l1_struct_0 : setprop, ∀esk21_1 : setset, ∀k1_struct_0 : setset, ∀v1_zfmisc_1 : setprop, ∀esk27_1 : setset, ∀esk20_1 : setset, ∀esk6_1 : setset, ∀v6_pre_topc : setprop, ∀esk24_1 : setset, ∀esk16_1 : setset, ∀esk14_0 : set, ∀esk13_0 : set, ∀o_0_0_xboole_0 : set, ∀esk23_1 : setset, ∀esk15_1 : setset, ∀v1_finset_1 : setprop, ∀v8_struct_0 : setprop, ∀esk26_1 : setset, ∀esk29_1 : setset, ∀np__1 : set, ∀v13_struct_0 : setsetprop, ∀esk19_1 : setset, ∀esk25_1 : setset, ∀esk28_1 : setset, ∀esk30_1 : setset, ∀esk9_2 : setsetset, ∀k6_setfam_1 : setsetset, ∀v1_xboole_0 : setprop, ∀esk31_2 : setsetset, ∀esk11_2 : setsetset, ∀k3_tarski : setset, ∀k1_connsp_1 : setsetset, ∀esk3_3 : setsetsetset, ∀k1_setfam_1 : setset, ∀k1_xboole_0 : set, ∀esk17_3 : setsetsetset, ∀a_2_1_connsp_3 : setsetset, ∀r2_hidden : setsetprop, ∀v2_pre_topc : setprop, ∀v3_connsp_1 : setsetprop, ∀esk18_4 : setsetsetsetset, ∀r1_tarski : setsetprop, ∀u1_struct_0 : setset, ∀k1_zfmisc_1 : setset, ∀m1_subset_1 : setsetprop, ∀l1_pre_topc : setprop, ∀v2_struct_0 : setprop, (∀X2 X4 X1 X3, (v2_struct_0 X3False)(r2_hidden X2 (a_2_1_connsp_3 X3 X4)False)X1 = X2v2_pre_topc X3l1_pre_topc X3v3_connsp_1 X1 X3m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X3))r1_tarski X1 (esk18_4 X2 X3 X4 X1)m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X3)))False)(∀X1 X3 X4 X2, (v2_struct_0 X2False)(r2_hidden X1 (a_2_1_connsp_3 X2 X3)False)(m1_subset_1 (esk18_4 X1 X2 X3 X4) (k1_zfmisc_1 (u1_struct_0 X2))False)X1 = X4v2_pre_topc X2l1_pre_topc X2v3_connsp_1 X4 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X1 X3 X4 X2, (v2_struct_0 X2False)(r2_hidden X1 (a_2_1_connsp_3 X2 X3)False)(r2_hidden (esk18_4 X1 X2 X3 X4) X3False)X1 = X4v2_pre_topc X2l1_pre_topc X2v3_connsp_1 X4 X2m1_subset_1 X4 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X3 X2 X1, (m1_connsp_3 X2 X1False)X2 = (k5_setfam_1 (u1_struct_0 X1) X3)l1_pre_topc X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))v3_connsp_1 (esk8_3 X1 X2 X3) X1m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1)))False)(∀X3 X1 X4 X2, (v2_struct_0 X2False)(r1_tarski (esk17_3 X4 X2 X3) X1False)v2_pre_topc X2l1_pre_topc X2r2_hidden X1 X3r2_hidden X4 (a_2_1_connsp_3 X2 X3)m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X3 X2 X1, (m1_connsp_3 X2 X1False)(m1_subset_1 (esk8_3 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X1))False)X2 = (k5_setfam_1 (u1_struct_0 X1) X3)l1_pre_topc X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1)))False)(∀X3 X2 X1, (m1_connsp_3 X2 X1False)(r2_hidden (esk8_3 X1 X2 X3) X3False)X2 = (k5_setfam_1 (u1_struct_0 X1) X3)l1_pre_topc X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1)))False)(∀X3 X1 X2, (v2_struct_0 X2False)(m1_subset_1 (esk17_3 X1 X2 X3) (k1_zfmisc_1 (u1_struct_0 X2))False)v2_pre_topc X2l1_pre_topc X2r2_hidden X1 (a_2_1_connsp_3 X2 X3)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X3 X1 X2, (v2_struct_0 X2False)(v3_connsp_1 (esk17_3 X1 X2 X3) X2False)v2_pre_topc X2l1_pre_topc X2r2_hidden X1 (a_2_1_connsp_3 X2 X3)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X3 X1 X2, ((esk17_3 X1 X2 X3) = X1False)(v2_struct_0 X2False)v2_pre_topc X2l1_pre_topc X2r2_hidden X1 (a_2_1_connsp_3 X2 X3)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X2)))False)(∀X3 X1 X2, (X2 = k1_xboole_0False)(r2_hidden X1 X3False)X3 = (k1_setfam_1 X2)r2_hidden X1 (esk3_3 X2 X3 X1)False)(∀X3 X1 X2, (v3_connsp_1 X1 X2False)l1_pre_topc X2m1_connsp_3 X3 X2r2_hidden X1 (esk7_2 X2 X3)m1_subset_1 X3 (k1_zfmisc_1 (u1_struct_0 X2))m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X2 X3 X1, (v2_struct_0 X1False)(r1_tarski (k1_connsp_1 X1 X3) X2False)v2_pre_topc X1l1_pre_topc X1r2_hidden X3 X2m1_connsp_3 X2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)r2_hidden (esk4_2 X1 X2) X2r2_hidden (esk4_2 X1 X2) (esk5_2 X1 X2)False)(∀X2 X1, (m1_subset_1 (esk7_2 X1 X2) (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 X1)))False)l1_pre_topc X1m1_connsp_3 X2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X3 X1, (X2 = (k1_connsp_1 X1 X3)False)(v2_struct_0 X1False)v2_pre_topc X1l1_pre_topc X1r2_hidden X3 X2v3_connsp_1 X2 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X3 X2 X1, (X2 = (k3_tarski X1)False)r2_hidden X3 X1r2_hidden (esk11_2 X1 X2) X3r2_hidden (esk11_2 X1 X2) X2False)(∀X1 X2 X3, (r2_hidden (esk10_3 X1 X2 X3) X1False)X2 = (k3_tarski X1)r2_hidden X3 X2False)(∀X2 X3 X1, (r2_hidden X1 (esk10_3 X2 X3 X1)False)X3 = (k3_tarski X2)r2_hidden X1 X3False)(∀X2 X3 X1, (X1 = k1_xboole_0False)(r2_hidden X3 X2False)(r2_hidden (esk3_3 X1 X2 X3) X1False)X2 = (k1_setfam_1 X1)False)(∀X1 X2, ((k5_setfam_1 (u1_struct_0 X2) (esk7_2 X2 X1)) = X1False)l1_pre_topc X2m1_connsp_3 X1 X2m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 X2))False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk11_2 X1 X2) X2False)(r2_hidden (esk11_2 X1 X2) (esk12_2 X1 X2)False)False)(∀X2 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)(r2_hidden (esk5_2 X1 X2) X1False)r2_hidden (esk4_2 X1 X2) X2False)(∀X2 X3 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)(r2_hidden (esk4_2 X1 X2) X3False)(r2_hidden (esk4_2 X1 X2) X2False)r2_hidden X3 X1False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk31_2 X3 X2)False)(∀X2 X1, (v4_pre_topc X2 X1False)v2_pre_topc X1l1_pre_topc X1v3_connsp_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (v2_struct_0 X1False)v2_pre_topc X1l1_pre_topc X1v1_xboole_0 X2v3_connsp_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (v2_struct_0 X1False)v2_pre_topc X1l1_pre_topc X1v1_xboole_0 (k1_connsp_1 X1 X2)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (m1_subset_1 (k1_connsp_1 X1 X2) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_pre_topc X1m1_subset_1 X2 (u1_struct_0 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, (m1_subset_1 (k6_setfam_1 X2 X1) (k1_zfmisc_1 X2)False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X2 X1, (v2_connsp_1 X2 X1False)l1_pre_topc X1v3_connsp_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (v2_struct_0 X1False)(v2_connsp_1 (k1_connsp_1 X1 X2) X1False)v2_pre_topc X1l1_pre_topc X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, (v4_pre_topc X2 X1False)v2_pre_topc X1l1_pre_topc X1v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk11_2 X1 X2) X2False)(r2_hidden (esk12_2 X1 X2) X1False)False)(∀X2 X1, (v2_connsp_1 X2 X1False)l1_pre_topc X1v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk9_2 X1 X2) X2False)(∀X1, (m1_connsp_3 X1 esk1_0False)r2_hidden X1 esk2_0m1_subset_1 X1 (k1_zfmisc_1 (u1_struct_0 esk1_0))False)(∀X3 X1 X2 X4, (X4 = k1_xboole_0False)(r2_hidden X1 X3False)X2 = (k1_setfam_1 X4)r2_hidden X3 X4r2_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, ((k6_setfam_1 X2 X1) = (k1_setfam_1 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, (r2_hidden (esk31_2 X1 X2) X2False)r2_hidden X1 X2False)(∀X2 X1, (m1_subset_1 X2 (k1_zfmisc_1 (u1_struct_0 X1))False)l1_pre_topc X1m1_connsp_3 X2 X1False)(∀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)(∀X1 X3 X2, (r2_hidden X3 X2False)r2_hidden X3 X1r1_tarski X1 X2False)(∀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)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk30_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)v2_pre_topc X1l1_pre_topc X1False)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk9_2 X1 X2) X1False)False)(∀X1, (m1_subset_1 (esk28_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)v2_pre_topc X1l1_pre_topc X1False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk25_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X2 X1, (X1 = X2False)r1_tarski X2 X1r1_tarski X1 X2False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_pre_topc X1False)(∀X1, (m1_subset_1 (k1_struct_0 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1 X2, (v1_zfmisc_1 X2False)v1_zfmisc_1 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, (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)(∀X1, (v2_struct_0 X1False)(v4_pre_topc (esk30_1 X1) X1False)v2_pre_topc X1l1_pre_topc X1False)(∀X1, (v2_struct_0 X1False)(m1_connsp_3 (k1_struct_0 X1) X1False)v2_pre_topc X1l1_pre_topc X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, (v2_struct_0 X1False)v2_pre_topc X1l1_pre_topc X1v1_xboole_0 (esk30_1 X1)False)(∀X1, (v4_pre_topc (esk28_1 X1) X1False)v2_pre_topc X1l1_pre_topc X1False)(∀X1, v2_struct_0 X1l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 k1_xboole_0False)(∀X1, (v2_struct_0 X1False)(v13_struct_0 X1 np__1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_zfmisc_1 X1False)(m1_subset_1 (esk29_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 X1)False)False)(∀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 (esk20_1 X1) (k1_zfmisc_1 X1)False)False)(∀X2 X1, v1_xboole_0 X1r2_hidden X2 X1False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v1_finset_1 (u1_struct_0 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (esk22_1 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk25_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk21_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (m1_connsp_3 (esk15_1 X1) X1False)l1_pre_topc X1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk26_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)(r2_hidden (esk6_1 X1) X1False)False)(∀X1, (v1_finset_1 (u1_struct_0 X1)False)l1_struct_0 X1v8_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u1_struct_0 X1)False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_xboole_0 (u1_struct_0 X1)False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_zfmisc_1 (esk21_1 X1)False)l1_struct_0 X1False)(∀X1, (v1_zfmisc_1 X1False)v1_zfmisc_1 (esk29_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk27_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk20_1 X1)False)(∀X1, (v6_pre_topc X1False)v2_struct_0 X1l1_pre_topc X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X1, (v1_xboole_0 (esk19_1 X1)False)l1_pre_topc X1False)(∀X1, (v1_xboole_0 (k1_struct_0 X1)False)l1_struct_0 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_zfmisc_1 (esk27_1 X1)False)False)(∀X2 X1, (X1 = k1_xboole_0False)X2 = k1_xboole_0X1 = (k1_setfam_1 X2)False)(∀X1, (l1_struct_0 X1False)l1_pre_topc X1False)(∀X1, ((k1_struct_0 X1) = k1_xboole_0False)l1_struct_0 X1False)(∀X2 X1, (X1 = (k1_setfam_1 X2)False)X2 = k1_xboole_0X1 = k1_xboole_0False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(m1_connsp_3 (k6_setfam_1 (u1_struct_0 esk1_0) esk2_0) esk1_0False)(∀X1, v1_subset_1 (esk24_1 X1) X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 np__1False)(v2_struct_0 esk1_0False)((m1_subset_1 esk2_0 (k1_zfmisc_1 (k1_zfmisc_1 (u1_struct_0 esk1_0)))False)False)(∀X1, (m1_subset_1 (k1_zfmisc_1 X1) (k1_zfmisc_1 (k1_zfmisc_1 X1))False)False)(∀X1, (m1_subset_1 (esk24_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 (esk16_1 X1) X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, (v1_xboole_0 (esk23_1 X1)False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((l1_struct_0 esk14_0False)False)((l1_pre_topc esk13_0False)False)((l1_pre_topc esk1_0False)False)((v2_pre_topc esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.