Theorem. (t31_midsp_1)
∀k4_tarski : setsetset, ∀k1_zfmisc_1 : setset, ∀k5_midsp_1 : setsetset, ∀k1_xtuple_0 : setset, ∀v4_relat_1 : setsetprop, ∀esk24_2 : setsetset, ∀v1_subset_1 : setsetprop, ∀esk20_1 : setset, ∀o_1_1_midsp_1 : setset, ∀v1_zfmisc_1 : setprop, ∀esk22_1 : setset, ∀esk10_1 : setset, ∀v8_struct_0 : setprop, ∀v1_finset_1 : setprop, ∀v3_relat_1 : setprop, ∀esk8_0 : set, ∀esk14_0 : set, ∀esk9_2 : setsetset, ∀esk16_1 : setset, ∀esk15_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk11_0 : set, ∀esk6_1 : setset, ∀esk18_2 : setsetset, ∀esk17_0 : set, ∀esk19_1 : setset, ∀v2_relat_1 : setprop, ∀esk21_1 : setset, ∀esk23_1 : setset, ∀k1_xboole_0 : set, ∀np__1 : set, ∀v13_struct_0 : setsetprop, ∀esk5_1 : setset, ∀r1_tarski : setsetprop, ∀esk12_1 : setset, ∀l1_struct_0 : setprop, ∀esk13_1 : setset, ∀v7_struct_0 : setprop, ∀v1_relat_1 : setprop, ∀v5_relat_1 : setsetprop, ∀k2_xtuple_0 : setset, ∀esk1_0 : set, ∀m1_midsp_1 : setsetprop, ∀esk2_1 : setset, ∀k4_midsp_1 : setsetset, ∀esk7_3 : setsetsetset, ∀r2_hidden : setsetprop, ∀a_2_0_midsp_1 : setsetset, ∀k1_domain_1 : setsetsetsetset, ∀v1_xboole_0 : setprop, ∀r2_midsp_1 : setsetsetprop, ∀l1_midsp_1 : setprop, ∀r1_midsp_1 : setsetsetsetsetprop, ∀k2_domain_1 : setsetsetset, ∀k3_domain_1 : setsetsetset, ∀u1_struct_0 : setset, ∀k2_zfmisc_1 : setsetset, ∀m1_subset_1 : setsetprop, ∀v2_midsp_1 : setprop, ∀v2_struct_0 : setprop, (∀X3 X2 X1, (v2_struct_0 X1False)(r2_midsp_1 X1 X2 X3False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))r1_midsp_1 X1 (k2_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X2) (k3_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X2) (k2_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X3) (k3_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X3)False)(∀X2 X3 X1, (v2_struct_0 X1False)(r1_midsp_1 X1 (k2_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X2) (k3_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X2) (k2_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X3) (k3_domain_1 (u1_struct_0 X1) (u1_struct_0 X1) X3)False)v2_midsp_1 X1l1_midsp_1 X1r2_midsp_1 X1 X2 X3m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X1 X4 X2 X3, (X2 = X3False)(v2_struct_0 X1False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)r1_midsp_1 X1 X2 X3 X4 X4False)(∀X2 X3 X1, (v2_struct_0 X1False)(r1_midsp_1 X1 X2 X2 X3 X3False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1 X4 X3 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k1_domain_1 X1 X2 X3 X4) (k2_zfmisc_1 X1 X2)False)m1_subset_1 X4 X2m1_subset_1 X3 X1False)(∀X2 X3 X1, (v2_struct_0 X1False)(r2_midsp_1 X1 X3 X2False)v2_midsp_1 X1l1_midsp_1 X1r2_midsp_1 X1 X2 X3m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X3 X1 X2, (v2_struct_0 X2False)(m1_subset_1 (esk7_3 X1 X2 X3) (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))False)v2_midsp_1 X2l1_midsp_1 X2r2_hidden X1 (a_2_0_midsp_1 X2 X3)m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))False)(∀X3 X4 X1 X2, (v2_struct_0 X2False)(r2_hidden X3 (a_2_0_midsp_1 X2 X4)False)X1 = X3v2_midsp_1 X2l1_midsp_1 X2r2_midsp_1 X2 X1 X4m1_subset_1 X4 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))m1_subset_1 X1 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))False)(∀X2 X3 X1, (v2_struct_0 X1False)(r2_hidden X2 (k4_midsp_1 X1 X3)False)v2_midsp_1 X1l1_midsp_1 X1r2_midsp_1 X1 X2 X3m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X3 X2 X1, (v2_struct_0 X1False)(r2_midsp_1 X1 (esk7_3 X2 X1 X3) X3False)v2_midsp_1 X1l1_midsp_1 X1r2_hidden X2 (a_2_0_midsp_1 X1 X3)m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X1 X3 X2, (v2_struct_0 X2False)(r2_midsp_1 X2 X1 X3False)v2_midsp_1 X2l1_midsp_1 X2r2_hidden X1 (k4_midsp_1 X2 X3)m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))m1_subset_1 X1 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))False)(∀X1 X4 X3 X2, ((k1_domain_1 X1 X2 X3 X4) = (k4_tarski X3 X4)False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X4 X2m1_subset_1 X3 X1False)(∀X2 X3 X1, (v2_struct_0 X1False)(r2_midsp_1 X1 X2 X2False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X2 X1, (v2_struct_0 X1False)(m1_subset_1 (k4_midsp_1 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1)))False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X1, (k2_domain_1 (u1_struct_0 esk1_0) (u1_struct_0 esk1_0) (esk2_1 X1)) = (k3_domain_1 (u1_struct_0 esk1_0) (u1_struct_0 esk1_0) (esk2_1 X1))m1_midsp_1 X1 esk1_0r2_hidden (esk2_1 X1) X1False)(∀X3 X1 X2, ((esk7_3 X1 X2 X3) = X1False)(v2_struct_0 X2False)v2_midsp_1 X2l1_midsp_1 X2r2_hidden X1 (a_2_0_midsp_1 X2 X3)m1_subset_1 X3 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2))False)(∀X1 X3 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k3_domain_1 X1 X2 X3) X2False)m1_subset_1 X3 (k2_zfmisc_1 X1 X2)False)(∀X1 X3 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k2_domain_1 X1 X2 X3) X1False)m1_subset_1 X3 (k2_zfmisc_1 X1 X2)False)(∀X1, ((k2_domain_1 (u1_struct_0 esk1_0) (u1_struct_0 esk1_0) (esk2_1 X1)) = (k3_domain_1 (u1_struct_0 esk1_0) (u1_struct_0 esk1_0) (esk2_1 X1))False)(r2_hidden (esk2_1 X1) X1False)m1_midsp_1 X1 esk1_0False)(∀X2 X1, (v2_struct_0 X1False)v2_midsp_1 X1l1_midsp_1 X1v1_xboole_0 (k4_midsp_1 X1 X2)m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X1 X2, (v2_struct_0 X2False)(m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 X2) (u1_struct_0 X2)))False)v2_midsp_1 X2l1_midsp_1 X2m1_midsp_1 X1 X2False)(∀X2 X1, (v2_struct_0 X1False)(m1_midsp_1 (k5_midsp_1 X1 X2) X1False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X2 X1, ((k5_midsp_1 X1 X2) = (k4_midsp_1 X1 X2)False)(v2_struct_0 X1False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X2 X1, ((k4_midsp_1 X1 X2) = (a_2_0_midsp_1 X1 X2)False)(v2_struct_0 X1False)v2_midsp_1 X1l1_midsp_1 X1m1_subset_1 X2 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1))False)(∀X1 X3 X2, ((k3_domain_1 X1 X2 X3) = (k2_xtuple_0 X3)False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X3 (k2_zfmisc_1 X1 X2)False)(∀X1 X3 X2, ((k2_domain_1 X1 X2 X3) = (k1_xtuple_0 X3)False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X3 (k2_zfmisc_1 X1 X2)False)(∀X3 X1 X2, (v5_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2))False)(∀X3 X1 X2, (v4_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X1))False)(∀X3 X2 X1, (v1_relat_1 X1False)m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3))False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk24_2 X3 X2)False)(∀X1, (m1_subset_1 (esk2_1 X1) (k2_zfmisc_1 (u1_struct_0 esk1_0) (u1_struct_0 esk1_0))False)m1_midsp_1 X1 esk1_0False)(∀X1 X3 X2, (v5_relat_1 X3 X2False)v1_relat_1 X1v5_relat_1 X1 X2m1_subset_1 X3 (k1_zfmisc_1 X1)False)(∀X1 X3 X2, (v4_relat_1 X3 X2False)v1_relat_1 X1v4_relat_1 X1 X2m1_subset_1 X3 (k1_zfmisc_1 X1)False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1, (r2_hidden (esk24_2 X1 X2) X2False)r2_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)(∀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 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_xboole_0 (k2_zfmisc_1 X1 X2)False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk13_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk12_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1 X2, (v2_struct_0 X2False)v2_midsp_1 X2l1_midsp_1 X2v1_xboole_0 X1m1_midsp_1 X1 X2False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (o_1_1_midsp_1 X1) (u1_struct_0 X1)False)v2_midsp_1 X1l1_midsp_1 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_relat_1 X2False)v1_relat_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)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 X2v1_relat_1 X1v5_relat_1 X1 X2False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 X2v1_relat_1 X1v4_relat_1 X1 X2False)(∀X1, (v2_struct_0 X1False)(m1_midsp_1 (esk5_1 X1) X1False)v2_midsp_1 X1l1_midsp_1 X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀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 (esk23_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk10_1 X1) (k1_zfmisc_1 X1)False)False)(∀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 (esk13_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 (esk20_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk12_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk21_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 (esk12_1 X1)False)l1_struct_0 X1False)(∀X1, (v1_zfmisc_1 X1False)v1_zfmisc_1 (esk23_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk22_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk10_1 X1)False)(∀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, (v2_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X1, (v3_relat_1 X1False)v1_xboole_0 X1v1_relat_1 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, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_zfmisc_1 (esk22_1 X1)False)False)(∀X1, (v1_relat_1 X1False)v1_xboole_0 X1False)(∀X1, (l1_struct_0 X1False)l1_midsp_1 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(∀X1, v1_subset_1 (esk19_1 X1) X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk17_0False)(v1_xboole_0 esk8_0False)(v1_xboole_0 np__1False)(v2_struct_0 esk14_0False)(v2_struct_0 esk1_0False)(∀X2 X1, (m1_subset_1 (esk9_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2))False)False)(∀X2 X1, (v5_relat_1 (esk18_2 X1 X2) X2False)False)(∀X2 X1, (v5_relat_1 (esk9_2 X1 X2) X2False)False)(∀X1 X2, (v4_relat_1 (esk18_2 X1 X2) X1False)False)(∀X1 X2, (v4_relat_1 (esk9_2 X1 X2) X1False)False)(∀X2 X1, ((k2_xtuple_0 (k4_tarski X1 X2)) = X2False)False)(∀X1 X2, ((k1_xtuple_0 (k4_tarski X1 X2)) = X1False)False)(∀X1 X2, (v1_relat_1 (esk18_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk9_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (k2_zfmisc_1 X1 X2)False)False)(∀X1 X2, (v1_xboole_0 (esk9_2 X1 X2)False)False)(∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk6_1 X1) X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, (v1_xboole_0 (esk16_1 X1)False)False)((v2_relat_1 esk15_0False)False)((v1_relat_1 esk15_0False)False)((v1_relat_1 esk8_0False)False)((v1_xboole_0 esk11_0False)False)((v1_xboole_0 k1_xboole_0False)False)((l1_struct_0 esk4_0False)False)((l1_midsp_1 esk14_0False)False)((l1_midsp_1 esk3_0False)False)((l1_midsp_1 esk1_0False)False)((v2_midsp_1 esk1_0False)False)False
Proof:
The rest of the proof is missing.