Theorem. (t6_coh_sp)
∀esk13_2 : setsetset, ∀esk35_0 : set, ∀k2_tarski : setsetset, ∀esk33_0 : set, ∀esk37_2 : setsetset, ∀esk36_1 : setset, ∀esk9_1 : setset, ∀esk11_2 : setsetset, ∀esk3_0 : set, ∀esk4_0 : set, ∀v1_xboole_0 : setprop, ∀v1_subset_1 : setsetprop, ∀v1_zfmisc_1 : setprop, ∀esk31_1 : setset, ∀esk30_1 : setset, ∀esk19_1 : setset, ∀v3_funct_1 : setprop, ∀v2_relat_1 : setprop, ∀esk26_1 : setset, ∀esk29_0 : set, ∀esk27_0 : set, ∀esk18_0 : set, ∀esk15_1 : setset, ∀esk22_0 : set, ∀esk17_0 : set, ∀esk20_0 : set, ∀o_0_0_xboole_0 : set, ∀esk21_0 : set, ∀esk25_0 : set, ∀esk23_1 : setset, ∀esk16_0 : set, ∀esk24_0 : set, ∀esk32_0 : set, ∀k1_xboole_0 : set, ∀v3_relat_1 : setprop, ∀v2_funct_1 : setprop, ∀esk28_1 : setset, ∀esk5_1 : setset, ∀esk6_1 : setset, ∀v4_funct_1 : setprop, ∀v1_relat_1 : setprop, ∀v1_funct_1 : setprop, ∀v1_classes1 : setprop, ∀k1_zfmisc_1 : setset, ∀m1_subset_1 : setsetprop, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk10_2 : setsetset, ∀esk34_0 : set, ∀esk14_2 : setsetset, ∀esk12_3 : setsetsetset, ∀v1_coh_sp : setprop, ∀esk8_2 : setsetset, ∀esk7_2 : setsetset, ∀k2_xboole_0 : setsetset, ∀r1_tarski : setsetprop, ∀r2_hidden : setsetprop, ∀k3_tarski : setset, (∀X2 X1, (r2_hidden (k3_tarski X2) X1False)v1_coh_sp X1r1_tarski X2 X1r2_hidden (k2_xboole_0 (esk7_2 X1 X2) (esk8_2 X1 X2)) X1False)(∀X3 X2 X1, (X2 = (k3_tarski X1)False)r2_hidden X3 X1r2_hidden (esk13_2 X1 X2) X3r2_hidden (esk13_2 X1 X2) X2False)(∀X1 X2 X3, (r2_hidden (esk12_3 X1 X2 X3) X1False)X2 = (k3_tarski X1)r2_hidden X3 X2False)(∀X2 X3 X1, (r2_hidden X1 (esk12_3 X2 X3 X1)False)X3 = (k3_tarski X2)r2_hidden X1 X3False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk13_2 X1 X2) X2False)(r2_hidden (esk13_2 X1 X2) (esk14_2 X1 X2)False)False)(∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0False)((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2False)r2_hidden X2 (esk36_1 X1)False)(∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0False)((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2False)r2_hidden X2 (esk36_1 X1)False)(∀X1 X3 X2, (v1_coh_sp X2False)(r2_hidden (k2_xboole_0 X1 X3) X2False)r2_hidden X3 (esk9_1 X2)r2_hidden X1 (esk9_1 X2)False)(∀X2 X1, (X2 = (k2_tarski X1 X1)False)(esk10_2 X1 X2) = X1r2_hidden (esk10_2 X1 X2) X2False)(∀X2 X1, ((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2False)esk35_0 = esk34_0r2_hidden X2 (esk36_1 X1)False)(∀X1 X2, (r2_hidden esk1_0 esk2_0False)(r2_hidden (k2_tarski X1 X2) esk2_0False)r2_hidden X2 esk1_0r2_hidden X1 esk1_0False)(∀X2 X1, (r2_hidden (k3_tarski X2) X1False)(r2_hidden (esk8_2 X1 X2) X2False)v1_coh_sp X1r1_tarski X2 X1False)(∀X2 X1, (r2_hidden (k3_tarski X2) X1False)(r2_hidden (esk7_2 X1 X2) X2False)v1_coh_sp X1r1_tarski X2 X1False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk13_2 X1 X2) X2False)(r2_hidden (esk14_2 X1 X2) X1False)False)(∀X3 X2 X1, (r1_tarski (k2_tarski X1 X3) X2False)r2_hidden X3 X2r2_hidden X1 X2False)(∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0False)(r2_hidden (esk37_2 X1 X2) X1False)r2_hidden X2 (esk36_1 X1)False)(∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0False)(r2_hidden (esk37_2 X1 X2) X1False)r2_hidden X2 (esk36_1 X1)False)(∀X2 X3 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0False)(r2_hidden X3 (esk36_1 X2)False)(k2_tarski X1 X1) = X3r2_hidden X1 X2False)(∀X2 X3 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0False)(r2_hidden X3 (esk36_1 X2)False)(k2_tarski X1 X1) = X3r2_hidden X1 X2False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk11_2 X1 X2) X2False)(∀X3 X1 X2, (r2_hidden X1 X2False)r1_tarski (k2_tarski X1 X3) X2False)(∀X3 X1 X2, (r2_hidden X1 X2False)r1_tarski (k2_tarski X3 X1) X2False)(∀X2 X1, (r2_hidden (esk37_2 X1 X2) X1False)esk35_0 = esk34_0r2_hidden X2 (esk36_1 X1)False)(∀X2 X1, (X2 = (k2_tarski X1 X1)False)((esk10_2 X1 X2) = X1False)(r2_hidden (esk10_2 X1 X2) X2False)False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(r2_hidden esk1_0 esk2_0r2_hidden (k2_tarski esk3_0 esk4_0) esk2_0False)(∀X1 X3 X2, (r2_hidden X3 (esk36_1 X2)False)esk35_0 = esk34_0(k2_tarski X1 X1) = X3r2_hidden X1 X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)X4 = (k3_tarski X3)r2_hidden X2 X3r2_hidden X1 X2False)(∀X2 X3 X1, (r2_hidden X3 X1False)v1_classes1 X1r2_hidden X2 X1r1_tarski X3 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)(∀X1 X3 X2, (r2_hidden X3 X2False)r2_hidden X3 X1r1_tarski X1 X2False)(∀X1 X2, (v4_funct_1 (k2_tarski X1 X2)False)v1_funct_1 X2v1_funct_1 X1v1_relat_1 X2v1_relat_1 X1False)(∀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, (v1_coh_sp X1False)r2_hidden (k3_tarski (esk9_1 X1)) X1False)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk11_2 X1 X2) X1False)False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X1 X2)False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X2 X1)False)(∀X1 X2, (v1_funct_1 X2False)v1_funct_1 X1v1_relat_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1 X3, (X1 = X3False)X2 = (k2_tarski X3 X3)r2_hidden X1 X2False)(∀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)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1, (v4_funct_1 (k2_tarski X1 X1)False)v1_funct_1 X1v1_relat_1 X1False)(∀X2 X1, (v1_relat_1 (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1False)(∀X1 X2, (v4_funct_1 X2False)v4_funct_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀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)(∀X2 X1 X3, (r2_hidden X1 X3False)X1 = X2X3 = (k2_tarski X2 X2)False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, (v1_classes1 X1False)r2_hidden (esk6_1 X1) X1False)(∀X2 X1, (v1_relat_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X2 X1, (v1_funct_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X1, (v1_zfmisc_1 X1False)(m1_subset_1 (esk31_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_classes1 X1False)(r1_tarski (esk6_1 X1) (esk5_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk30_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk28_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)((r2_hidden esk4_0 esk1_0False)r2_hidden esk1_0 esk2_0False)((r2_hidden esk3_0 esk1_0False)r2_hidden esk1_0 esk2_0False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v2_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v1_coh_sp X1False)(r1_tarski (esk9_1 X1) X1False)False)(∀X1, (v1_classes1 X1False)(r2_hidden (esk5_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk28_1 X1) X1False)False)(∀X1, (v1_zfmisc_1 X1False)v1_zfmisc_1 (esk31_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk30_1 X1)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk19_1 X1)False)(∀X1, (v2_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X1, (v3_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v1_xboole_0 X1False)(v1_zfmisc_1 (esk30_1 X1)False)False)(∀X1, (v4_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v1_relat_1 X1False)v1_xboole_0 X1False)(∀X1, (v1_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(∀X1, v1_xboole_0 (k2_tarski X1 X1)False)(∀X1 X2, v1_xboole_0 (k2_tarski X1 X2)False)(∀X1, v1_subset_1 (esk26_1 X1) X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v3_funct_1 esk29_0False)(v1_xboole_0 esk32_0False)(v1_xboole_0 esk27_0False)(v1_xboole_0 esk24_0False)(v1_xboole_0 esk18_0False)(v1_xboole_0 esk16_0False)(v1_xboole_0 esk2_0False)(∀X1 X2, ((k2_xboole_0 (k2_tarski X1 X1) (k2_tarski X2 X2)) = (k2_tarski X1 X2)False)False)(∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1)False)False)(∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1)False)False)(∀X1, (m1_subset_1 (esk26_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 (esk15_1 X1) X1False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1False)False)(∀X1, (v1_xboole_0 (esk23_1 X1)False)False)((v4_funct_1 esk32_0False)False)((v2_relat_1 esk27_0False)False)((v2_relat_1 esk25_0False)False)((v2_relat_1 esk22_0False)False)((v2_funct_1 esk21_0False)False)((v1_relat_1 esk29_0False)False)((v1_relat_1 esk27_0False)False)((v1_relat_1 esk25_0False)False)((v1_relat_1 esk22_0False)False)((v1_relat_1 esk21_0False)False)((v1_relat_1 esk18_0False)False)((v1_relat_1 esk17_0False)False)((v1_funct_1 esk29_0False)False)((v1_funct_1 esk27_0False)False)((v1_funct_1 esk25_0False)False)((v1_funct_1 esk21_0False)False)((v1_funct_1 esk17_0False)False)((v1_coh_sp esk16_0False)False)((v1_coh_sp esk2_0False)False)((v1_classes1 esk16_0False)False)((v1_classes1 esk2_0False)False)((v1_xboole_0 esk20_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((v1_xboole_0 k1_xboole_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.