Theorem. (
t6_coh_sp)
∀esk13_2 : set → set → set, ∀esk35_0 : set, ∀k2_tarski : set → set → set, ∀esk33_0 : set, ∀esk37_2 : set → set → set, ∀esk36_1 : set → set, ∀esk9_1 : set → set, ∀esk11_2 : set → set → set, ∀esk3_0 : set, ∀esk4_0 : set, ∀v1_xboole_0 : set → prop, ∀v1_subset_1 : set → set → prop, ∀v1_zfmisc_1 : set → prop, ∀esk31_1 : set → set, ∀esk30_1 : set → set, ∀esk19_1 : set → set, ∀v3_funct_1 : set → prop, ∀v2_relat_1 : set → prop, ∀esk26_1 : set → set, ∀esk29_0 : set, ∀esk27_0 : set, ∀esk18_0 : set, ∀esk15_1 : set → set, ∀esk22_0 : set, ∀esk17_0 : set, ∀esk20_0 : set, ∀o_0_0_xboole_0 : set, ∀esk21_0 : set, ∀esk25_0 : set, ∀esk23_1 : set → set, ∀esk16_0 : set, ∀esk24_0 : set, ∀esk32_0 : set, ∀k1_xboole_0 : set, ∀v3_relat_1 : set → prop, ∀v2_funct_1 : set → prop, ∀esk28_1 : set → set, ∀esk5_1 : set → set, ∀esk6_1 : set → set, ∀v4_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀v1_funct_1 : set → prop, ∀v1_classes1 : set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk10_2 : set → set → set, ∀esk34_0 : set, ∀esk14_2 : set → set → set, ∀esk12_3 : set → set → set → set, ∀v1_coh_sp : set → prop, ∀esk8_2 : set → set → set, ∀esk7_2 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀r1_tarski : set → set → prop, ∀r2_hidden : set → set → prop, ∀k3_tarski : set → set, (∀X2 X1, (r2_hidden (k3_tarski X2) X1 → False) → v1_coh_sp X1 → r1_tarski X2 X1 → r2_hidden (k2_xboole_0 (esk7_2 X1 X2) (esk8_2 X1 X2)) X1 → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk13_2 X1 X2) X3 → r2_hidden (esk13_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk12_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk12_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk13_2 X1 X2) X2 → False) → (r2_hidden (esk13_2 X1 X2) (esk14_2 X1 X2) → False) → False) → (∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0 → False) → ((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2 → False) → r2_hidden X2 (esk36_1 X1) → False) → (∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0 → False) → ((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2 → False) → r2_hidden X2 (esk36_1 X1) → False) → (∀X1 X3 X2, (v1_coh_sp X2 → False) → (r2_hidden (k2_xboole_0 X1 X3) X2 → False) → 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) = X1 → r2_hidden (esk10_2 X1 X2) X2 → False) → (∀X2 X1, ((k2_tarski (esk37_2 X1 X2) (esk37_2 X1 X2)) = X2 → False) → esk35_0 = esk34_0 → r2_hidden X2 (esk36_1 X1) → False) → (∀X1 X2, (r2_hidden esk1_0 esk2_0 → False) → (r2_hidden (k2_tarski X1 X2) esk2_0 → False) → r2_hidden X2 esk1_0 → r2_hidden X1 esk1_0 → False) → (∀X2 X1, (r2_hidden (k3_tarski X2) X1 → False) → (r2_hidden (esk8_2 X1 X2) X2 → False) → v1_coh_sp X1 → r1_tarski X2 X1 → False) → (∀X2 X1, (r2_hidden (k3_tarski X2) X1 → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → v1_coh_sp X1 → r1_tarski X2 X1 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk13_2 X1 X2) X2 → False) → (r2_hidden (esk14_2 X1 X2) X1 → False) → False) → (∀X3 X2 X1, (r1_tarski (k2_tarski X1 X3) X2 → False) → r2_hidden X3 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0 → False) → (r2_hidden (esk37_2 X1 X2) X1 → False) → r2_hidden X2 (esk36_1 X1) → False) → (∀X2 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0 → False) → (r2_hidden (esk37_2 X1 X2) X1 → False) → r2_hidden X2 (esk36_1 X1) → False) → (∀X2 X3 X1, ((k2_tarski esk33_0 esk33_0) = esk35_0 → False) → (r2_hidden X3 (esk36_1 X2) → False) → (k2_tarski X1 X1) = X3 → r2_hidden X1 X2 → False) → (∀X2 X3 X1, ((k2_tarski esk33_0 esk33_0) = esk34_0 → False) → (r2_hidden X3 (esk36_1 X2) → False) → (k2_tarski X1 X1) = X3 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk11_2 X1 X2) X2 → False) → (∀X3 X1 X2, (r2_hidden X1 X2 → False) → r1_tarski (k2_tarski X1 X3) X2 → False) → (∀X3 X1 X2, (r2_hidden X1 X2 → False) → r1_tarski (k2_tarski X3 X1) X2 → False) → (∀X2 X1, (r2_hidden (esk37_2 X1 X2) X1 → False) → esk35_0 = esk34_0 → r2_hidden X2 (esk36_1 X1) → False) → (∀X2 X1, (X2 = (k2_tarski X1 X1) → False) → ((esk10_2 X1 X2) = X1 → False) → (r2_hidden (esk10_2 X1 X2) X2 → False) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (r2_hidden esk1_0 esk2_0 → r2_hidden (k2_tarski esk3_0 esk4_0) esk2_0 → False) → (∀X1 X3 X2, (r2_hidden X3 (esk36_1 X2) → False) → esk35_0 = esk34_0 → (k2_tarski X1 X1) = X3 → r2_hidden X1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → r2_hidden X1 X2 → False) → (∀X2 X3 X1, (r2_hidden X3 X1 → False) → v1_classes1 X1 → r2_hidden X2 X1 → r1_tarski X3 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) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r2_hidden X3 X1 → r1_tarski X1 X2 → False) → (∀X1 X2, (v4_funct_1 (k2_tarski X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_relat_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, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1, (v1_coh_sp X1 → False) → r2_hidden (k3_tarski (esk9_1 X1)) X1 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk11_2 X1 X2) X1 → 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) → (∀X1 X2, (v1_funct_1 X2 → False) → v1_funct_1 X1 → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (X1 = X3 → False) → X2 = (k2_tarski X3 X3) → r2_hidden X1 X2 → 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) → (∀X1, (v4_funct_1 (k2_tarski X1 X1) → False) → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k2_xboole_0 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X2, (v4_funct_1 X2 → False) → v4_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_zfmisc_1 X2 → False) → v1_zfmisc_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 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) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k2_tarski X2 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, (v1_classes1 X1 → False) → r2_hidden (esk6_1 X1) X1 → False) → (∀X2 X1, (v1_relat_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_funct_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk31_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_classes1 X1 → False) → (r1_tarski (esk6_1 X1) (esk5_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk30_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk28_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → ((r2_hidden esk4_0 esk1_0 → False) → r2_hidden esk1_0 esk2_0 → False) → ((r2_hidden esk3_0 esk1_0 → False) → r2_hidden esk1_0 esk2_0 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v1_coh_sp X1 → False) → (r1_tarski (esk9_1 X1) X1 → False) → False) → (∀X1, (v1_classes1 X1 → False) → (r2_hidden (esk5_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk28_1 X1) X1 → False) → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk31_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk30_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk19_1 X1) → False) → (∀X1, (v2_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_xboole_0 X1 → v1_relat_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_zfmisc_1 (esk30_1 X1) → False) → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀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) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v3_funct_1 esk29_0 → False) → (v1_xboole_0 esk32_0 → False) → (v1_xboole_0 esk27_0 → False) → (v1_xboole_0 esk24_0 → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk2_0 → False) → (∀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) 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, (v1_xboole_0 (esk23_1 X1) → False) → False) → ((v4_funct_1 esk32_0 → False) → False) → ((v2_relat_1 esk27_0 → False) → False) → ((v2_relat_1 esk25_0 → False) → False) → ((v2_relat_1 esk22_0 → False) → False) → ((v2_funct_1 esk21_0 → False) → False) → ((v1_relat_1 esk29_0 → False) → False) → ((v1_relat_1 esk27_0 → False) → False) → ((v1_relat_1 esk25_0 → False) → False) → ((v1_relat_1 esk22_0 → False) → False) → ((v1_relat_1 esk21_0 → False) → False) → ((v1_relat_1 esk18_0 → False) → False) → ((v1_relat_1 esk17_0 → False) → False) → ((v1_funct_1 esk29_0 → False) → False) → ((v1_funct_1 esk27_0 → False) → False) → ((v1_funct_1 esk25_0 → False) → False) → ((v1_funct_1 esk21_0 → False) → False) → ((v1_funct_1 esk17_0 → False) → False) → ((v1_coh_sp esk16_0 → False) → False) → ((v1_coh_sp esk2_0 → False) → False) → ((v1_classes1 esk16_0 → False) → False) → ((v1_classes1 esk2_0 → False) → False) → ((v1_xboole_0 esk20_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False