Theorem. (
t3_funcop_1)
∀esk5_2 : set → set → set, ∀esk7_2 : set → set → set, ∀esk6_2 : set → set → set, ∀esk26_2 : set → set → set, ∀v2_relat_1 : set → prop, ∀r1_tarski : set → set → prop, ∀v1_subset_1 : set → set → prop, ∀k3_xboole_0 : set → set → set, ∀esk24_1 : set → set, ∀esk21_1 : set → set, ∀v2_funct_1 : set → prop, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk19_1 : set → set, ∀esk25_0 : set, ∀esk17_0 : set, ∀esk8_1 : set → set, ∀esk18_0 : set, ∀esk14_0 : set, ∀esk9_0 : set, ∀esk12_0 : set, ∀esk15_0 : set, ∀esk13_0 : set, ∀esk16_1 : set → set, ∀v1_xtuple_0 : set → prop, ∀esk10_0 : set, ∀esk20_0 : set, ∀esk22_0 : set, ∀k1_xboole_0 : set, ∀v3_funct_1 : set → prop, ∀esk11_1 : set → set, ∀esk23_1 : set → set, ∀v1_zfmisc_1 : set → prop, ∀v3_relat_1 : set → prop, ∀v4_funct_1 : set → prop, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀k5_relat_1 : set → set → set, ∀k1_funcop_1 : set → set, ∀k9_xtuple_0 : set → set, ∀r2_hidden : set → set → prop, ∀v1_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀k2_tarski : set → set → set, ∀esk4_3 : set → set → set → set, ∀esk3_3 : set → set → set → set, ∀k1_tarski : set → set, ∀k1_funct_1 : set → set → set, (∀X2 X3 X1, ((k1_funct_1 X1 X2) = (k1_funct_1 X3 X2) → False) → ((k2_tarski (k2_tarski (esk3_3 X1 X3 X2) (esk4_3 X1 X3 X2)) (k1_tarski (esk3_3 X1 X3 X2))) = (k1_funct_1 X1 X2) → False) → X3 = (k1_funcop_1 X1) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → r2_hidden X2 (k9_xtuple_0 X1) → False) → (∀X4 X3 X2 X1, (X2 = (k1_funcop_1 X1) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk5_2 X1 X2)) = (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) → (k2_tarski (k2_tarski (esk7_2 X1 X2) (esk6_2 X1 X2)) (k1_tarski (esk7_2 X1 X2))) = (k1_funct_1 X2 (esk5_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (X2 = (k1_funcop_1 X1) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk5_2 X1 X2)) = (k1_funct_1 X2 (esk5_2 X1 X2)) → (k2_tarski (k2_tarski (esk7_2 X1 X2) (esk6_2 X1 X2)) (k1_tarski (esk7_2 X1 X2))) = (k1_funct_1 X2 (esk5_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X3 X4 X2 X1, (X2 = (k1_funcop_1 X1) → False) → ((k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) = (k1_funct_1 X1 (esk5_2 X1 X2)) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk5_2 X1 X2)) = (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (X2 = (k1_funcop_1 X1) → False) → ((k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) = (k1_funct_1 X1 (esk5_2 X1 X2)) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk5_2 X1 X2)) = (k1_funct_1 X2 (esk5_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X4 X3 X2 X5, ((k2_tarski (k2_tarski X4 X3) (k1_tarski X4)) = (k1_funct_1 X5 X2) → False) → X5 = (k1_funcop_1 X1) → (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) = (k1_funct_1 X1 X2) → v1_relat_1 X5 → v1_relat_1 X1 → v1_funct_1 X5 → v1_funct_1 X1 → r2_hidden X2 (k9_xtuple_0 X1) → False) → (∀X2 X3 X1, ((k1_funct_1 (k5_relat_1 X1 X3) X2) = (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X2 (k9_xtuple_0 (k5_relat_1 X1 X3)) → False) → (∀X1 X2, (X1 = X2 → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk26_2 X1 X2)) = (k1_funct_1 X2 (esk26_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k5_relat_1 X1 X2) → m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 X1)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_relat_1 X1 → v1_xboole_0 (k1_funct_1 X1 X2) → m1_subset_1 X2 (k9_xtuple_0 X1) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 X1)) → False) → (∀X1 X2, (X2 = (k1_funcop_1 X1) → False) → (r2_hidden (esk5_2 X1 X2) (k9_xtuple_0 X1) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk26_2 X1 X2) (k9_xtuple_0 X1) → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (r1_tarski (k9_xtuple_0 (k5_relat_1 X1 X2)) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → 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) → (∀X2 X1, ((k5_relat_1 (k5_relat_1 X1 X2) X2) = (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X1 X2, (v4_funct_1 (k2_tarski X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_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) → (∀X2 X1, ((k9_xtuple_0 (k5_relat_1 X1 X2)) = (k3_xboole_0 (k9_xtuple_0 X1) X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v3_relat_1 X1 → False) → (∀X1 X2, (v1_funct_1 X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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 X2, ((k9_xtuple_0 X1) = (k9_xtuple_0 X2) → False) → X1 = (k1_funcop_1 X2) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (v3_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v3_relat_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_xboole_0 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_funct_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v3_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_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_xboole_0 X2 → False) → v1_xboole_0 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) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_relat_1 (k3_xboole_0 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 (k9_xtuple_0 X1) → False) → (∀X2 X1, (v1_funct_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_relat_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk24_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk23_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk11_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k9_xtuple_0 X1) → False) → (∀X1, ((k5_relat_1 X1 (k9_xtuple_0 X1)) = X1 → False) → v1_relat_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_xboole_0 X1 → False) → (∀X1, ((k1_funcop_1 (k1_funcop_1 X1)) = X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk21_1 X1) X1 → False) → False) → (∀X1, (v4_funct_1 (k1_tarski X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_zfmisc_1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v1_funct_1 (k1_funcop_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_relat_1 (k1_funcop_1 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk24_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk23_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk11_1 X1) → False) → (∀X1, (v2_relat_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 (k9_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 (k9_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_zfmisc_1 (esk23_1 X1) → False) → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k1_funcop_1 (k5_relat_1 esk1_0 esk2_0)) = (k5_relat_1 (k1_funcop_1 esk1_0) esk2_0) → False) → (∀X1 X2, v1_xboole_0 (k2_tarski X1 X2) → False) → (∀X1, v1_subset_1 (esk19_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v3_funct_1 esk22_0 → False) → (v1_xboole_0 esk25_0 → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk17_0 → False) → (v1_xboole_0 esk10_0 → False) → (∀X1 X2 X3 X4, (v1_relat_1 (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_tarski (k2_tarski X3 X4) (k1_tarski X3))) → False) → False) → (∀X1 X2, (v1_funct_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) → False) → False) → (∀X1 X2, (v1_relat_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) → False) → False) → (∀X2 X1, (v1_xtuple_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → 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 (esk8_1 X1) X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → (∀X1, (v1_xboole_0 (esk16_1 X1) → False) → False) → ((v1_xtuple_0 esk13_0 → False) → False) → ((v4_funct_1 esk25_0 → False) → False) → ((v2_relat_1 esk20_0 → False) → False) → ((v2_relat_1 esk18_0 → False) → False) → ((v2_relat_1 esk15_0 → False) → False) → ((v2_funct_1 esk14_0 → False) → False) → ((v1_xboole_0 esk12_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_funct_1 esk22_0 → False) → False) → ((v1_funct_1 esk20_0 → False) → False) → ((v1_funct_1 esk18_0 → False) → False) → ((v1_funct_1 esk14_0 → False) → False) → ((v1_funct_1 esk9_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v1_relat_1 esk22_0 → False) → False) → ((v1_relat_1 esk20_0 → False) → False) → ((v1_relat_1 esk18_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v1_relat_1 esk14_0 → False) → False) → ((v1_relat_1 esk10_0 → False) → False) → ((v1_relat_1 esk9_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → False