Theorem. (
t57_funct_3)
∀k13_funct_3 : set → set → set, ∀v1_relat_1 : set → prop, ∀v1_funct_1 : set → prop, ∀esk12_3 : set → set → set → set, ∀k1_funct_1 : set → set → set, ∀k3_xboole_0 : set → set → set, ∀k9_xtuple_0 : set → set, ∀k8_relat_1 : set → set → set, ∀esk11_3 : set → set → set → set, ∀esk24_2 : set → set → set, ∀v1_zfmisc_1 : set → prop, ∀v2_funct_1 : set → prop, ∀k1_xboole_0 : set, ∀esk22_0 : set, ∀esk21_0 : set, ∀esk15_0 : set, ∀esk13_1 : set → set, ∀esk18_0 : set, ∀esk14_0 : set, ∀esk16_0 : set, ∀esk17_0 : set, ∀esk20_0 : set, ∀esk19_0 : set, ∀esk23_0 : set, ∀esk2_0 : set, ∀esk4_0 : set, ∀esk1_0 : set, ∀esk3_0 : set, ∀v3_funct_1 : set → prop, ∀v3_relat_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v2_relat_1 : set → prop, ∀m1_subset_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀esk10_3 : set → set → set → set, ∀esk7_3 : set → set → set → set, ∀esk9_3 : set → set → set → set, ∀esk8_3 : set → set → set → set, ∀k1_tarski : set → set, ∀esk5_4 : set → set → set → set → set, ∀esk6_4 : set → set → set → set → set, ∀k2_tarski : set → set → set, ∀k2_zfmisc_1 : set → set → set, ∀r2_hidden : set → set → prop, (∀X3 X2 X4 X1, ((k2_tarski (k2_tarski (esk5_4 X2 X3 X4 X1) (esk6_4 X2 X3 X4 X1)) (k1_tarski (esk5_4 X2 X3 X4 X1))) = X1 → False) → X4 = (k2_zfmisc_1 X2 X3) → r2_hidden X1 X4 → False) → (∀X2 X1 X3, (X1 = (k13_funct_3 X2 X3) → False) → (k9_xtuple_0 X1) = (k3_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3)) → (k2_tarski (k2_tarski (k1_funct_1 X2 (esk12_3 X2 X3 X1)) (k1_funct_1 X3 (esk12_3 X2 X3 X1))) (k1_tarski (k1_funct_1 X2 (esk12_3 X2 X3 X1)))) = (k1_funct_1 X1 (esk12_3 X2 X3 X1)) → v1_relat_1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X3 X2 X1, (X3 = (k2_zfmisc_1 X1 X2) → False) → ((k2_tarski (k2_tarski (esk8_3 X1 X2 X3) (esk9_3 X1 X2 X3)) (k1_tarski (esk8_3 X1 X2 X3))) = (esk7_3 X1 X2 X3) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → False) → (∀X2 X3 X1, (X3 = (k8_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden (esk11_3 X1 X2 X3) X3 → r2_hidden (esk11_3 X1 X2 X3) (k9_xtuple_0 X1) → r2_hidden (k1_funct_1 X1 (esk11_3 X1 X2 X3)) X2 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk10_3 X1 X2 X3) X3 → r2_hidden (esk10_3 X1 X2 X3) X2 → r2_hidden (esk10_3 X1 X2 X3) X1 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk6_4 X1 X2 X3 X4) X2 → False) → X3 = (k2_zfmisc_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk5_4 X1 X2 X3 X4) X1 → False) → X3 = (k2_zfmisc_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X5 X4 X1 X2 X3, (X3 = (k2_zfmisc_1 X1 X2) → False) → (esk7_3 X1 X2 X3) = (k2_tarski (k2_tarski X4 X5) (k1_tarski X4)) → r2_hidden X5 X2 → r2_hidden X4 X1 → r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (∀X2 X3 X1, (X3 = (k8_relat_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (k1_funct_1 X1 (esk11_3 X1 X2 X3)) X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1 X3 X2, ((k2_tarski (k2_tarski (k1_funct_1 X1 X3) (k1_funct_1 X2 X3)) (k1_tarski (k1_funct_1 X1 X3))) = (k1_funct_1 (k13_funct_3 X1 X2) X3) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → r2_hidden X3 (k3_xboole_0 (k9_xtuple_0 X1) (k9_xtuple_0 X2)) → False) → (∀X1 X3 X4 X2, ((k1_funct_1 X2 X1) = (k2_tarski (k2_tarski (k1_funct_1 X3 X1) (k1_funct_1 X4 X1)) (k1_tarski (k1_funct_1 X3 X1))) → False) → X2 = (k13_funct_3 X3 X4) → v1_relat_1 X4 → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → False) → (∀X3 X2 X1, (X3 = (k8_relat_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (esk11_3 X1 X2 X3) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X2 → False) → False) → (∀X2 X3 X1, (X3 = (k2_zfmisc_1 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk9_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k2_zfmisc_1 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X2 X1 X3, (X3 = (k13_funct_3 X1 X2) → False) → (r2_hidden (esk12_3 X1 X2 X3) (k9_xtuple_0 X3) → False) → (k9_xtuple_0 X3) = (k3_xboole_0 (k9_xtuple_0 X1) (k9_xtuple_0 X2)) → v1_relat_1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X4 X2 X3 X1 X5 X6, (r2_hidden X5 X6 → False) → X6 = (k2_zfmisc_1 X2 X4) → X5 = (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) → r2_hidden X3 X4 → r2_hidden X1 X2 → False) → (∀X2 X3 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k8_relat_1 X2 X3) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → r2_hidden (k1_funct_1 X2 X1) X3 → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) = (k2_tarski (k2_tarski X2 X4) (k1_tarski X2)) → False) → (∀X3 X4 X1 X2, (X1 = X2 → False) → (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) = (k2_tarski (k2_tarski X4 X2) (k1_tarski X4)) → False) → (∀X1 X2, (X1 = X2 → False) → r2_hidden (esk24_2 X1 X2) X2 → r2_hidden (esk24_2 X1 X2) 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) → (∀X4 X2 X1 X3, (r2_hidden (k1_funct_1 X1 X2) X3 → False) → X4 = (k8_relat_1 X1 X3) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X2 X4 → False) → (∀X2 X1 X3, ((k9_xtuple_0 X1) = (k3_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3)) → False) → X1 = (k13_funct_3 X2 X3) → v1_relat_1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X3 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_xboole_0 X2 X3) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk24_2 X1 X2) X2 → False) → (r2_hidden (esk24_2 X1 X2) X1 → False) → False) → (∀X3 X4 X1 X2, (r2_hidden X1 (k9_xtuple_0 X2) → False) → X3 = (k8_relat_1 X2 X4) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 X3 → False) → (∀X2 X1, (v1_funct_1 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_funct_1 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_xboole_0 (k13_funct_3 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X4 X2) → r2_hidden X1 X3 → 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) → (∀X1 X2, (v1_funct_1 (k13_funct_3 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k13_funct_3 X1 X2) → False) → 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_xboole_0 (k2_zfmisc_1 X1 X2) → 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) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v1_xboole_0 (k8_relat_1 X1 X2) → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_xboole_0 (k8_relat_1 X1 X2) → False) → v1_xboole_0 X2 → v1_relat_1 X1 → 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, (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 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, (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_xboole_0 X1 → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → v1_funct_1 X1 → 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, (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) → (∀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, (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) → ((k8_relat_1 (k13_funct_3 esk3_0 esk4_0) (k2_zfmisc_1 esk1_0 esk2_0)) = (k3_xboole_0 (k8_relat_1 esk3_0 esk1_0) (k8_relat_1 esk4_0 esk2_0)) → False) → (∀X1 X2, v1_xboole_0 (k2_tarski X1 X2) → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v3_funct_1 esk22_0 → False) → (v1_xboole_0 esk23_0 → False) → (v1_xboole_0 esk21_0 → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk2_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) → (∀X1 X2, (v1_relat_1 (k2_zfmisc_1 X1 X2) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk13_1 X1) X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((v4_funct_1 esk23_0 → False) → False) → ((v2_relat_1 esk21_0 → False) → False) → ((v2_relat_1 esk20_0 → False) → False) → ((v2_relat_1 esk18_0 → False) → False) → ((v2_funct_1 esk17_0 → False) → False) → ((v1_funct_1 esk22_0 → False) → False) → ((v1_funct_1 esk21_0 → False) → False) → ((v1_funct_1 esk20_0 → False) → False) → ((v1_funct_1 esk17_0 → False) → False) → ((v1_funct_1 esk14_0 → False) → False) → ((v1_funct_1 esk4_0 → False) → False) → ((v1_funct_1 esk3_0 → False) → False) → ((v1_relat_1 esk22_0 → False) → False) → ((v1_relat_1 esk21_0 → False) → False) → ((v1_relat_1 esk20_0 → False) → False) → ((v1_relat_1 esk18_0 → False) → False) → ((v1_relat_1 esk17_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v1_relat_1 esk14_0 → False) → False) → ((v1_relat_1 esk4_0 → False) → False) → ((v1_relat_1 esk3_0 → False) → False) → ((v1_xboole_0 esk16_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → False