Theorem. (
t34_funct_3)
∀r2_hidden : set → set → prop, ∀k9_xtuple_0 : set → set, ∀k1_funct_1 : set → set → set, ∀esk22_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀m1_subset_1 : set → set → prop, ∀v2_relat_1 : set → prop, ∀v1_zfmisc_1 : set → prop, ∀v1_setfam_1 : set → prop, ∀esk19_1 : set → set, ∀esk16_1 : set → set, ∀k1_xboole_0 : set, ∀esk14_1 : set → set, ∀esk17_0 : set, ∀esk15_0 : set, ∀esk6_0 : set, ∀esk4_1 : set → set, ∀esk10_0 : set, ∀esk5_0 : set, ∀esk9_0 : set, ∀esk8_0 : set, ∀esk13_0 : set, ∀esk11_1 : set → set, ∀esk12_0 : set, ∀esk20_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk7_1 : set → set, ∀esk18_1 : set → set, ∀v3_funct_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v3_relat_1 : set → prop, ∀v1_subset_1 : set → set → prop, ∀esk21_2 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀esk3_2 : set → set → set, ∀k3_funct_3 : set → set, ∀v2_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀v1_funct_1 : set → prop, ∀k8_relat_1 : set → set → set, ∀k3_relat_1 : set → set → set, ∀k10_xtuple_0 : set → set, ∀r1_tarski : set → set → prop, (∀X1 X3 X2, (r1_tarski X3 (k10_xtuple_0 (k3_relat_1 X1 X2)) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → r1_tarski X3 (k10_xtuple_0 X2) → r1_tarski (k8_relat_1 X2 X3) (k10_xtuple_0 X1) → False) → (∀X2 X1 X3, (r2_hidden X1 (k9_xtuple_0 (k3_relat_1 X2 X3)) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → r2_hidden (k1_funct_1 X2 X1) (k9_xtuple_0 X3) → False) → (∀X1 X3 X2, (r1_tarski (k8_relat_1 X2 X3) (k10_xtuple_0 X1) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v2_funct_1 X2 → r1_tarski X3 (k10_xtuple_0 (k3_relat_1 X1 X2)) → False) → (∀X1 X2 X3, (r2_hidden (k1_funct_1 X1 X2) (k9_xtuple_0 X3) → False) → v1_relat_1 X3 → v1_relat_1 X1 → v1_funct_1 X3 → v1_funct_1 X1 → r2_hidden X2 (k9_xtuple_0 (k3_relat_1 X1 X3)) → False) → (∀X1 X2, (X1 = (k3_funct_3 X2) → False) → (k9_xtuple_0 X1) = (k1_zfmisc_1 (k10_xtuple_0 X2)) → (k8_relat_1 X2 (esk3_2 X2 X1)) = (k1_funct_1 X1 (esk3_2 X2 X1)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X2, (X1 = X2 → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk22_2 X1 X2)) = (k1_funct_1 X2 (esk22_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X3 X1 X2, (r2_hidden X1 (k9_xtuple_0 X2) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 (k3_relat_1 X2 X3)) → False) → (∀X1 X3 X2, ((k1_funct_1 (k3_relat_1 X1 X2) X3) = (k1_funct_1 X2 (k1_funct_1 X1 X3)) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → r2_hidden X3 (k9_xtuple_0 X1) → False) → (∀X1 X2, (X1 = X2 → False) → r2_hidden (esk21_2 X1 X2) X2 → r2_hidden (esk21_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) → (∀X1 X2, (X2 = (k3_funct_3 X1) → False) → (r1_tarski (esk3_2 X1 X2) (k10_xtuple_0 X1) → False) → (k9_xtuple_0 X2) = (k1_zfmisc_1 (k10_xtuple_0 X1)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1, ((k1_funct_1 (k3_funct_3 X1) X2) = (k8_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X2 (k9_xtuple_0 (k3_funct_3 X1)) → False) → (∀X1 X3 X2, ((k8_relat_1 X2 X1) = (k1_funct_1 X3 X1) → False) → X3 = (k3_funct_3 X2) → v1_relat_1 X3 → v1_relat_1 X2 → v1_funct_1 X3 → v1_funct_1 X2 → r1_tarski X1 (k10_xtuple_0 X2) → False) → (∀X3 X2 X1, ((k8_relat_1 (k3_relat_1 X1 X2) X3) = (k8_relat_1 X1 (k8_relat_1 X2 X3)) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X2 X1, (r1_tarski (k10_xtuple_0 (k3_relat_1 X1 X2)) (k10_xtuple_0 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk22_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 (esk21_2 X1 X2) X2 → False) → (r2_hidden (esk21_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v2_funct_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v2_funct_1 X2 → v2_funct_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v2_funct_1 X2 → v2_funct_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 X3, (r1_tarski X1 X3 → False) → r1_tarski X2 X3 → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_funct_1 (k3_relat_1 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 (k3_relat_1 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) → (∀X1 X2, (v2_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v2_relat_1 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) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v2_relat_1 X2 → False) → (∀X1 X2, ((k9_xtuple_0 X1) = (k1_zfmisc_1 (k10_xtuple_0 X2)) → False) → X1 = (k3_funct_3 X2) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_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) → (∀X2 X1, (v1_xboole_0 (k8_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_xboole_0 (k8_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X1 X2, (v1_xboole_0 (k3_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_xboole_0 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_xboole_0 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, (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) → (∀X1, (v3_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_zfmisc_1 (k10_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_setfam_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v2_relat_1 X1 → False) → (∀X1, (v1_zfmisc_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v3_funct_1 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk16_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk7_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 (k10_xtuple_0 X1) → 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_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, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk16_1 X1) X1 → False) → False) → (∀X1, (v1_zfmisc_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_zfmisc_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 (k3_funct_3 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_relat_1 (k3_funct_3 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk19_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk18_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk7_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 (k10_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 (esk18_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) → ((k3_relat_1 (k3_funct_3 esk2_0) (k3_funct_3 esk1_0)) = (k3_funct_3 (k3_relat_1 esk1_0 esk2_0)) → False) → (∀X1, v1_subset_1 (esk14_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v3_funct_1 esk17_0 → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk12_0 → False) → (v1_xboole_0 esk6_0 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk14_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk11_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk4_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, (v1_xboole_0 (esk11_1 X1) → False) → False) → ((v4_funct_1 esk20_0 → False) → False) → ((v2_relat_1 esk15_0 → False) → False) → ((v2_relat_1 esk13_0 → False) → False) → ((v2_relat_1 esk10_0 → False) → False) → ((v1_xboole_0 esk8_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_funct_1 esk9_0 → False) → False) → ((v2_funct_1 esk2_0 → False) → False) → ((v1_funct_1 esk17_0 → False) → False) → ((v1_funct_1 esk15_0 → False) → False) → ((v1_funct_1 esk13_0 → False) → False) → ((v1_funct_1 esk9_0 → False) → False) → ((v1_funct_1 esk5_0 → False) → False) → ((v1_funct_1 esk2_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v1_relat_1 esk17_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v1_relat_1 esk13_0 → False) → False) → ((v1_relat_1 esk10_0 → False) → False) → ((v1_relat_1 esk9_0 → False) → False) → ((v1_relat_1 esk6_0 → False) → False) → ((v1_relat_1 esk5_0 → False) → False) → ((v1_relat_1 esk2_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → False