Theorem. (
t27_funct_1)
∀esk5_3 : set → set → set → set, ∀k10_xtuple_0 : set → set, ∀esk6_2 : set → set → set, ∀k1_tarski : set → set, ∀esk4_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀v2_relat_1 : set → prop, ∀esk19_1 : set → set, ∀k1_xboole_0 : set, ∀v3_relat_1 : set → prop, ∀esk17_0 : set, ∀esk14_0 : set, ∀esk15_0 : set, ∀esk13_0 : set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk10_1 : set → set, ∀esk12_0 : set, ∀esk16_0 : set, ∀v1_zfmisc_1 : set → prop, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk18_1 : set → set, ∀esk9_1 : set → set, ∀esk8_1 : set → set, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀esk7_2 : set → set → set, ∀esk1_0 : set, ∀v2_funct_1 : set → prop, ∀r1_tarski : set → set → prop, ∀esk20_2 : set → set → set, ∀v1_relat_1 : set → prop, ∀v1_funct_1 : set → prop, ∀k9_xtuple_0 : set → set, ∀r2_hidden : set → set → prop, ∀k3_relat_1 : set → set → set, ∀k1_funct_1 : set → set → set, (∀X1 X3 X2, ((k1_funct_1 (k3_relat_1 X2 X1) X3) = (k1_funct_1 X1 (k1_funct_1 X2 X3)) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → r2_hidden X3 (k9_xtuple_0 (k3_relat_1 X2 X1)) → False) → (∀X3 X2 X1, (r2_hidden (esk5_3 X1 X2 X3) (k9_xtuple_0 X1) → False) → X2 = (k10_xtuple_0 X1) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X3 X2 → False) → (∀X1 X2, (X1 = X2 → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk20_2 X1 X2)) = (k1_funct_1 X2 (esk20_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X1 X3 X2, ((k1_funct_1 X2 (esk5_3 X2 X3 X1)) = X1 → False) → X3 = (k10_xtuple_0 X2) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 X3 → False) → (∀X2 X1, (X1 = X2 → False) → (v2_funct_1 esk1_0 → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k3_relat_1 X1 esk1_0) = (k3_relat_1 X2 esk1_0) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → r1_tarski (k10_xtuple_0 X2) (k9_xtuple_0 esk1_0) → r1_tarski (k10_xtuple_0 X1) (k9_xtuple_0 esk1_0) → False) → (∀X3 X2 X1, (X2 = (k10_xtuple_0 X1) → False) → (esk6_2 X1 X2) = (k1_funct_1 X1 X3) → v1_relat_1 X1 → v1_funct_1 X1 → r2_hidden X3 (k9_xtuple_0 X1) → r2_hidden (esk6_2 X1 X2) X2 → 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 X3, (X2 = X3 → False) → (k1_funct_1 X1 X2) = (k1_funct_1 X1 X3) → v1_relat_1 X1 → v1_funct_1 X1 → v2_funct_1 X1 → r2_hidden X3 (k9_xtuple_0 X1) → r2_hidden X2 (k9_xtuple_0 X1) → False) → (∀X2 X1, (X2 = (k10_xtuple_0 X1) → False) → ((k1_funct_1 X1 (esk7_2 X1 X2)) = (esk6_2 X1 X2) → False) → (r2_hidden (esk6_2 X1 X2) X2 → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1, (X2 = (k10_xtuple_0 X1) → False) → (r2_hidden (esk6_2 X1 X2) X2 → False) → (r2_hidden (esk7_2 X1 X2) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1 X3 X4, (r2_hidden X3 X4 → False) → X4 = (k10_xtuple_0 X2) → X3 = (k1_funct_1 X2 X1) → v1_relat_1 X2 → v1_funct_1 X2 → r2_hidden X1 (k9_xtuple_0 X2) → False) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → (esk4_2 X1 X2) = X1 → r2_hidden (esk4_2 X1 X2) X2 → False) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk20_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, ((k9_xtuple_0 (k3_relat_1 X1 X2)) = (k9_xtuple_0 X1) → False) → v1_relat_1 X2 → v1_relat_1 X1 → r1_tarski (k10_xtuple_0 X1) (k9_xtuple_0 X2) → 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 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, ((k1_tarski (k1_funct_1 X1 X2)) = (k10_xtuple_0 X1) → False) → (k1_tarski X2) = (k9_xtuple_0 X1) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → ((esk4_2 X1 X2) = X1 → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → False) → (∀X1, ((k1_funct_1 X1 (esk8_1 X1)) = (k1_funct_1 X1 (esk9_1 X1)) → False) → (v2_funct_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → 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) → (∀X1 X2, (v2_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v2_relat_1 X2 → 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) → (∀X2 X1, ((k1_funct_1 (esk19_1 X2) X1) = X2 → False) → r2_hidden X1 (k1_tarski k1_xboole_0) → False) → (∀X2 X1, ((k1_funct_1 (esk18_1 X2) X1) = X2 → False) → r2_hidden X1 (k1_tarski k1_xboole_0) → False) → (∀X2 X1, (r2_hidden X1 X2 → False) → r1_tarski (k1_tarski X1) X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1, (v2_funct_1 X1 → False) → (r2_hidden (esk9_1 X1) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → (r2_hidden (esk8_1 X1) (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 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, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (r1_tarski (k1_tarski X1) X2 → False) → r2_hidden X1 X2 → 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) → (∀X2 X1 X3, (X1 = X3 → False) → X2 = (k1_tarski X3) → r2_hidden X1 X2 → False) → (∀X1, (v2_funct_1 X1 → False) → (esk8_1 X1) = (esk9_1 X1) → v1_relat_1 X1 → v1_funct_1 X1 → 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, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k10_xtuple_0 X1) → False) → (((k3_relat_1 esk3_0 esk1_0) = (k3_relat_1 esk2_0 esk1_0) → False) → v2_funct_1 esk1_0 → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k1_tarski X2) → False) → ((r1_tarski (k10_xtuple_0 esk3_0) (k9_xtuple_0 esk1_0) → False) → v2_funct_1 esk1_0 → False) → ((r1_tarski (k10_xtuple_0 esk2_0) (k9_xtuple_0 esk1_0) → False) → v2_funct_1 esk1_0 → False) → (∀X1, (v1_zfmisc_1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v1_zfmisc_1 (k10_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_zfmisc_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 (k10_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_zfmisc_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_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) → (((k9_xtuple_0 esk3_0) = (k9_xtuple_0 esk2_0) → False) → v2_funct_1 esk1_0 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((v1_funct_1 esk3_0 → False) → v2_funct_1 esk1_0 → False) → ((v1_funct_1 esk2_0 → False) → v2_funct_1 esk1_0 → False) → ((v1_relat_1 esk3_0 → False) → v2_funct_1 esk1_0 → False) → ((v1_relat_1 esk2_0 → False) → v2_funct_1 esk1_0 → False) → (esk3_0 = esk2_0 → v2_funct_1 esk1_0 → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v1_zfmisc_1 esk17_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk12_0 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk10_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k9_xtuple_0 (esk19_1 X1)) = (k1_tarski k1_xboole_0) → False) → False) → (∀X1, ((k9_xtuple_0 (esk18_1 X1)) = (k1_tarski k1_xboole_0) → False) → False) → (∀X1, (v1_zfmisc_1 (k1_tarski X1) → False) → False) → (∀X1, (v1_funct_1 (esk19_1 X1) → False) → False) → (∀X1, (v1_funct_1 (esk18_1 X1) → False) → False) → (∀X1, (v1_relat_1 (esk19_1 X1) → False) → False) → (∀X1, (v1_relat_1 (esk18_1 X1) → False) → False) → ((v2_relat_1 esk15_0 → False) → False) → ((v1_zfmisc_1 esk14_0 → False) → False) → ((v1_xboole_0 esk13_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_funct_1 esk11_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v1_relat_1 esk15_0 → False) → False) → ((v1_relat_1 esk12_0 → False) → False) → ((v1_relat_1 esk11_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False