Theorem. (
t140_pboole)
∀esk5_3 : set → set → set → set, ∀r2_hidden : set → set → prop, ∀v2_funct_1 : set → prop, ∀v1_xboole_0 : set → prop, ∀m1_subset_1 : set → set → prop, ∀v1_zfmisc_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v5_ordinal1 : set → prop, ∀v3_funct_1 : set → prop, ∀v2_funcop_1 : set → prop, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v7_ordinal1 : set → prop, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk18_0 : set, ∀esk14_0 : set, ∀esk11_0 : set, ∀esk6_1 : set → set, ∀esk10_0 : set, ∀esk8_0 : set, ∀esk7_0 : set, ∀o_0_0_xboole_0 : set, ∀esk9_0 : set, ∀esk12_0 : set, ∀esk15_0 : set, ∀esk13_0 : set, ∀esk17_0 : set, ∀esk16_0 : set, ∀k1_xboole_0 : set, ∀v3_ordinal1 : set → prop, ∀esk19_2 : set → set → set, ∀k9_xtuple_0 : set → set, ∀k3_xboole_0 : set → set → set, ∀k1_funct_1 : set → set → set, ∀esk4_3 : set → set → set → set, ∀k3_relat_1 : set → set → set, ∀v1_funct_1 : set → prop, ∀v1_funcop_1 : set → prop, ∀v1_relat_1 : set → prop, ∀k8_pboole : set → set → set, (∀X2 X1 X3, (X1 = (k8_pboole X2 X3) → False) → (k9_xtuple_0 X1) = (k3_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3)) → (k3_relat_1 (k1_funct_1 X2 (esk4_3 X2 X3 X1)) (k1_funct_1 X3 (esk4_3 X2 X3 X1))) = (k1_funct_1 X1 (esk4_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 → v1_funcop_1 X3 → v1_funcop_1 X2 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk5_3 X1 X2 X3) X3 → r2_hidden (esk5_3 X1 X2 X3) X2 → r2_hidden (esk5_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (r2_hidden (esk5_3 X1 X2 X3) X2 → False) → False) → (∀X2 X1 X3, (X3 = (k8_pboole X1 X2) → False) → (r2_hidden (esk4_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 → v1_funcop_1 X2 → v1_funcop_1 X1 → False) → (∀X1 X3 X4 X2, ((k1_funct_1 X2 X1) = (k3_relat_1 (k1_funct_1 X3 X1) (k1_funct_1 X4 X1)) → False) → X2 = (k8_pboole 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 → v1_funcop_1 X4 → v1_funcop_1 X3 → r2_hidden X1 (k9_xtuple_0 X2) → False) → (∀X1 X2, (X1 = X2 → False) → (k9_xtuple_0 X1) = (k9_xtuple_0 X2) → (k1_funct_1 X1 (esk19_2 X1 X2)) = (k1_funct_1 X2 (esk19_2 X1 X2)) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → False) → (∀X2 X1 X3, ((k9_xtuple_0 X1) = (k3_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3)) → False) → X1 = (k8_pboole 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 → v1_funcop_1 X3 → v1_funcop_1 X2 → False) → (∀X1 X2 X3, ((k3_relat_1 (k3_relat_1 X1 X2) X3) = (k3_relat_1 X1 (k3_relat_1 X2 X3)) → False) → v1_relat_1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X2, (X1 = X2 → False) → (r2_hidden (esk19_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 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, (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_funcop_1 (k8_pboole X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → v1_funcop_1 X1 → False) → (∀X1 X2, (v1_funct_1 (k8_pboole X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → v1_funcop_1 X1 → False) → (∀X1 X2, (v1_funct_1 (k8_pboole X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → v1_funcop_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) → (∀X1 X2, (v1_relat_1 (k8_pboole X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → v1_funcop_1 X1 → False) → (∀X1 X2, (v1_relat_1 (k8_pboole X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → v1_funcop_1 X1 → False) → (∀X1 X2, (v1_funcop_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funcop_1 X2 → 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 → v1_funcop_1 X2 → 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, (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_funct_1 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_funcop_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k1_funct_1 X1 X2) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_funcop_1 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden 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 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 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, (v3_ordinal1 (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v1_funct_1 X1 → v5_ordinal1 X1 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → 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, (v2_funcop_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_funcop_1 X1 → False) → (∀X1, (v1_funcop_1 X1 → False) → v1_relat_1 X1 → v1_funct_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 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) → ((k8_pboole (k8_pboole esk1_0 esk2_0) esk3_0) = (k8_pboole esk1_0 (k8_pboole esk2_0 esk3_0)) → False) → (v3_funct_1 esk16_0 → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk17_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk13_0 → False) → (v1_xboole_0 esk11_0 → False) → (∀X2 X3 X1, ((k3_xboole_0 (k3_xboole_0 X1 X2) X3) = (k3_xboole_0 X1 (k3_xboole_0 X2 X3)) → False) → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk6_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 esk18_0 → False) → False) → ((v7_ordinal1 esk17_0 → False) → False) → ((v7_ordinal1 esk15_0 → False) → False) → ((v3_funct_1 esk11_0 → False) → False) → ((v2_funct_1 esk12_0 → False) → False) → ((v2_ordinal1 esk13_0 → False) → False) → ((v1_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk13_0 → False) → False) → ((v3_ordinal1 esk9_0 → False) → False) → ((v1_xboole_0 esk10_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_funcop_1 esk7_0 → False) → False) → ((v1_funcop_1 esk3_0 → False) → False) → ((v1_funcop_1 esk2_0 → False) → False) → ((v1_funcop_1 esk1_0 → False) → False) → ((v1_funct_1 esk16_0 → False) → False) → ((v1_funct_1 esk12_0 → False) → False) → ((v1_funct_1 esk11_0 → False) → False) → ((v1_funct_1 esk8_0 → False) → False) → ((v1_funct_1 esk7_0 → False) → False) → ((v1_funct_1 esk3_0 → False) → False) → ((v1_funct_1 esk2_0 → False) → False) → ((v1_funct_1 esk1_0 → False) → False) → ((v1_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk12_0 → False) → False) → ((v1_relat_1 esk11_0 → False) → False) → ((v1_relat_1 esk8_0 → False) → False) → ((v1_relat_1 esk7_0 → False) → False) → ((v1_relat_1 esk3_0 → False) → False) → ((v1_relat_1 esk2_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False