Theorem. (
t42_partfun2)
∀r2_hidden : set → set → prop, ∀k9_subset_1 : set → set → set → set, ∀k1_relset_1 : set → set → set, ∀o_5_0_partfun2 : set → set → set → set → set → set, ∀k3_xboole_0 : set → set → set, ∀esk7_4 : set → set → set → set → set, ∀k1_funct_1 : set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk8_3 : set → set → set → set, ∀k5_relat_1 : set → set → set, ∀esk6_3 : set → set → set → set, ∀v4_relat_1 : set → set → prop, ∀r1_tarski : set → set → prop, ∀r1_xboole_0 : set → set → prop, ∀k1_xboole_0 : set, ∀v1_zfmisc_1 : set → prop, ∀v2_funct_1 : set → prop, ∀esk3_0 : set, ∀esk5_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk4_0 : set, ∀esk14_0 : set, ∀esk12_2 : set → set → set, ∀esk15_2 : set → set → set, ∀esk10_1 : set → set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk13_0 : set, ∀esk16_0 : set, ∀v4_funct_1 : set → prop, ∀v5_relat_1 : set → set → prop, ∀v1_relat_1 : set → prop, ∀k9_xtuple_0 : set → set, ∀esk9_3 : set → set → set → set, ∀k8_subset_1 : set → set → set → set, ∀esk17_4 : set → set → set → set → set, ∀k7_partfun1 : set → set → set → set, ∀esk18_5 : set → set → set → set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀k2_zfmisc_1 : set → set → set, ∀v1_funct_1 : set → prop, ∀v3_funct_1 : set → prop, ∀k2_partfun1 : set → set → set → set → set, ∀v1_xboole_0 : set → prop, (∀X1 X5 X3 X2 X4, (v1_xboole_0 X4 → False) → (v1_xboole_0 X1 → False) → (v3_funct_1 (k2_partfun1 X4 X1 X2 X3) → False) → (k7_partfun1 X1 X2 (esk18_5 X3 X1 X4 X2 X5)) = X5 → v1_funct_1 X2 → m1_subset_1 X5 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X4 X1)) → False) → (∀X2 X5 X1 X4 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v3_funct_1 (k2_partfun1 X3 X2 X4 X1) → False) → (r2_hidden (esk18_5 X1 X2 X3 X4 X5) (k9_subset_1 X3 X1 (k1_relset_1 X3 X4)) → False) → v1_funct_1 X4 → m1_subset_1 X5 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X2 X5 X1 X4 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v3_funct_1 (k2_partfun1 X3 X2 X4 X1) → False) → (m1_subset_1 (esk18_5 X1 X2 X3 X4 X5) X3 → False) → v1_funct_1 X4 → m1_subset_1 X5 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X1 X4 X5 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (o_5_0_partfun2 X4 X5 X1 X2 X3) (k9_subset_1 X1 (k3_xboole_0 X4 X5) (k1_relset_1 X1 X3)) → False) → v1_funct_1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X2 X1 X3 X4 X5, ((k7_partfun1 X5 X4 X1) = (esk17_4 X3 X5 X2 X4) → False) → (v1_xboole_0 X5 → False) → (v1_xboole_0 X2 → False) → v1_funct_1 X4 → m1_subset_1 X1 X2 → v3_funct_1 (k2_partfun1 X2 X5 X4 X3) → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X5)) → r2_hidden X1 (k9_subset_1 X2 X3 (k1_relset_1 X2 X4)) → False) → (∀X2 X1 X4 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 (esk17_4 X1 X2 X3 X4) X2 → False) → v1_funct_1 X4 → v3_funct_1 (k2_partfun1 X3 X2 X4 X1) → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X1 X3 X5 X4 X2, ((k7_partfun1 X2 (k2_partfun1 X1 X2 X4 X5) X3) = (k7_partfun1 X2 X4 X3) → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_funct_1 X4 → m1_subset_1 X3 X1 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → r2_hidden X3 (k8_subset_1 X1 (k1_relset_1 X1 X4) X5) → False) → (∀X2 X4 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v3_funct_1 X1 → False) → (k1_funct_1 X1 (esk7_4 X2 X3 X1 X4)) = X4 → v1_funct_1 X1 → m1_subset_1 X4 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X4 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (v3_funct_1 X3 → False) → (r2_hidden (esk7_4 X1 X2 X3 X4) (k1_relset_1 X1 X3) → False) → v1_funct_1 X3 → m1_subset_1 X4 X2 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X4 X2 X1 X3, (m1_subset_1 (k2_partfun1 X1 X2 X3 X4) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → v1_funct_1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X4 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (v3_funct_1 X3 → False) → (m1_subset_1 (esk7_4 X1 X2 X3 X4) X1 → False) → v1_funct_1 X3 → m1_subset_1 X4 X2 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X4 X2 X1 X3, (v1_funct_1 (k2_partfun1 X1 X2 X3 X4) → False) → v1_funct_1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk9_3 X1 X2 X3) X3 → r2_hidden (esk9_3 X1 X2 X3) X2 → r2_hidden (esk9_3 X1 X2 X3) X1 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X2 → False) → (∀X4 X3 X2 X1, ((k2_partfun1 X2 X3 X1 X4) = (k5_relat_1 X1 X4) → False) → v1_funct_1 X1 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X2 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X2 X1 X3 X4, ((k1_funct_1 X3 X1) = (esk6_3 X2 X4 X3) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X2 → False) → v1_funct_1 X3 → v3_funct_1 X3 → m1_subset_1 X1 X2 → r2_hidden X1 (k1_relset_1 X2 X3) → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X2 X4)) → False) → (∀X4 X2 X3 X1, (v1_relat_1 (k9_xtuple_0 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X3) X4)) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (esk6_3 X1 X2 X3) X2 → False) → v1_funct_1 X3 → v3_funct_1 X3 → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk9_3 X1 X2 X3) X3 → False) → (r2_hidden (esk9_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk9_3 X1 X2 X3) X3 → False) → (r2_hidden (esk9_3 X1 X2 X3) X2 → False) → False) → (∀X3 X2 X1, (m1_subset_1 (k9_subset_1 X2 X3 X1) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_subset_1 (k8_subset_1 X2 X1 X3) (k1_zfmisc_1 X2) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, (m1_subset_1 (k7_partfun1 X2 X1 X3) X2 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v5_relat_1 X1 X2 → False) → (∀X3 X2 X1, ((k9_subset_1 X2 X1 X3) = (k9_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k8_subset_1 X2 X1 X3) = (k8_subset_1 X2 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X3 X1, ((k7_partfun1 X2 X1 X3) = (k1_funct_1 X1 X3) → False) → v1_funct_1 X1 → v1_relat_1 X1 → v5_relat_1 X1 X2 → r2_hidden X3 (k9_xtuple_0 X1) → False) → (∀X3 X1 X2, (v5_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X3 X1 X2, (v4_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → False) → (∀X1 X3 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X1)) → False) → (∀X3 X2 X1, (v1_relat_1 X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → 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) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X1) = (k3_xboole_0 X3 X1) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X3 X2 X1, ((k8_subset_1 X2 X1 X3) = (k3_xboole_0 X1 X3) → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1 X2 X3, (v5_relat_1 (k2_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v5_relat_1 X3 X2 → v5_relat_1 X1 X2 → False) → (∀X1 X2 X3, (v4_relat_1 (k2_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v4_relat_1 X3 X2 → v4_relat_1 X1 X2 → 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) → (∀X3 X2 X1, ((k9_subset_1 X2 X3 X3) = X3 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, ((k8_subset_1 X2 X1 X1) = X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → 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 X3, (v5_relat_1 (k3_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v5_relat_1 X1 X2 → False) → (∀X1 X2 X3, (v4_relat_1 (k3_xboole_0 X1 X3) X2 → False) → v1_relat_1 X3 → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 (k1_relset_1 X2 X1) (k1_zfmisc_1 X2) → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X2 = (k2_xboole_0 X3 X4) → r2_hidden X1 X2 → False) → (∀X2 X3 X1, (v1_relat_1 (k1_funct_1 X1 X2) → False) → v1_funct_1 X1 → v1_relat_1 X1 → v4_funct_1 X3 → v5_relat_1 X1 X3 → False) → (∀X2 X3 X1, (v1_funct_1 (k1_funct_1 X1 X2) → False) → v1_funct_1 X1 → v1_relat_1 X1 → v4_funct_1 X3 → v5_relat_1 X1 X3 → 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) → (∀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) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X2 X4) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X4 X2) → r2_hidden X1 X2 → 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) → (∀X1 X2, (v1_funct_1 X2 → False) → v1_funct_1 X1 → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, ((k1_relset_1 X2 X1) = (k9_xtuple_0 X1) → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → 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_relat_1 (k5_relat_1 X1 X2) → False) → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X2 X1, (v1_funct_1 (k5_relat_1 X1 X2) → False) → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1 X2, (v4_funct_1 X2 → False) → v4_funct_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 (k5_relat_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (r1_xboole_0 X1 X2 → False) → (k3_xboole_0 X1 X2) = k1_xboole_0 → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = k1_xboole_0 → False) → r1_xboole_0 X1 X2 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 (k9_xtuple_0 X1) → False) → (∀X2 X1, (v1_relat_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_funct_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, (v2_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 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, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (v3_funct_1 (k2_partfun1 esk3_0 esk4_0 esk5_0 (k2_xboole_0 esk1_0 esk2_0)) → False) → (r1_xboole_0 (k3_xboole_0 esk1_0 esk2_0) (k1_relset_1 esk3_0 esk5_0) → False) → (v3_funct_1 esk14_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk4_0 → False) → (v1_xboole_0 esk3_0 → False) → ((v3_funct_1 (k2_partfun1 esk3_0 esk4_0 esk5_0 esk2_0) → False) → False) → ((v3_funct_1 (k2_partfun1 esk3_0 esk4_0 esk5_0 esk1_0) → False) → False) → (∀X2 X1, (m1_subset_1 (esk12_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → ((m1_subset_1 esk5_0 (k1_zfmisc_1 (k2_zfmisc_1 esk3_0 esk4_0)) → False) → False) → (∀X2 X1, (v5_relat_1 (esk15_2 X1 X2) X2 → False) → False) → (∀X2 X1, (v5_relat_1 (esk12_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk15_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v4_relat_1 (esk12_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_relat_1 (esk15_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (esk12_2 X1 X2) → False) → False) → (∀X1 X2, (v1_funct_1 (esk15_2 X1 X2) → False) → False) → (∀X1 X2, (v1_xboole_0 (esk12_2 X1 X2) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk10_1 X1) X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → ((v4_funct_1 esk16_0 → False) → False) → ((v2_funct_1 esk13_0 → False) → False) → ((v1_relat_1 esk14_0 → False) → False) → ((v1_relat_1 esk13_0 → False) → False) → ((v1_relat_1 esk11_0 → False) → False) → ((v1_funct_1 esk14_0 → False) → False) → ((v1_funct_1 esk13_0 → False) → False) → ((v1_funct_1 esk11_0 → False) → False) → ((v1_funct_1 esk5_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False