Theorem. (t50_nat_1)
∀r2_relset_1 : set → set → set → set → prop, ∀v1_funct_2 : set → set → set → prop, ∀esk39_4 : set → set → set → set → set, ∀k1_funct_1 : set → set → set, ∀r2_funct_2 : set → set → set → set → prop, ∀k8_nat_1 : set → set → set → set, ∀esk7_2 : set → set → set, ∀v1_xcmplx_0 : set → prop, ∀v2_xxreal_0 : set → prop, ∀v1_xreal_0 : set → prop, ∀r1_tarski : set → set → prop, ∀esk38_2 : set → set → set, ∀esk30_1 : set → set, ∀esk15_1 : set → set, ∀v1_card_1 : set → prop, ∀v3_card_1 : set → set → prop, ∀esk37_1 : set → set, ∀k4_ordinal1 : set, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v5_ordinal1 : set → prop, ∀esk27_1 : set → set, ∀esk24_0 : set, ∀esk25_0 : set, ∀esk19_0 : set, ∀esk9_2 : set → set → set, ∀esk21_1 : set → set, ∀esk12_1 : set → set, ∀esk6_1 : set → set, ∀esk22_0 : set, ∀esk33_0 : set, ∀esk34_0 : set, ∀esk29_0 : set, ∀esk16_0 : set, ∀esk31_0 : set, ∀o_0_0_xboole_0 : set, ∀esk8_0 : set, ∀esk11_0 : set, ∀esk17_0 : set, ∀esk28_0 : set, ∀esk23_0 : set, ∀esk18_0 : set, ∀v2_card_1 : set → prop, ∀esk13_0 : set, ∀esk26_1 : set → set, ∀esk14_2 : set → set → set, ∀esk10_0 : set, ∀esk20_0 : set, ∀esk36_0 : set, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀v1_xxreal_0 : set → prop, ∀esk35_1 : set → set, ∀esk32_1 : set → set, ∀v3_ordinal1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v1_finset_1 : set → prop, ∀v1_subset_1 : set → set → prop, ∀v3_xxreal_0 : set → prop, ∀k1_numbers : set, ∀k2_nat_1 : set → set → set, ∀m2_subset_1 : set → set → set → prop, ∀r2_hidden : set → set → prop, ∀k1_xboole_0 : set, ∀k10_nat_1 : set → set → set → set, ∀v5_relat_1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀esk5_3 : set → set → set → set, ∀k2_xcmplx_0 : set → set → set, ∀v1_relat_1 : set → prop, ∀k5_numbers : set, ∀v1_partfun1 : set → set → prop, ∀v4_relat_1 : set → set → prop, ∀v7_ordinal1 : set → prop, ∀k9_nat_1 : set → set → set, ∀k3_relat_1 : set → set → set, ∀k1_partfun1 : set → 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, (∀X5 X3 X4 X1 X2 X6, (m1_subset_1 (k1_partfun1 X1 X2 X3 X4 X5 X6) (k1_zfmisc_1 (k2_zfmisc_1 X1 X4)) → False) → v1_funct_1 X6 → v1_funct_1 X5 → m1_subset_1 X6 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X5 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X5 X3 X4 X1 X2 X6, (v1_funct_1 (k1_partfun1 X1 X2 X3 X4 X5 X6) → False) → v1_funct_1 X6 → v1_funct_1 X5 → m1_subset_1 X6 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X5 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X5 X6 X2 X3 X4, ((k1_partfun1 X2 X3 X5 X6 X1 X4) = (k3_relat_1 X1 X4) → False) → v1_funct_1 X4 → v1_funct_1 X1 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X5 X6)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X3 X2 X4, (r2_relset_1 X2 X3 X1 X4 → False) → (k1_funct_1 X1 (esk39_4 X2 X3 X1 X4)) = (k1_funct_1 X4 (esk39_4 X2 X3 X1 X4)) → v1_funct_1 X4 → v1_funct_1 X1 → v1_funct_2 X4 X2 X3 → v1_funct_2 X1 X2 X3 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X3 X2 X1 X4, (r2_relset_1 X1 X2 X3 X4 → False) → (m1_subset_1 (esk39_4 X1 X2 X3 X4) X1 → False) → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_2 X4 X1 X2 → v1_funct_2 X3 X1 X2 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X3 X2 X4, (r2_funct_2 X2 X3 X4 X1 → False) → v1_funct_1 X4 → v1_funct_1 X1 → v1_funct_2 X4 X2 X3 → v1_funct_2 X1 X2 X3 → r2_funct_2 X2 X3 X1 X4 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X4 X1 X2 X3, (r2_relset_1 X2 X3 X4 X1 → False) → r2_relset_1 X2 X3 X1 X4 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X2 X3 X4, (X3 = X4 → False) → v1_funct_1 X4 → v1_funct_1 X3 → v1_funct_2 X4 X1 X2 → v1_funct_2 X3 X1 X2 → r2_funct_2 X1 X2 X3 X4 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X1 X3 X2, (X1 = (k9_nat_1 X2 X3) → False) → (k1_funct_1 X1 (esk5_3 X2 X3 X1)) = (k1_funct_1 X2 (k2_xcmplx_0 (esk5_3 X2 X3 X1) X3)) → v1_funct_1 X2 → v1_funct_1 X1 → v7_ordinal1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → v1_partfun1 X2 k5_numbers → v1_partfun1 X1 k5_numbers → v4_relat_1 X2 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X3 X4 X1 X2, (r2_funct_2 X3 X4 X1 X2 → False) → X1 = X2 → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X3 X4 → v1_funct_2 X1 X3 X4 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → False) → (∀X4 X1 X3 X2, (r2_funct_2 X2 X3 X1 X1 → False) → v1_funct_1 X4 → v1_funct_1 X1 → v1_funct_2 X4 X2 X3 → v1_funct_2 X1 X2 X3 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X2 X1 X3 X4, (X3 = X4 → False) → r2_relset_1 X1 X2 X3 X4 → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → (∀X4 X3 X1 X2 X5, (v1_xboole_0 X5 → False) → (v1_funct_2 (k3_relat_1 X1 X2) X3 X4 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X5 X4 → v1_funct_2 X1 X3 X5 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X5 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X5)) → False) → (∀X1 X4 X3 X2, (v1_funct_2 (k3_relat_1 X1 X2) X3 X4 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X3 X4 → v1_funct_2 X1 X3 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X3)) → False) → (∀X1 X3 X4 X2, (v1_funct_2 (k3_relat_1 X1 X2) X3 X4 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X4 X4 → v1_funct_2 X1 X3 X4 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X4 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → False) → (∀X4 X3 X1 X2, (r2_relset_1 X3 X4 X1 X2 → False) → X1 = X2 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → False) → (∀X4 X1 X3 X2, (r2_relset_1 X2 X3 X1 X1 → False) → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X1 X2 X4 X5 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X3 X5 → v1_funct_2 X1 X4 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X5)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X4 X3)) → False) → (∀X3 X4 X2 X1, (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X3 X3 → v1_funct_2 X1 X4 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X4 X3)) → False) → (∀X3 X4 X2 X1, (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 X3 X4 → v1_funct_2 X1 X3 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X3)) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v5_relat_1 (k3_relat_1 X1 X2) X3 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v4_relat_1 (k3_relat_1 X1 X2) k5_numbers → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_partfun1 (k3_relat_1 X1 X2) k5_numbers → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_funct_2 X2 k5_numbers X3 → v1_funct_2 X1 k5_numbers k5_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X3)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k10_nat_1 X1 X2 X3) (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X1)) → False) → v1_funct_1 X2 → v7_ordinal1 X3 → v1_funct_2 X2 k5_numbers X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X1)) → False) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (v1_funct_2 (k10_nat_1 X1 X2 X3) k5_numbers X1 → False) → v1_funct_1 X2 → v7_ordinal1 X3 → v1_funct_2 X2 k5_numbers X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X1)) → False) → (∀X1 X5 X4 X2 X3, (X3 = k1_xboole_0 → False) → ((k1_funct_1 (k3_relat_1 X1 X4) X5) = (k1_funct_1 X4 (k1_funct_1 X1 X5)) → False) → v1_funct_1 X4 → v1_funct_1 X1 → v1_relat_1 X4 → r2_hidden X5 X2 → v1_funct_2 X1 X2 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X3 X2 X1, (m1_subset_1 (k8_nat_1 X2 X1 X3) X2 → False) → v1_funct_1 X1 → v7_ordinal1 X3 → v1_funct_2 X1 k5_numbers X2 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X2)) → False) → (∀X2 X3 X1, (v1_xboole_0 X1 → False) → (v1_funct_1 (k10_nat_1 X1 X2 X3) → False) → v1_funct_1 X2 → v7_ordinal1 X3 → v1_funct_2 X2 k5_numbers X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X1)) → False) → (∀X3 X1 X2 X4, (v1_xboole_0 X4 → False) → (v4_relat_1 (k3_relat_1 X1 X2) X3 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_partfun1 X2 X4 → v4_relat_1 X2 X4 → v1_funct_2 X1 X3 X4 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → False) → (∀X3 X1 X2 X4, (v1_xboole_0 X4 → False) → (v1_partfun1 (k3_relat_1 X1 X2) X3 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_partfun1 X2 X4 → v4_relat_1 X2 X4 → v1_funct_2 X1 X3 X4 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X4)) → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_partfun1 X2 X3 → v4_relat_1 X2 X3 → v1_funct_2 X1 X4 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X4 X3)) → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 (k3_relat_1 X1 X2) → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_partfun1 X2 X3 → v4_relat_1 X2 X3 → v1_funct_2 X1 X4 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X4 X3)) → False) → (∀X2 X3 X1, ((k10_nat_1 X1 X2 X3) = (k9_nat_1 X2 X3) → False) → (v1_xboole_0 X1 → False) → v1_funct_1 X2 → v7_ordinal1 X3 → v1_funct_2 X2 k5_numbers X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X1)) → False) → (∀X3 X2 X1, ((k8_nat_1 X2 X1 X3) = (k1_funct_1 X1 X3) → False) → v1_funct_1 X1 → v7_ordinal1 X3 → v1_funct_2 X1 k5_numbers X2 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers X2)) → False) → (∀X1 X2 X3, (X3 = (k9_nat_1 X1 X2) → False) → (v7_ordinal1 (esk5_3 X1 X2 X3) → False) → v1_funct_1 X3 → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X3 → v1_relat_1 X1 → v1_partfun1 X3 k5_numbers → v1_partfun1 X1 k5_numbers → v4_relat_1 X3 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_funct_2 X1 X2 X3 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X3 X2 X1, (v1_partfun1 X2 X1 → False) → v1_xboole_0 X1 → v1_funct_2 X2 X1 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (v1_partfun1 X2 X3 → False) → v1_funct_2 X2 X3 X1 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X3 X1)) → False) → (∀X2 X1, (v1_partfun1 X1 X2 → False) → v1_funct_2 X1 X2 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X2)) → False) → (∀X4 X2 X3 X1, ((k1_funct_1 X1 X4) = (k1_funct_1 X2 (k2_xcmplx_0 X4 X3)) → False) → X1 = (k9_nat_1 X2 X3) → v1_funct_1 X2 → v1_funct_1 X1 → v7_ordinal1 X4 → v7_ordinal1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → v1_partfun1 X2 k5_numbers → v1_partfun1 X1 k5_numbers → v4_relat_1 X2 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X3 X1 X2, (v1_funct_2 X1 X2 X3 → False) → v1_partfun1 X1 X2 → 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 → False) → (m1_subset_1 X3 X1 → False) → m2_subset_1 X3 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m1_subset_1 X1 X3 → False) → m2_subset_1 X1 X2 X3 → m1_subset_1 X3 (k1_zfmisc_1 X2) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v5_relat_1 (k9_nat_1 X1 X2) X3 → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v5_relat_1 X1 X3 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v4_relat_1 (k9_nat_1 X1 X2) k5_numbers → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v5_relat_1 X1 X3 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_partfun1 (k9_nat_1 X1 X2) k5_numbers → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v5_relat_1 X1 X3 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk7_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_relat_1 (k9_nat_1 X1 X2) → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v5_relat_1 X1 X3 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X1 X2 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 (k9_nat_1 X1 X2) → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v5_relat_1 X1 X3 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X2 X1 X3, (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (m2_subset_1 X1 X3 X2 → False) → m1_subset_1 X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X3 X2 X1, (v1_relat_1 X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X2 X1, (m2_subset_1 (k2_nat_1 X1 X2) k1_numbers k5_numbers → False) → v7_ordinal1 X2 → m1_subset_1 X1 k5_numbers → False) → (∀X1 X2 X3, ((k2_xcmplx_0 (k2_xcmplx_0 X1 X2) X3) = (k2_xcmplx_0 X1 (k2_xcmplx_0 X2 X3)) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (v4_relat_1 (k9_nat_1 X1 X2) k5_numbers → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X2 X1, (v1_partfun1 (k9_nat_1 X1 X2) k5_numbers → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X2 X1, (v1_relat_1 (k9_nat_1 X1 X2) → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X2 X1, (v1_funct_1 (k9_nat_1 X1 X2) → False) → v1_funct_1 X1 → v7_ordinal1 X2 → v1_relat_1 X1 → v1_partfun1 X1 k5_numbers → v4_relat_1 X1 k5_numbers → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → v1_partfun1 X1 X2 → v4_relat_1 X1 X2 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k2_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 (k2_xcmplx_0 X1 X2) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → v1_xboole_0 (k2_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → v1_xboole_0 (k2_xcmplx_0 X2 X1) → 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, (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, (v1_xboole_0 X2 → False) → (v1_finset_1 X1 → False) → v1_finset_1 (k2_zfmisc_1 X1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_finset_1 X1 → False) → v1_finset_1 (k2_zfmisc_1 X2 X1) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_zfmisc_1 X1 X2) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 (k2_xcmplx_0 X2 X1) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 (k2_xcmplx_0 X2 X1) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X2 X1, ((k2_nat_1 X1 X2) = (k2_xcmplx_0 X1 X2) → False) → v7_ordinal1 X2 → m1_subset_1 X1 k5_numbers → False) → (∀X2 X1, ((k2_nat_1 X1 X2) = (k2_nat_1 X2 X1) → False) → v7_ordinal1 X2 → m1_subset_1 X1 k5_numbers → 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 X1 → False) → (v5_relat_1 (esk38_2 X1 X2) X1 → False) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v4_relat_1 (esk38_2 X1 X2) X2 → False) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_partfun1 (esk38_2 X1 X2) X2 → False) → False) → (∀X2 X1, (v1_xreal_0 (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v7_ordinal1 (k2_xcmplx_0 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 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) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X2 X1, ((k2_xcmplx_0 X1 X2) = (k2_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → 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, (v1_xboole_0 X1 → False) → (v1_relat_1 (esk38_2 X1 X2) → False) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_funct_1 (esk38_2 X1 X2) → False) → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → (m1_subset_1 (esk30_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk32_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v3_card_1 (esk37_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, (v3_card_1 (esk35_1 X1) X1 → False) → v1_card_1 X1 → False) → (∀X1, v3_xxreal_0 X1 → m1_subset_1 X1 k5_numbers → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk32_1 X1) X1 → False) → False) → (∀X1, (v1_finset_1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v7_ordinal1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1, (v1_xboole_0 X1 → False) → v3_card_1 X1 k1_xboole_0 → False) → (∀X1, v3_xxreal_0 X1 → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v3_xxreal_0 X1 → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v3_xxreal_0 X1 → v1_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v3_xxreal_0 X1 → v1_xxreal_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (esk30_1 X1) → False) → (∀X1, (v1_finset_1 X1 → False) → v1_finset_1 (k1_zfmisc_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk15_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v3_card_1 X1 k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v3_ordinal1 X1 → v1_finset_1 X1 → False) → (∀X1, (v1_relat_1 (esk37_1 X1) → False) → v1_card_1 X1 → False) → (∀X1, (v1_funct_1 (esk37_1 X1) → False) → v1_card_1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, v7_ordinal1 X1 → v3_xxreal_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → v7_ordinal1 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) → v1_card_1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_card_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r2_funct_2 k5_numbers esk1_0 (k10_nat_1 esk1_0 (k1_partfun1 k5_numbers k5_numbers k5_numbers esk1_0 esk4_0 esk2_0) esk3_0) (k1_partfun1 k5_numbers k5_numbers k5_numbers esk1_0 (k10_nat_1 k5_numbers esk4_0 esk3_0) esk2_0) → False) → (∀X1, v1_subset_1 (esk27_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_finset_1 esk24_0 → False) → (v1_finset_1 k4_ordinal1 → False) → (v1_finset_1 k1_numbers → False) → (v1_xboole_0 esk36_0 → False) → (v1_xboole_0 esk25_0 → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 esk1_0 → False) → (v1_xboole_0 k4_ordinal1 → False) → (v1_xboole_0 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (esk14_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → (∀X2 X1, (m1_subset_1 (esk9_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → (∀X2 X1, (v1_funct_2 (esk9_2 X1 X2) X1 X2 → False) → False) → ((m1_subset_1 esk4_0 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers k5_numbers)) → False) → False) → ((m1_subset_1 esk2_0 (k1_zfmisc_1 (k2_zfmisc_1 k5_numbers esk1_0)) → False) → False) → ((v1_funct_2 esk4_0 k5_numbers k5_numbers → False) → False) → ((v1_funct_2 esk2_0 k5_numbers esk1_0 → False) → False) → (∀X2 X1, (v5_relat_1 (esk14_2 X1 X2) X2 → False) → False) → (∀X2 X1, (v5_relat_1 (esk9_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk14_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v4_relat_1 (esk9_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_relat_1 (esk14_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (esk9_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X1 X2, (v1_funct_1 (esk9_2 X1 X2) → False) → False) → (∀X1 X2, (v1_xboole_0 (esk14_2 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk27_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v5_relat_1 (esk26_1 X1) X1 → False) → False) → (∀X1, (v4_relat_1 (esk12_1 X1) X1 → False) → False) → (∀X1, (v1_partfun1 (esk12_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 (esk6_1 X1) X1 → False) → False) → ((m1_subset_1 esk19_0 (k1_zfmisc_1 k1_numbers) → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((m1_subset_1 esk25_0 k5_numbers → False) → False) → ((m1_subset_1 esk13_0 k1_numbers → False) → False) → ((m1_subset_1 k1_xboole_0 k4_ordinal1 → False) → False) → (∀X1, (v5_ordinal1 (esk26_1 X1) → False) → False) → (∀X1, (v1_relat_1 (esk26_1 X1) → False) → False) → (∀X1, (v1_relat_1 (esk12_1 X1) → False) → False) → (∀X1, (v1_funct_1 (esk26_1 X1) → False) → False) → (∀X1, (v1_funct_1 (esk12_1 X1) → False) → False) → (∀X1, (v1_xboole_0 (esk21_1 X1) → False) → False) → ((v2_card_1 k4_ordinal1 → False) → False) → ((v1_finset_1 esk25_0 → False) → False) → ((v1_finset_1 esk18_0 → False) → False) → ((v1_finset_1 esk10_0 → False) → False) → ((v2_xxreal_0 esk23_0 → False) → False) → ((v2_xxreal_0 esk22_0 → False) → False) → ((v2_xxreal_0 esk13_0 → False) → False) → ((v1_xcmplx_0 esk33_0 → False) → False) → ((v1_xcmplx_0 esk28_0 → False) → False) → ((v1_xcmplx_0 esk25_0 → False) → False) → ((v1_xcmplx_0 esk22_0 → False) → False) → ((v1_xcmplx_0 esk13_0 → False) → False) → ((v1_xcmplx_0 esk10_0 → False) → False) → ((v1_xxreal_0 esk34_0 → False) → False) → ((v1_xxreal_0 esk33_0 → False) → False) → ((v1_xxreal_0 esk29_0 → False) → False) → ((v1_xxreal_0 esk28_0 → False) → False) → ((v1_xxreal_0 esk25_0 → False) → False) → ((v1_xxreal_0 esk23_0 → False) → False) → ((v1_xxreal_0 esk22_0 → False) → False) → ((v1_xxreal_0 esk17_0 → False) → False) → ((v1_xxreal_0 esk13_0 → False) → False) → ((v1_xxreal_0 esk10_0 → False) → False) → ((v3_xxreal_0 esk29_0 → False) → False) → ((v3_xxreal_0 esk28_0 → False) → False) → ((v1_xreal_0 esk33_0 → False) → False) → ((v1_xreal_0 esk28_0 → False) → False) → ((v1_xreal_0 esk25_0 → False) → False) → ((v1_xreal_0 esk22_0 → False) → False) → ((v1_xreal_0 esk16_0 → False) → False) → ((v1_xreal_0 esk13_0 → False) → False) → ((v1_xreal_0 esk10_0 → False) → False) → ((v2_ordinal1 esk25_0 → False) → False) → ((v2_ordinal1 esk20_0 → False) → False) → ((v2_ordinal1 esk18_0 → False) → False) → ((v2_ordinal1 esk10_0 → False) → False) → ((v1_ordinal1 esk25_0 → False) → False) → ((v1_ordinal1 esk20_0 → False) → False) → ((v1_ordinal1 esk18_0 → False) → False) → ((v1_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 esk25_0 → False) → False) → ((v3_ordinal1 esk20_0 → False) → False) → ((v3_ordinal1 esk19_0 → False) → False) → ((v3_ordinal1 esk18_0 → False) → False) → ((v3_ordinal1 esk11_0 → False) → False) → ((v3_ordinal1 esk10_0 → False) → False) → ((v3_ordinal1 k4_ordinal1 → False) → False) → ((v1_card_1 esk25_0 → False) → False) → ((v1_card_1 esk18_0 → False) → False) → ((v1_card_1 esk10_0 → False) → False) → ((v1_card_1 esk8_0 → False) → False) → ((v1_card_1 k4_ordinal1 → False) → False) → ((v7_ordinal1 esk36_0 → False) → False) → ((v7_ordinal1 esk31_0 → False) → False) → ((v7_ordinal1 esk25_0 → False) → False) → ((v7_ordinal1 esk10_0 → False) → False) → ((v7_ordinal1 esk3_0 → False) → False) → ((v1_funct_1 esk4_0 → False) → False) → ((v1_funct_1 esk2_0 → False) → False) → ((v1_xboole_0 esk34_0 → False) → False) → ((v1_xboole_0 esk33_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((k1_xboole_0 = o_0_0_xboole_0 → False) → False) → ((k4_ordinal1 = k5_numbers → False) → False) → False
In Proofgold the corresponding term root is 04c987... and proposition id is 51c8fa...
Proof:
The rest of the proof is missing.