Theorem. (
t6_metric_6)
∀v1_xcmplx_0 : set → prop, ∀k3_xcmplx_0 : set → set → set, ∀k7_xcmplx_0 : set → set → set, ∀k6_xcmplx_0 : set → set → set, ∀v4_relat_1 : set → set → prop, ∀k3_numbers : set, ∀v2_xxreal_0 : set → prop, ∀r2_hidden : set → set → prop, ∀v3_valued_0 : set → prop, ∀v1_valued_0 : set → prop, ∀r1_tarski : set → set → prop, ∀v6_ordinal1 : set → prop, ∀v3_ordinal1 : set → prop, ∀k4_ordinal1 : set, ∀k1_xboole_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk27_0 : set, ∀esk17_0 : set, ∀esk10_2 : set → set → set, ∀esk28_1 : set → set, ∀esk21_1 : set → set, ∀esk23_0 : set, ∀esk20_0 : set, ∀esk25_0 : set, ∀esk14_0 : set, ∀esk13_0 : set, ∀esk11_0 : set, ∀esk15_0 : set, ∀esk24_0 : set, ∀esk16_0 : set, ∀esk26_0 : set, ∀esk19_0 : set, ∀esk22_0 : set, ∀esk8_1 : set → set, ∀esk12_2 : set → set → set, ∀esk18_0 : set, ∀v1_finset_1 : set → prop, ∀np__2 : set, ∀np__0 : set, ∀v5_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀v1_ordinal1 : set → prop, ∀k5_numbers : set, ∀v1_xxreal_0 : set → prop, ∀v2_valued_0 : set → prop, ∀k8_real_1 : set → set → set, ∀k9_real_1 : set → set → set, ∀k4_xcmplx_0 : set → set, ∀v3_xxreal_0 : set → prop, ∀k4_numbers : set, ∀v1_xreal_0 : set → prop, ∀esk9_2 : set → set → set, ∀v5_relat_1 : set → set → prop, ∀v1_relat_1 : set → prop, ∀v4_valued_0 : set → prop, ∀v7_ordinal1 : set → prop, ∀m2_subset_1 : set → set → set → prop, ∀v1_partfun1 : set → set → prop, ∀k2_xcmplx_0 : set → set → set, ∀k1_binop_1 : set → set → set → set, ∀v1_xboole_0 : set → prop, ∀esk3_3 : set → set → set → set, ∀esk4_3 : set → set → set → set, ∀np__1 : set, ∀k10_real_1 : set → set → set, ∀k1_metric_6 : set → set → set, ∀esk5_2 : set → set → set, ∀esk6_2 : set → set → set, ∀v1_funct_2 : set → set → set → prop, ∀k1_numbers : set, ∀k2_zfmisc_1 : set → set → set, ∀esk7_2 : set → set → set, ∀k7_real_1 : set → set → set, ∀r1_xxreal_0 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀v1_funct_1 : set → prop, ∀k1_metric_1 : set → set → set → set → set → set, ∀k6_numbers : set, ∀r1_pcomps_1 : set → set → prop, (∀X1 X2, (r1_pcomps_1 X1 X2 → False) → (esk6_2 X1 X2) = (esk5_2 X1 X2) → (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) = k6_numbers → (k1_metric_1 X1 X1 X2 (esk6_2 X1 X2) (esk5_2 X1 X2)) = (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → r1_xxreal_0 (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk7_2 X1 X2)) (k7_real_1 (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) (k1_metric_1 X1 X1 X2 (esk6_2 X1 X2) (esk7_2 X1 X2))) → False) → (∀X1 X2, ((esk6_2 X1 X2) = (esk5_2 X1 X2) → False) → ((k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) = k6_numbers → False) → (r1_pcomps_1 X1 X2 → False) → (k1_metric_1 X1 X1 X2 (esk6_2 X1 X2) (esk5_2 X1 X2)) = (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → r1_xxreal_0 (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk7_2 X1 X2)) (k7_real_1 (k1_metric_1 X1 X1 X2 (esk5_2 X1 X2) (esk6_2 X1 X2)) (k1_metric_1 X1 X1 X2 (esk6_2 X1 X2) (esk7_2 X1 X2))) → False) → (∀X3 X2 X1, (X2 = (k1_metric_6 X1 X3) → False) → (v1_xboole_0 X1 → False) → (k10_real_1 (k1_metric_1 X1 X1 X3 (esk3_3 X1 X3 X2) (esk4_3 X1 X3 X2)) (k7_real_1 np__1 (k1_metric_1 X1 X1 X3 (esk3_3 X1 X3 X2) (esk4_3 X1 X3 X2)))) = (k1_metric_1 X1 X1 X2 (esk3_3 X1 X3 X2) (esk4_3 X1 X3 X2)) → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_2 X3 (k2_zfmisc_1 X1 X1) k1_numbers → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X5 X3 X4 X2, (r1_xxreal_0 (k1_metric_1 X1 X1 X2 X3 X4) (k7_real_1 (k1_metric_1 X1 X1 X2 X3 X5) (k1_metric_1 X1 X1 X2 X5 X4)) → False) → v1_funct_1 X2 → m1_subset_1 X5 X1 → m1_subset_1 X4 X1 → m1_subset_1 X3 X1 → r1_pcomps_1 X1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X3 X4 X5 X2, ((k1_metric_1 X2 X2 X1 X4 X5) = (k10_real_1 (k1_metric_1 X2 X2 X3 X4 X5) (k7_real_1 np__1 (k1_metric_1 X2 X2 X3 X4 X5))) → False) → (v1_xboole_0 X2 → False) → X1 = (k1_metric_6 X2 X3) → v1_funct_1 X3 → v1_funct_1 X1 → m1_subset_1 X5 X2 → m1_subset_1 X4 X2 → v1_funct_2 X3 (k2_zfmisc_1 X2 X2) k1_numbers → v1_funct_2 X1 (k2_zfmisc_1 X2 X2) k1_numbers → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X2) k1_numbers)) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X2) k1_numbers)) → False) → (∀X5 X1 X2 X4 X3, ((k1_metric_1 X1 X1 X2 X3 X4) = (k1_metric_1 X1 X1 X2 X4 X3) → False) → v1_funct_1 X2 → m1_subset_1 X5 X1 → m1_subset_1 X4 X1 → m1_subset_1 X3 X1 → r1_pcomps_1 X1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X2 X3 X4 X1, (v1_xboole_0 X1 → False) → (r1_xxreal_0 k6_numbers (k1_metric_1 X1 X1 X2 X3 X4) → False) → v1_funct_1 X2 → m1_subset_1 X4 X1 → m1_subset_1 X3 X1 → r1_pcomps_1 X1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X3 X5 X4 X2 X1, (m1_subset_1 (k1_metric_1 X2 X3 X1 X4 X5) k1_numbers → False) → v1_funct_1 X1 → m1_subset_1 X5 X3 → m1_subset_1 X4 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X3) k1_numbers)) → False) → (∀X2 X1 X5 X3 X4, (X3 = X4 → False) → (k1_metric_1 X1 X1 X2 X3 X4) = k6_numbers → v1_funct_1 X2 → m1_subset_1 X5 X1 → m1_subset_1 X4 X1 → m1_subset_1 X3 X1 → r1_pcomps_1 X1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X5 X3 X4 X1 X2, ((k1_metric_1 X3 X3 X4 X1 X2) = k6_numbers → False) → X1 = X2 → v1_funct_1 X4 → m1_subset_1 X5 X3 → m1_subset_1 X2 X3 → m1_subset_1 X1 X3 → r1_pcomps_1 X3 X4 → v1_funct_2 X4 (k2_zfmisc_1 X3 X3) k1_numbers → m1_subset_1 X4 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X3 X3) k1_numbers)) → False) → (∀X3 X5 X4 X2 X1, ((k1_metric_1 X2 X3 X1 X4 X5) = (k1_binop_1 X1 X4 X5) → False) → v1_funct_1 X1 → m1_subset_1 X5 X3 → m1_subset_1 X4 X2 → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X2 X3) k1_numbers)) → False) → (∀X3 X2 X1, (X3 = (k1_metric_6 X1 X2) → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (esk4_3 X1 X2 X3) X1 → False) → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_2 X3 (k2_zfmisc_1 X1 X1) k1_numbers → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X3 X2 X1, (X3 = (k1_metric_6 X1 X2) → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (esk3_3 X1 X2 X3) X1 → False) → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_2 X3 (k2_zfmisc_1 X1 X1) k1_numbers → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X3 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k1_metric_6 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_funct_2 (k1_metric_6 X1 X2) (k2_zfmisc_1 X1 X1) k1_numbers → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X2, (r1_pcomps_1 X1 X2 → False) → (m1_subset_1 (esk7_2 X1 X2) X1 → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X2, (r1_pcomps_1 X1 X2 → False) → (m1_subset_1 (esk6_2 X1 X2) X1 → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X2, (r1_pcomps_1 X1 X2 → False) → (m1_subset_1 (esk5_2 X1 X2) X1 → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_funct_1 (k1_metric_6 X1 X2) → False) → v1_funct_1 X2 → v1_funct_2 X2 (k2_zfmisc_1 X1 X1) k1_numbers → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X1 X1) k1_numbers)) → False) → (∀X1 X3 X4 X2, (X2 = k6_numbers → False) → (X1 = k6_numbers → False) → ((k7_xcmplx_0 (k6_xcmplx_0 (k3_xcmplx_0 X3 X2) (k3_xcmplx_0 X4 X1)) (k3_xcmplx_0 X1 X2)) = (k6_xcmplx_0 (k7_xcmplx_0 X3 X1) (k7_xcmplx_0 X4 X2)) → False) → v1_xcmplx_0 X4 → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X3 X4 X2, (X2 = k6_numbers → False) → (X1 = k6_numbers → False) → ((k7_xcmplx_0 (k2_xcmplx_0 (k3_xcmplx_0 X3 X2) (k3_xcmplx_0 X4 X1)) (k3_xcmplx_0 X1 X2)) = (k2_xcmplx_0 (k7_xcmplx_0 X3 X1) (k7_xcmplx_0 X4 X2)) → False) → v1_xcmplx_0 X4 → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → 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) → (∀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) → (∀X3 X2 X1, (v7_ordinal1 (k1_binop_1 X1 X2 X3) → False) → v1_funct_1 X1 → v1_relat_1 X1 → v4_valued_0 X1 → False) → (∀X3 X1 X2, (v4_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → (∀X3 X1 X2, (v5_relat_1 X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X3 X2)) → False) → (∀X1 X2 X3, ((k2_xcmplx_0 (k3_xcmplx_0 X1 X3) (k3_xcmplx_0 X2 X3)) = (k3_xcmplx_0 (k2_xcmplx_0 X1 X2) X3) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → 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 (esk9_2 X1 X2) X1 X2 → False) → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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) → (∀X1 X2 X3, ((k3_xcmplx_0 (k3_xcmplx_0 X1 X2) X3) = (k3_xcmplx_0 X1 (k3_xcmplx_0 X2 X3)) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → 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) → (∀X1 X2 X3, ((k7_xcmplx_0 (k3_xcmplx_0 X1 X2) X3) = (k3_xcmplx_0 X1 (k7_xcmplx_0 X2 X3)) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2, (r1_xxreal_0 X2 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 k6_numbers (k6_xcmplx_0 X1 X2) → False) → (∀X1 X2, (r1_xxreal_0 k6_numbers (k6_xcmplx_0 X2 X1) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v5_relat_1 X2 k4_numbers → False) → v1_relat_1 X1 → v5_relat_1 X1 k4_numbers → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v5_relat_1 X2 k3_numbers → False) → v1_relat_1 X1 → v5_relat_1 X1 k3_numbers → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 (k7_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 (k3_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, (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k3_xcmplx_0 X1 X2) → False) → (∀X2 X1, (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k3_xcmplx_0 X2 X1) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 (k6_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k7_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k7_xcmplx_0 X2 X1) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k6_xcmplx_0 X2 X1) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 (k7_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 (k3_xcmplx_0 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) → (∀X2 X1, ((k2_xcmplx_0 (k4_xcmplx_0 X1) (k4_xcmplx_0 X2)) = (k4_xcmplx_0 (k2_xcmplx_0 X1 X2)) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 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, (m1_subset_1 (k9_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k10_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k8_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k7_real_1 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 (k6_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 (k6_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) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v3_xxreal_0 (k6_xcmplx_0 X2 X1) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → 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, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 (k6_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X2 X1, ((k10_real_1 X1 X2) = (k7_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k9_real_1 X1 X2) = (k6_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k8_real_1 X1 X2) = (k8_real_1 X2 X1) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k8_real_1 X1 X2) = (k3_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k7_real_1 X1 X2) = (k7_real_1 X2 X1) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k7_real_1 X1 X2) = (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k6_xcmplx_0 (k4_xcmplx_0 X1) (k4_xcmplx_0 X2)) = (k6_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2, (v4_valued_0 X2 → False) → v1_relat_1 X1 → v4_valued_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v3_valued_0 X2 → False) → v1_relat_1 X1 → v3_valued_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v2_valued_0 X2 → False) → v1_relat_1 X1 → v2_valued_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_valued_0 X2 → False) → v1_relat_1 X1 → v1_valued_0 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v2_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 X2 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v3_xxreal_0 X2 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, ((k2_xcmplx_0 X1 (k4_xcmplx_0 X2)) = (k6_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 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_xreal_0 (k7_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xreal_0 (k6_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xreal_0 (k3_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xreal_0 (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (r1_xxreal_0 X2 X1 → False) → (r1_xxreal_0 X1 X2 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X2 X1, ((k3_xcmplx_0 X1 X2) = (k3_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → 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) → (∀X1, (v5_relat_1 X1 k3_numbers → False) → v1_relat_1 X1 → v5_relat_1 X1 k4_numbers → False) → (∀X1 X2, (X2 = k6_numbers → False) → (X1 = k6_numbers → False) → (k7_xcmplx_0 X1 X2) = k6_numbers → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2, (X2 = k6_numbers → False) → (X1 = k6_numbers → False) → (k3_xcmplx_0 X1 X2) = k6_numbers → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X2 → False) → (r1_xxreal_0 X1 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X2 → False) → (r1_xxreal_0 X1 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v4_valued_0 X1 → False) → v1_relat_1 X1 → v5_relat_1 X1 k5_numbers → False) → (∀X1, (v3_valued_0 X1 → False) → v1_relat_1 X1 → v5_relat_1 X1 k4_numbers → False) → (∀X1, (v3_valued_0 X1 → False) → v1_relat_1 X1 → v5_relat_1 X1 k3_numbers → False) → (∀X1, (v3_valued_0 X1 → False) → v1_relat_1 X1 → v5_relat_1 X1 k1_numbers → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xxreal_0 X1 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1, (v3_xxreal_0 X1 → False) → v1_xreal_0 X1 → v2_xxreal_0 (k4_xcmplx_0 X1) → False) → (∀X1, (v2_xxreal_0 X1 → False) → v1_xreal_0 X1 → v3_xxreal_0 (k4_xcmplx_0 X1) → False) → (∀X1, ((k3_xcmplx_0 X1 (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v5_relat_1 X1 k4_numbers → False) → v1_relat_1 X1 → v4_valued_0 X1 → False) → (∀X1, (v5_relat_1 X1 k3_numbers → False) → v1_relat_1 X1 → v4_valued_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → m1_subset_1 X1 k4_ordinal1 → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v3_xxreal_0 X1 → False) → (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v2_xxreal_0 X1 → False) → (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v2_xxreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v2_xxreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v1_xxreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, v1_xboole_0 X1 → v1_xxreal_0 X1 → v3_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 → False) → (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v2_xxreal_0 X1 → False) → (v3_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, ((k3_xcmplx_0 np__1 X1) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k7_xcmplx_0 X1 np__1) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k6_xcmplx_0 X1 k6_numbers) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k2_xcmplx_0 X1 k6_numbers) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k7_xcmplx_0 k6_numbers X1) = k6_numbers → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k3_xcmplx_0 X1 k6_numbers) = k6_numbers → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X1, (v4_valued_0 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_valued_0 X1 → False) → v1_relat_1 X1 → v4_valued_0 X1 → False) → (∀X1, (v2_valued_0 X1 → False) → v1_relat_1 X1 → v3_valued_0 X1 → False) → (∀X1, (v1_valued_0 X1 → False) → v1_relat_1 X1 → v3_valued_0 X1 → False) → (∀X1, ((k4_xcmplx_0 (k4_xcmplx_0 X1)) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 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) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_xxreal_0 (k7_xcmplx_0 np__1 np__2) np__0 → False) → (r1_xxreal_0 np__2 (k7_xcmplx_0 np__1 np__2) → False) → (r1_xxreal_0 np__1 (