Theorem. (
t10_cfuncdom)
∀m1_subset_1 : set → set → prop, ∀v1_funct_1 : set → prop, ∀k1_zfmisc_1 : set → set, ∀k2_zfmisc_1 : set → set → set, ∀v1_funct_2 : set → set → set → prop, ∀r2_relset_1 : set → set → set → set → prop, ∀esk13_4 : set → set → set → set → set, ∀k1_funct_1 : set → set → set, ∀m1_funct_2 : set → set → set → prop, ∀k8_funcop_1 : set → set → set → set, ∀v5_relat_1 : set → set → prop, ∀esk6_2 : set → set → set, ∀v1_relat_1 : set → prop, ∀v1_xcmplx_0 : set → prop, ∀k2_xcmplx_0 : set → set → set, ∀k1_numbers : set, ∀k6_numbers : set, ∀k1_funct_2 : set → set → set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk10_0 : set, ∀esk3_2 : set → set → set, ∀esk4_1 : set → set, ∀esk8_0 : set, ∀k4_ordinal1 : set, ∀esk9_0 : set, ∀k5_complex1 : set, ∀k5_numbers : set, ∀esk7_2 : set → set → set, ∀esk11_0 : set, ∀v1_finset_1 : set → prop, ∀k1_xboole_0 : set, ∀r1_tarski : set → set → prop, ∀r2_hidden : set → set → prop, ∀k2_funcop_1 : set → set → set, ∀k4_tarski : set → set → set, ∀v4_relat_1 : set → set → prop, ∀m2_subset_1 : set → set → set → prop, ∀k4_cfuncdom : set → set, ∀esk5_3 : set → set → set → set, ∀k1_binop_1 : set → set → set → set, ∀r2_funct_2 : set → set → set → set → prop, ∀k2_numbers : set, ∀k1_cfuncdom : set → set, ∀k1_funcsdom : set → set → set → set → set → set, ∀esk12_4 : set → set → set → set → set, ∀k3_funct_2 : set → set → set → set → set, ∀k8_complex1 : set → set → set, ∀m2_funct_2 : set → set → set → set → prop, ∀k9_funct_2 : set → set → set, ∀v1_xboole_0 : set → prop, (∀X4 X3 X2 X1, (v1_xboole_0 X1 → False) → (r2_funct_2 X1 k2_numbers X2 (k1_funcsdom X1 k2_numbers (k1_cfuncdom X1) X3 X4) → False) → (k8_complex1 (k3_funct_2 X1 k2_numbers X3 (esk12_4 X1 X2 X3 X4)) (k3_funct_2 X1 k2_numbers X4 (esk12_4 X1 X2 X3 X4))) = (k3_funct_2 X1 k2_numbers X2 (esk12_4 X1 X2 X3 X4)) → m2_funct_2 X4 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X3 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X2 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → False) → (∀X5 X3 X2 X4 X1, ((k3_funct_2 X1 k2_numbers X2 X5) = (k8_complex1 (k3_funct_2 X1 k2_numbers X3 X5) (k3_funct_2 X1 k2_numbers X4 X5)) → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X5 X1 → m2_funct_2 X4 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X3 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X2 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → r2_funct_2 X1 k2_numbers X2 (k1_funcsdom X1 k2_numbers (k1_cfuncdom X1) X3 X4) → False) → (∀X4 X3 X2 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk12_4 X1 X2 X3 X4) X1 → False) → (r2_funct_2 X1 k2_numbers X2 (k1_funcsdom X1 k2_numbers (k1_cfuncdom X1) X3 X4) → False) → m2_funct_2 X4 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X3 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → m2_funct_2 X2 X1 k2_numbers (k9_funct_2 X1 k2_numbers) → False) → (∀X2 X4 X3 X5 X1, (v1_xboole_0 X1 → False) → (m2_funct_2 (k1_funcsdom X3 X1 X2 X4 X5) X3 X1 (k9_funct_2 X3 X1) → False) → v1_funct_1 X2 → m1_subset_1 X5 (k9_funct_2 X3 X1) → m1_subset_1 X4 (k9_funct_2 X3 X1) → v1_funct_2 X2 (k2_zfmisc_1 (k9_funct_2 X3 X1) (k9_funct_2 X3 X1)) (k9_funct_2 X3 X1) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 X3 X1) (k9_funct_2 X3 X1)) (k9_funct_2 X3 X1))) → False) → (∀X2 X4 X3 X5 X1, ((k1_funcsdom X3 X1 X2 X4 X5) = (k1_binop_1 X2 X4 X5) → False) → (v1_xboole_0 X1 → False) → v1_funct_1 X2 → m1_subset_1 X5 (k9_funct_2 X3 X1) → m1_subset_1 X4 (k9_funct_2 X3 X1) → v1_funct_2 X2 (k2_zfmisc_1 (k9_funct_2 X3 X1) (k9_funct_2 X3 X1)) (k9_funct_2 X3 X1) → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 X3 X1) (k9_funct_2 X3 X1)) (k9_funct_2 X3 X1))) → False) → (∀X1 X3 X2 X4, (r2_relset_1 X2 X3 X1 X4 → False) → (k1_funct_1 X1 (esk13_4 X2 X3 X1 X4)) = (k1_funct_1 X4 (esk13_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 (esk13_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) → (∀X2 X3 X4 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k3_funct_2 X1 X3 X2 X4) X3 → False) → v1_funct_1 X2 → m1_subset_1 X4 X1 → v1_funct_2 X2 X1 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → 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) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k1_cfuncdom X1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (k9_funct_2 X1 k2_numbers) (k9_funct_2 X1 k2_numbers)) (k9_funct_2 X1 k2_numbers))) → False) → 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) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (m1_subset_1 X1 (k1_zfmisc_1 (k2_zfmisc_1 X2 X3)) → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_funct_2 X1 X2 X3 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X2 X3 X4 X1, ((k3_funct_2 X1 X3 X2 X4) = (k1_funct_1 X2 X4) → False) → (v1_xboole_0 X1 → False) → v1_funct_1 X2 → m1_subset_1 X4 X1 → v1_funct_2 X2 X1 X3 → m1_subset_1 X2 (k1_zfmisc_1 (k2_zfmisc_1 X1 X3)) → False) → (∀X4 X1 X2 X3, (v1_xboole_0 X3 → False) → (m1_subset_1 X1 X4 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 X3 X4 → False) → (∀X1 X2 X4 X3, (v1_xboole_0 X3 → False) → (v1_funct_1 X1 → False) → m1_funct_2 X4 X2 X3 → m2_funct_2 X1 X2 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) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (m2_funct_2 (esk5_3 X3 X1 X2) X3 X1 X2 → False) → m1_funct_2 X2 X3 X1 → False) → (∀X2 X1 X3 X4, (v1_xboole_0 X4 → False) → (m2_funct_2 X1 X3 X4 X2 → False) → m1_subset_1 X1 X2 → m1_funct_2 X2 X3 X4 → False) → (∀X1, (v1_xboole_0 X1 → False) → (m2_funct_2 (k4_cfuncdom X1) X1 k2_numbers (k9_funct_2 X1 k2_numbers) → False) → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k8_funcop_1 X1 X2 X3) (k1_zfmisc_1 (k2_zfmisc_1 X2 X1)) → False) → m1_subset_1 X3 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_funct_2 (k1_cfuncdom X1) (k2_zfmisc_1 (k9_funct_2 X1 k2_numbers) (k9_funct_2 X1 k2_numbers)) (k9_funct_2 X1 k2_numbers) → False) → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (v1_funct_2 (k8_funcop_1 X1 X2 X3) X2 X1 → False) → m1_subset_1 X3 X1 → 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, (v1_xboole_0 X1 → False) → (v1_funct_1 (k8_funcop_1 X1 X2 X3) → False) → m1_subset_1 X3 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) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk6_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) → (∀X3 X2 X1, ((k1_funct_1 X1 (k4_tarski X2 X3)) = (k1_binop_1 X1 X2 X3) → False) → v1_relat_1 X1 → v1_funct_1 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) → (∀X3 X2 X1, ((k8_funcop_1 X1 X3 X2) = (k2_funcop_1 X3 X2) → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X2 X1 → False) → (∀X3 X2 X1, v1_xboole_0 X1 → m1_funct_2 X1 X2 X3 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (m1_funct_2 (k9_funct_2 X2 X1) X2 X1 → False) → False) → (∀X2 X1, (m1_subset_1 (k8_complex1 X1 X2) k2_numbers → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → 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, ((k8_complex1 X1 X2) = (k8_complex1 X2 X1) → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → False) → (∀X2 X1, ((k8_complex1 X1 X2) = (k2_xcmplx_0 X1 X2) → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → False) → (∀X3 X2 X1, ((k1_funct_1 (k2_funcop_1 X2 X3) X1) = X3 → False) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1, ((k8_funcop_1 k1_numbers X1 k6_numbers) = (k4_cfuncdom X1) → False) → (v1_xboole_0 X1 → False) → 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_xcmplx_0 (k2_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 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, ((k1_funct_2 X2 X1) = (k9_funct_2 X2 X1) → False) → (v1_xboole_0 X1 → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v1_xcmplx_0 X1 → False) → m1_subset_1 X1 k2_numbers → False) → (∀X1, ((k2_xcmplx_0 X1 k6_numbers) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_funct_1 (k1_cfuncdom X1) → False) → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r2_funct_2 esk1_0 k2_numbers (k1_funcsdom esk1_0 k2_numbers (k1_cfuncdom esk1_0) (k4_cfuncdom esk1_0) esk2_0) esk2_0 → False) → (v1_finset_1 k1_numbers → False) → (v1_finset_1 k2_numbers → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 esk1_0 → False) → (v1_xboole_0 k1_numbers → False) → (v1_xboole_0 k2_numbers → False) → ((m2_funct_2 esk2_0 esk1_0 k2_numbers (k9_funct_2 esk1_0 k2_numbers) → False) → False) → (∀X2 X1, (m1_subset_1 (esk7_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → (∀X2 X1, (m1_funct_2 (esk3_2 X1 X2) X1 X2 → False) → False) → ((m2_subset_1 k6_numbers k1_numbers k5_numbers → False) → False) → (∀X2 X1, (v5_relat_1 (esk7_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk7_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_relat_1 (esk7_2 X1 X2) → False) → False) → (∀X1 X2, (v1_xboole_0 (esk7_2 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk4_1 X1) X1 → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((m1_subset_1 k5_complex1 k2_numbers → False) → False) → ((v1_xcmplx_0 esk11_0 → False) → False) → ((v1_xcmplx_0 esk9_0 → False) → False) → ((v1_xboole_0 esk8_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((k5_numbers = k4_ordinal1 → False) → False) → ((k5_complex1 = k1_xboole_0 → False) → False) → ((k1_xboole_0 = k6_numbers → False) → False) → False