Theorem. (
t13_cfuncdom)
∀esk13_4 : set → set → set → set → set, ∀k2_zfmisc_1 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀v1_funct_2 : set → set → set → prop, ∀v1_funct_1 : set → prop, ∀r2_relset_1 : set → set → set → set → prop, ∀esk14_4 : set → set → set → set → set, ∀m1_funct_2 : set → set → set → prop, ∀esk7_3 : set → set → set → set, ∀k4_tarski : set → set → set, ∀v5_relat_1 : set → set → prop, ∀v1_relat_1 : set → prop, ∀r2_hidden : set → set → prop, ∀k5_binop_2 : set → set → set, ∀k1_funct_2 : set → set → set, ∀np__1 : set, ∀k1_xboole_0 : set, ∀v1_finset_1 : set → prop, ∀esk11_0 : set, ∀esk5_2 : set → set → set, ∀esk9_0 : set, ∀esk10_0 : set, ∀esk6_1 : set → set, ∀esk8_2 : set → set → set, ∀esk12_0 : set, ∀esk1_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀r1_tarski : set → set → prop, ∀k3_xcmplx_0 : set → set → set, ∀v1_xcmplx_0 : set → prop, ∀v4_relat_1 : set → set → prop, ∀k1_funct_1 : set → set → set, ∀v1_xboole_0 : set → prop, ∀r2_funct_2 : set → set → set → set → prop, ∀k3_cfuncdom : set → set, ∀k1_domain_1 : set → set → set → set → set, ∀k2_funcsdom : set → set → set → set → set → set → set, ∀k9_funct_2 : set → set → set, ∀m2_funct_2 : set → set → set → set → prop, ∀m1_subset_1 : set → set → prop, ∀k9_complex1 : set → set → set, ∀k3_funct_2 : set → set → set → set → set, ∀k2_numbers : set, (∀X5 X4 X2 X3 X1, ((k3_funct_2 X1 k2_numbers X2 X5) = (k9_complex1 X3 (k3_funct_2 X1 k2_numbers X4 X5)) → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X5 X1 → m1_subset_1 X3 k2_numbers → m2_funct_2 X4 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 (k2_funcsdom X1 k2_numbers k2_numbers (k9_funct_2 X1 k2_numbers) (k3_cfuncdom X1) (k1_domain_1 k2_numbers (k9_funct_2 X1 k2_numbers) X3 X4)) → False) → (∀X4 X3 X2 X1, (v1_xboole_0 X1 → False) → (r2_funct_2 X1 k2_numbers X2 (k2_funcsdom X1 k2_numbers k2_numbers (k9_funct_2 X1 k2_numbers) (k3_cfuncdom X1) (k1_domain_1 k2_numbers (k9_funct_2 X1 k2_numbers) X4 X3)) → False) → (k3_funct_2 X1 k2_numbers X2 (esk13_4 X1 X2 X3 X4)) = (k9_complex1 X4 (k3_funct_2 X1 k2_numbers X3 (esk13_4 X1 X2 X3 X4))) → m1_subset_1 X4 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) → (∀X4 X3 X2 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk13_4 X1 X2 X3 X4) X1 → False) → (r2_funct_2 X1 k2_numbers X2 (k2_funcsdom X1 k2_numbers k2_numbers (k9_funct_2 X1 k2_numbers) (k3_cfuncdom X1) (k1_domain_1 k2_numbers (k9_funct_2 X1 k2_numbers) X4 X3)) → False) → m1_subset_1 X4 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) → (∀X3 X1 X6 X5 X2 X4, (v1_xboole_0 X4 → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_funct_2 (k2_funcsdom X1 X2 X3 X4 X5 X6) X1 X2 (k9_funct_2 X1 X2) → False) → v1_funct_1 X5 → m1_subset_1 X6 (k2_zfmisc_1 X3 X4) → v1_funct_2 X5 (k2_zfmisc_1 X3 X4) (k9_funct_2 X1 X2) → m1_subset_1 X5 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X3 X4) (k9_funct_2 X1 X2))) → False) → (∀X3 X1 X6 X5 X2 X4, ((k2_funcsdom X1 X2 X3 X4 X5 X6) = (k1_funct_1 X5 X6) → False) → (v1_xboole_0 X4 → False) → (v1_xboole_0 X3 → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_funct_1 X5 → m1_subset_1 X6 (k2_zfmisc_1 X3 X4) → v1_funct_2 X5 (k2_zfmisc_1 X3 X4) (k9_funct_2 X1 X2) → m1_subset_1 X5 (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 X3 X4) (k9_funct_2 X1 X2))) → False) → (∀X1 X3 X2 X4, (r2_relset_1 X2 X3 X1 X4 → False) → (k1_funct_1 X1 (esk14_4 X2 X3 X1 X4)) = (k1_funct_1 X4 (esk14_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 (esk14_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) → (∀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 X4 X3 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m1_subset_1 (k1_domain_1 X1 X2 X3 X4) (k2_zfmisc_1 X1 X2) → False) → m1_subset_1 X4 X2 → m1_subset_1 X3 X1 → 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) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k3_cfuncdom X1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 k2_numbers (k9_funct_2 X1 k2_numbers)) (k9_funct_2 X1 k2_numbers))) → False) → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (m2_funct_2 (esk7_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 X4 X3 X2, ((k1_domain_1 X1 X2 X3 X4) = (k4_tarski X3 X4) → False) → (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → m1_subset_1 X4 X2 → m1_subset_1 X3 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_funct_2 (k3_cfuncdom X1) (k2_zfmisc_1 k2_numbers (k9_funct_2 X1 k2_numbers)) (k9_funct_2 X1 k2_numbers) → False) → 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 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) → (∀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 (k9_complex1 X1 X2) k2_numbers → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → v1_xboole_0 (k3_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) → (∀X2 X1, ((k9_complex1 X1 X2) = (k9_complex1 X2 X1) → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → False) → (∀X2 X1, ((k9_complex1 X1 X2) = (k3_xcmplx_0 X1 X2) → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X1, (m1_subset_1 (k5_binop_2 X1 X2) k2_numbers → 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_xcmplx_0 (k3_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, ((k3_xcmplx_0 X1 X2) = (k3_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k5_binop_2 X1 X2) = (k3_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k5_binop_2 X1 X2) = (k5_binop_2 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 k2_numbers → False) → (∀X1, (v1_xcmplx_0 X1 → False) → r2_hidden X1 k2_numbers → False) → (∀X1, ((k3_xcmplx_0 np__1 X1) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, (r2_hidden X1 k2_numbers → 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 (k3_cfuncdom X1) → False) → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k2_funcsdom esk1_0 k2_numbers k2_numbers (k9_funct_2 esk1_0 k2_numbers) (k3_cfuncdom esk1_0) (k1_domain_1 k2_numbers (k9_funct_2 esk1_0 k2_numbers) (k5_binop_2 esk3_0 esk4_0) esk2_0)) = (k1_funct_1 (k3_cfuncdom esk1_0) (k4_tarski esk3_0 (k1_funct_1 (k3_cfuncdom esk1_0) (k4_tarski esk4_0 esk2_0)))) → False) → (v1_finset_1 k2_numbers → False) → (v1_xboole_0 esk12_0 → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 esk1_0 → False) → (v1_xboole_0 np__1 → 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 (esk8_2 X1 X2) (k1_zfmisc_1 (k2_zfmisc_1 X1 X2)) → False) → False) → (∀X2 X1, (m1_funct_2 (esk5_2 X1 X2) X1 X2 → False) → False) → (∀X2 X1, (v5_relat_1 (esk8_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk8_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_relat_1 (esk8_2 X1 X2) → False) → False) → (∀X1 X2, (v1_xboole_0 (esk8_2 X1 X2) → False) → False) → (∀X1, (m1_subset_1 (esk6_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (((k3_xcmplx_0 np__1 np__1) = np__1 → False) → False) → ((v1_xcmplx_0 esk12_0 → False) → False) → ((v1_xcmplx_0 esk10_0 → False) → False) → ((v1_xcmplx_0 esk4_0 → False) → False) → ((v1_xcmplx_0 esk3_0 → False) → False) → ((v1_xboole_0 esk9_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → False