Theorem. (
l13_xcmplx_0)
∀k1_numbers : set, ∀m1_subset_1 : set → set → prop, ∀k2_numbers : set, ∀v1_xboole_0 : set → prop, ∀v1_funct_1 : set → prop, ∀v2_funct_1 : set → prop, ∀k1_xboole_0 : set, ∀v1_finset_1 : set → prop, ∀esk16_0 : set, ∀esk17_0 : set, ∀esk12_0 : set, ∀esk9_0 : set, ∀esk11_0 : set, ∀esk10_0 : set, ∀esk13_0 : set, ∀esk8_1 : set → set, ∀esk14_0 : set, ∀esk15_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀v1_zfmisc_1 : set → prop, ∀v3_funct_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀r2_hidden : set → set → prop, ∀esk6_3 : set → set → set → set, ∀esk5_3 : set → set → set → set, ∀k2_arytm_0 : set → set → set, ∀esk7_3 : set → set → set → set, ∀esk4_3 : set → set → set → set, ∀k1_arytm_0 : set → set → set, ∀k3_arytm_0 : set → set, ∀k5_arytm_0 : set → set → set, ∀k3_xcmplx_0 : set → set → set, ∀v1_xcmplx_0 : set → prop, (∀X1 X3 X2, ((k5_arytm_0 (k1_arytm_0 (k2_arytm_0 (esk4_3 X2 X3 X1) (esk6_3 X2 X3 X1)) (k3_arytm_0 (k2_arytm_0 (esk5_3 X2 X3 X1) (esk7_3 X2 X3 X1)))) (k1_arytm_0 (k2_arytm_0 (esk4_3 X2 X3 X1) (esk7_3 X2 X3 X1)) (k2_arytm_0 (esk5_3 X2 X3 X1) (esk6_3 X2 X3 X1)))) = X1 → False) → X1 = (k3_xcmplx_0 X2 X3) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → False) → (∀X4 X3 X1 X2 X5 X6 X7, (X7 = (k3_xcmplx_0 X5 X6) → False) → X6 = (k5_arytm_0 X3 X4) → X5 = (k5_arytm_0 X1 X2) → X7 = (k5_arytm_0 (k1_arytm_0 (k2_arytm_0 X1 X3) (k3_arytm_0 (k2_arytm_0 X2 X4))) (k1_arytm_0 (k2_arytm_0 X1 X4) (k2_arytm_0 X2 X3))) → v1_xcmplx_0 X6 → v1_xcmplx_0 X5 → m1_subset_1 X4 k1_numbers → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X3 X2 X1, ((k5_arytm_0 (esk6_3 X2 X1 X3) (esk7_3 X2 X1 X3)) = X1 → False) → X3 = (k3_xcmplx_0 X2 X1) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X3 X2 X1, ((k5_arytm_0 (esk4_3 X1 X2 X3) (esk5_3 X1 X2 X3)) = X1 → False) → X3 = (k3_xcmplx_0 X1 X2) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2 X3, ((k1_arytm_0 (k2_arytm_0 X1 X2) (k2_arytm_0 X1 X3)) = (k2_arytm_0 X1 (k1_arytm_0 X2 X3)) → False) → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X3 X2 X1, (m1_subset_1 (esk7_3 X1 X2 X3) k1_numbers → False) → X3 = (k3_xcmplx_0 X1 X2) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X3 X2 X1, (m1_subset_1 (esk6_3 X1 X2 X3) k1_numbers → False) → X3 = (k3_xcmplx_0 X1 X2) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X3 X2 X1, (m1_subset_1 (esk5_3 X1 X2 X3) k1_numbers → False) → X3 = (k3_xcmplx_0 X1 X2) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X3 X2 X1, (m1_subset_1 (esk4_3 X1 X2 X3) k1_numbers → False) → X3 = (k3_xcmplx_0 X1 X2) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2 X3, ((k2_arytm_0 (k2_arytm_0 X1 X2) X3) = (k2_arytm_0 X1 (k2_arytm_0 X2 X3)) → False) → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X1 X2 X3, ((k1_arytm_0 (k1_arytm_0 X1 X2) X3) = (k1_arytm_0 X1 (k1_arytm_0 X2 X3)) → False) → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X4 X3 X1 X2, (X1 = X2 → False) → (k5_arytm_0 X1 X3) = (k5_arytm_0 X2 X4) → m1_subset_1 X4 k1_numbers → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X4 X3 X1 X2, (X1 = X2 → False) → (k5_arytm_0 X3 X1) = (k5_arytm_0 X4 X2) → m1_subset_1 X4 k1_numbers → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k1_arytm_0 (k3_arytm_0 X1) (k3_arytm_0 X2)) = (k3_arytm_0 (k1_arytm_0 X1 X2)) → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k3_arytm_0 (k2_arytm_0 X1 X2)) = (k2_arytm_0 (k3_arytm_0 X1) X2) → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k5_arytm_0 X1 X2) k2_numbers → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k2_arytm_0 X1 X2) k1_numbers → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 (k1_arytm_0 X1 X2) k1_numbers → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k2_arytm_0 X1 X2) = (k2_arytm_0 X2 X1) → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, ((k1_arytm_0 X1 X2) = (k1_arytm_0 X2 X1) → False) → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k1_numbers → 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, ((k3_xcmplx_0 X1 X2) = (k3_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, (m1_subset_1 (k3_arytm_0 X1) k1_numbers → False) → m1_subset_1 X1 k1_numbers → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → 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, ((k3_arytm_0 (k3_arytm_0 X1)) = X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_zfmisc_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_zfmisc_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v2_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_zfmisc_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_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) → ((k3_xcmplx_0 (k3_xcmplx_0 esk1_0 esk2_0) esk3_0) = (k3_xcmplx_0 esk1_0 (k3_xcmplx_0 esk2_0 esk3_0)) → False) → (v1_finset_1 k2_numbers → False) → (v1_finset_1 k1_numbers → False) → (v3_funct_1 esk16_0 → False) → (v1_zfmisc_1 esk15_0 → False) → (v1_xboole_0 esk17_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk12_0 → False) → (v1_xboole_0 k2_numbers → False) → (v1_xboole_0 k1_numbers → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → ((v4_funct_1 esk17_0 → False) → False) → ((v2_funct_1 esk13_0 → False) → False) → ((v1_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk13_0 → False) → False) → ((v1_relat_1 esk9_0 → False) → False) → ((v1_zfmisc_1 esk12_0 → False) → False) → ((v1_funct_1 esk16_0 → False) → False) → ((v1_funct_1 esk13_0 → False) → False) → ((v1_funct_1 esk9_0 → False) → False) → ((v1_xboole_0 esk10_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_xcmplx_0 esk11_0 → False) → False) → ((v1_xcmplx_0 esk3_0 → False) → False) → ((v1_xcmplx_0 esk2_0 → False) → False) → ((v1_xcmplx_0 esk1_0 → False) → False) → False