Theorem. (
t72_complex2)
∀v1_xboole_0 : set → prop, ∀k1_zfmisc_1 : set → set, ∀m2_subset_1 : set → set → set → prop, ∀v1_xcmplx_0 : set → prop, ∀v1_xreal_0 : set → prop, ∀v3_xxreal_0 : set → prop, ∀k4_xcmplx_0 : set → set, ∀v4_membered : set → prop, ∀v2_membered : set → prop, ∀v6_membered : set → prop, ∀esk4_0 : set, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk16_0 : set, ∀esk14_0 : set, ∀np__1 : set, ∀np__0 : set, ∀k4_ordinal1 : set, ∀esk21_0 : set, ∀esk18_0 : set, ∀esk22_0 : set, ∀esk13_0 : set, ∀esk12_0 : set, ∀esk10_0 : set, ∀esk11_0 : set, ∀esk9_0 : set, ∀esk23_0 : set, ∀esk17_0 : set, ∀esk20_0 : set, ∀k5_complex1 : set, ∀esk7_0 : set, ∀esk5_1 : set → set, ∀esk8_0 : set, ∀esk15_0 : set, ∀esk19_0 : set, ∀v1_finset_1 : set → prop, ∀k1_xboole_0 : set, ∀v7_membered : set → prop, ∀k5_numbers : set, ∀k1_numbers : set, ∀v1_xxreal_0 : set → prop, ∀v1_rat_1 : set → prop, ∀v7_ordinal1 : set → prop, ∀v1_membered : set → prop, ∀v3_membered : set → prop, ∀v5_membered : set → prop, ∀v1_int_1 : set → prop, ∀r1_tarski : set → set → prop, ∀r2_hidden : set → set → prop, ∀k6_xcmplx_0 : set → set → set, ∀v2_xxreal_0 : set → prop, ∀k8_complex1 : set → set → set, ∀k2_xcmplx_0 : set → set → set, ∀esk6_2 : set → set → set, ∀k4_complex2 : set → set → set → set, ∀k11_complex1 : set → set → set, ∀k6_numbers : set, ∀k2_numbers : set, ∀m1_subset_1 : set → set → prop, (∀X1 X2 X3, ((k4_complex2 (k11_complex1 X1 X2) k6_numbers (k11_complex1 X3 X2)) = (k4_complex2 X1 X2 X3) → False) → m1_subset_1 X3 k2_numbers → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → 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_xreal_0 (k4_complex2 X1 X2 X3) → False) → v1_xcmplx_0 X3 → v1_xcmplx_0 X2 → v1_xcmplx_0 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) → (∀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, (m1_subset_1 (k11_complex1 X1 X2) k2_numbers → False) → m1_subset_1 X2 k2_numbers → m1_subset_1 X1 k2_numbers → 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) → (∀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) → (∀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 (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 → 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, ((k11_complex1 X1 X2) = (k6_xcmplx_0 X1 X2) → 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) → (∀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 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, ((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) → (∀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, ((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_int_1 (k6_xcmplx_0 X1 X2) → False) → v1_int_1 X2 → v1_int_1 X1 → False) → (∀X2 X1, (v1_int_1 (k2_xcmplx_0 X1 X2) → False) → v1_int_1 X2 → v1_int_1 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 (k2_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xcmplx_0 (k6_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (v1_xcmplx_0 (k2_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2, (v5_membered X2 → False) → v5_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v4_membered X2 → False) → v4_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v3_membered X2 → False) → v3_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v2_membered X2 → False) → v2_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_membered X2 → False) → v1_membered X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v6_membered X2 → False) → v6_membered 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) → (∀X1 X2, (v7_ordinal1 X2 → False) → v6_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_int_1 X2 → False) → v5_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_rat_1 X2 → False) → v4_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xreal_0 X2 → False) → v3_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xxreal_0 X2 → False) → v2_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v1_xcmplx_0 X2 → False) → v1_membered X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v3_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k1_numbers) → False) → (∀X1, (v1_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k2_numbers) → False) → (∀X1, (v6_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k5_numbers) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → 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, (v1_xboole_0 X1 → False) → v1_xcmplx_0 X1 → v1_xboole_0 (k4_xcmplx_0 X1) → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → 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, (v6_membered X1 → False) → m1_subset_1 X1 k5_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_xboole_0 X1 → False) → (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xcmplx_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_xxreal_0 X1 → v1_xboole_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v1_xboole_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v1_xboole_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v1_xboole_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, ((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, ((k4_xcmplx_0 (k4_xcmplx_0 X1)) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v1_int_1 (k4_xcmplx_0 X1) → False) → v1_int_1 X1 → False) → (∀X1, (v1_xreal_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_int_1 X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v7_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_int_1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v5_membered X1 → False) → v6_membered X1 → False) → (∀X1, (v4_membered X1 → False) → v5_membered X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → v1_int_1 X1 → False) → (∀X1, (v3_membered X1 → False) → v4_membered X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v2_membered X1 → False) → v3_membered X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xcmplx_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_membered X1 → False) → v3_membered X1 → False) → (∀X1, (v6_membered X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k4_complex2 (k8_complex1 esk1_0 esk4_0) (k8_complex1 esk2_0 esk4_0) (k8_complex1 esk3_0 esk4_0)) = (k4_complex2 esk1_0 esk2_0 esk3_0) → False) → (v1_finset_1 k1_numbers → False) → (v1_finset_1 k2_numbers → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk16_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk8_0 → False) → (v1_xboole_0 np__1 → False) → (v1_xboole_0 k1_numbers → False) → (v1_xboole_0 k2_numbers → False) → ((m2_subset_1 np__1 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 np__0 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 k6_numbers k1_numbers k5_numbers → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) (k4_xcmplx_0 np__1)) = np__0 → False) → False) → (∀X1, (m1_subset_1 (esk5_1 X1) X1 → False) → False) → (((k6_xcmplx_0 (k4_xcmplx_0 np__1) np__0) = (k4_xcmplx_0 np__1) → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) np__0) = (k4_xcmplx_0 np__1) → False) → False) → (((k2_xcmplx_0 np__0 (k4_xcmplx_0 np__1)) = (k4_xcmplx_0 np__1) → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (((k2_xcmplx_0 (k4_xcmplx_0 np__1) np__1) = np__0 → False) → False) → (((k6_xcmplx_0 np__0 (k4_xcmplx_0 np__1)) = np__1 → False) → False) → (((k2_xcmplx_0 np__1 (k4_xcmplx_0 np__1)) = np__0 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (((k6_xcmplx_0 np__0 np__1) = (k4_xcmplx_0 np__1) → False) → False) → ((m1_subset_1 esk7_0 k1_numbers → False) → False) → ((m1_subset_1 esk4_0 k2_numbers → False) → False) → ((m1_subset_1 esk3_0 k2_numbers → False) → False) → ((m1_subset_1 esk2_0 k2_numbers → False) → False) → ((m1_subset_1 esk1_0 k2_numbers → False) → False) → ((m1_subset_1 np__1 k1_numbers → False) → False) → ((m1_subset_1 np__1 k5_numbers → False) → False) → ((m1_subset_1 np__0 k1_numbers → False) → False) → ((m1_subset_1 np__0 k5_numbers → False) → False) → ((m1_subset_1 k1_xboole_0 k4_ordinal1 → False) → False) → ((m1_subset_1 k5_complex1 k2_numbers → False) → False) → (((k6_xcmplx_0 np__1 np__1) = np__0 → False) → False) → (((k6_xcmplx_0 np__1 np__0) = np__1 → False) → False) → (((k2_xcmplx_0 np__1 np__0) = np__1 → False) → False) → (((k2_xcmplx_0 np__0 np__1) = np__1 → False) → False) → (((k2_xcmplx_0 np__0 np__0) = np__0 → False) → False) → (((k4_xcmplx_0 (k4_xcmplx_0 np__1)) = np__1 → False) → False) → ((v3_xxreal_0 esk21_0 → False) → False) → ((v3_xxreal_0 esk20_0 → False) → False) → ((v2_xxreal_0 esk18_0 → False) → False) → ((v2_xxreal_0 esk17_0 → False) → False) → ((v2_xxreal_0 np__1 → False) → False) → ((v7_membered esk19_0 → False) → False) → ((v7_membered k4_ordinal1 → False) → False) → ((v7_membered k1_numbers → False) → False) → ((v7_membered k2_numbers → False) → False) → ((v1_xboole_0 esk23_0 → False) → False) → ((v1_xboole_0 esk22_0 → False) → False) → ((v1_xboole_0 esk9_0 → False) → False) → ((v1_xboole_0 np__0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_int_1 esk13_0 → False) → False) → ((v1_int_1 esk7_0 → False) → False) → ((v1_xreal_0 esk22_0 → False) → False) → ((v1_xreal_0 esk20_0 → False) → False) → ((v1_xreal_0 esk17_0 → False) → False) → ((v1_xreal_0 esk11_0 → False) → False) → ((v1_xreal_0 esk7_0 → False) → False) → ((v3_membered k1_numbers → False) → False) → ((v1_xxreal_0 esk23_0 → False) → False) → ((v1_xxreal_0 esk22_0 → False) → False) → ((v1_xxreal_0 esk21_0 → False) → False) → ((v1_xxreal_0 esk20_0 → False) → False) → ((v1_xxreal_0 esk18_0 → False) → False) → ((v1_xxreal_0 esk17_0 → False) → False) → ((v1_xxreal_0 esk12_0 → False) → False) → ((v1_xxreal_0 esk7_0 → False) → False) → ((v1_xcmplx_0 esk22_0 → False) → False) → ((v1_xcmplx_0 esk20_0 → False) → False) → ((v1_xcmplx_0 esk17_0 → False) → False) → ((v1_xcmplx_0 esk16_0 → False) → False) → ((v1_xcmplx_0 esk10_0 → False) → False) → ((v1_xcmplx_0 esk7_0 → False) → False) → ((v1_membered k2_numbers → False) → False) → ((v6_membered esk19_0 → False) → False) → ((v6_membered esk14_0 → False) → False) → ((v6_membered esk8_0 → False) → False) → ((v6_membered k4_ordinal1 → False) → False) → ((