Theorem. (t17_extreal2)
∀v1_xcmplx_0 : set → prop, ∀k3_xcmplx_0 : set → set → set, ∀k4_xxreal_3 : set → set → set, ∀k13_complex1 : set → set → set, ∀k17_complex1 : set → set, ∀r2_hidden : set → set → prop, ∀k10_real_1 : set → set → set, ∀k6_numbers : set, ∀k5_xxreal_3 : set → set, ∀r1_tarski : set → set → prop, ∀v5_membered : set → prop, ∀v3_membered : set → prop, ∀v1_membered : set → prop, ∀k1_xxreal_0 : set, ∀v7_ordinal1 : set → prop, ∀v1_rat_1 : set → prop, ∀k16_complex1 : set → set, ∀k1_xboole_0 : set, ∀k2_supinf_1 : set, ∀v1_finset_1 : set → prop, ∀esk15_0 : set, ∀esk10_0 : set, ∀esk9_0 : set, ∀np__0 : set, ∀esk3_1 : set → set, ∀k4_ordinal1 : set, ∀esk13_0 : set, ∀esk17_0 : set, ∀esk19_0 : set, ∀esk6_0 : set, ∀esk7_0 : set, ∀esk8_0 : set, ∀esk18_0 : set, ∀esk16_0 : set, ∀esk12_0 : set, ∀esk14_0 : set, ∀esk5_0 : set, ∀esk11_0 : set, ∀esk1_0 : set, ∀k1_supinf_1 : set, ∀esk2_0 : set, ∀v7_membered : set → prop, ∀k4_xcmplx_0 : set → set, ∀k5_numbers : set, ∀v1_int_1 : set → prop, ∀k2_supinf_2 : set → set, ∀v6_membered : set → prop, ∀v2_membered : set → prop, ∀v4_membered : set → prop, ∀k2_xxreal_0 : set, ∀k18_complex1 : set → set, ∀k3_extreal1 : set → set, ∀k2_numbers : set, ∀k5_xcmplx_0 : set → set, ∀k2_xxreal_3 : set → set, ∀r1_xxreal_0 : set → set → prop, ∀k6_xxreal_3 : set → set → set, ∀v1_xxreal_0 : set → prop, ∀v3_xxreal_0 : set → prop, ∀v1_xreal_0 : set → prop, ∀v2_xxreal_0 : set → prop, ∀k7_xcmplx_0 : set → set → set, ∀k1_numbers : set, ∀k7_numbers : set, ∀k12_binop_2 : set → set → set, ∀k2_extreal1 : set → set → set, ∀esk4_2 : set → set → set, ∀m2_subset_1 : set → set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀v1_xboole_0 : set → prop, (∀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, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (m2_subset_1 (esk4_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 X1 X2 X4, ((k12_binop_2 X3 X4) = (k2_extreal1 X1 X2) → False) → X2 = X4 → X1 = X3 → m1_subset_1 X4 k1_numbers → m1_subset_1 X3 k1_numbers → m1_subset_1 X2 k7_numbers → m1_subset_1 X1 k7_numbers → 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, ((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) → (∀X2 X1, (m1_subset_1 (k2_extreal1 X1 X2) k7_numbers → False) → m1_subset_1 X2 k7_numbers → m1_subset_1 X1 k7_numbers → 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_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 (k6_xxreal_3 X1 X2) → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 (k4_xxreal_3 X1 X2) → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k7_xcmplx_0 X1 X2) → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k7_xcmplx_0 X2 X1) → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v2_xxreal_0 (k6_xxreal_3 X1 X2) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k3_xcmplx_0 X1 X2) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → v2_xxreal_0 (k3_xcmplx_0 X2 X1) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v2_xxreal_0 (k6_xxreal_3 X1 X2) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v2_xxreal_0 (k4_xxreal_3 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 (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_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 (k6_xxreal_3 X1 X2) → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 (k4_xxreal_3 X1 X2) → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v1_xboole_0 (k4_xxreal_3 X1 X2) → False) → (∀X1 X2, (r1_xxreal_0 X2 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 (k2_xxreal_3 X1) (k2_xxreal_3 X2) → False) → (∀X2 X1, ((k13_complex1 (k17_complex1 X1) (k17_complex1 X2)) = (k17_complex1 (k13_complex1 X1 X2)) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k3_xcmplx_0 (k5_xcmplx_0 X1) (k5_xcmplx_0 X2)) = (k5_xcmplx_0 (k3_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, ((k2_extreal1 X1 X2) = (k6_xxreal_3 X1 X2) → False) → m1_subset_1 X2 k7_numbers → m1_subset_1 X1 k7_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) → (∀X3 X1 X2 X4, ((k7_xcmplx_0 X3 X4) = (k6_xxreal_3 X1 X2) → False) → X2 = X4 → X1 = X3 → v1_xcmplx_0 X4 → v1_xcmplx_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X3 X1 X2 X4, ((k4_xxreal_3 X1 X2) = (k3_xcmplx_0 X3 X4) → False) → X2 = X4 → X1 = X3 → v1_xcmplx_0 X4 → v1_xcmplx_0 X3 → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X1 X2, (r1_xxreal_0 (k2_xxreal_3 X2) (k2_xxreal_3 X1) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (v2_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v2_xxreal_0 X2 → v2_xxreal_0 X1 → False) → (∀X1 X2, (v2_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 X2 → v3_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 X2 → v2_xxreal_0 X1 → False) → (∀X1 X2, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v2_xxreal_0 X2 → v2_xxreal_0 X1 → False) → (∀X1 X2, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 X2 → v2_xxreal_0 X1 → False) → (∀X1 X2, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v3_xxreal_0 X2 → v3_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, ((k7_xcmplx_0 (k5_xcmplx_0 X1) (k5_xcmplx_0 X2)) = (k7_xcmplx_0 X2 X1) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v2_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → (v1_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → (v1_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v3_xxreal_0 X1 → False) → (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v1_xboole_0 X1 → False) → (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (m1_subset_1 (k13_complex1 X1 X2) k2_numbers → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, (m1_subset_1 (k12_binop_2 X1 X2) k1_numbers → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, ((k18_complex1 X2) = (k3_extreal1 X1) → False) → X1 = X2 → m1_subset_1 X2 k1_numbers → m1_subset_1 X1 k7_numbers → False) → (∀X2 X1, (v1_xboole_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v1_xboole_0 X1 → False) → (∀X2 X1, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → v1_xboole_0 X1 → False) → (∀X1, (X1 = k6_numbers → False) → m1_subset_1 X1 k7_numbers → r1_xxreal_0 (k3_extreal1 X1) k6_numbers → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X2 → False) → v1_xreal_0 X2 → v1_xreal_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) → (∀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, (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) → (∀X2 X1, ((k3_xcmplx_0 X1 (k5_xcmplx_0 X2)) = (k7_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k4_xxreal_3 X1 (k5_xxreal_3 X2)) = (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → r2_hidden X1 k1_numbers → r1_xxreal_0 X1 k2_xxreal_0 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X1, ((k3_extreal1 X1) = X1 → False) → m1_subset_1 X1 k7_numbers → r1_xxreal_0 k6_numbers X1 → False) → (∀X1, ((k3_extreal1 X1) = X1 → False) → m1_subset_1 X1 k7_numbers → r1_xxreal_0 k6_numbers X1 → 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_xxreal_3 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xreal_0 (k4_xxreal_3 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_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xxreal_0 (k6_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xxreal_0 (k4_xxreal_3 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_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, (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, ((k13_complex1 X1 X2) = (k7_xcmplx_0 X1 X2) → False) → v1_xcmplx_0 X2 → v1_xcmplx_0 X1 → False) → (∀X2 X1, ((k12_binop_2 X1 X2) = (k7_xcmplx_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, ((k4_xxreal_3 X1 X2) = (k4_xxreal_3 X2 X1) → False) → v1_xxreal_0 X2 → v1_xxreal_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, ((k3_extreal1 X1) = (k2_supinf_2 X1) → False) → (r1_xxreal_0 k6_numbers X1 → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, ((k3_extreal1 X1) = (k2_supinf_2 X1) → False) → (r1_xxreal_0 k6_numbers X1 → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, (m1_subset_1 (k2_supinf_2 X1) k7_numbers → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, (m1_subset_1 (k3_extreal1 X1) k7_numbers → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → False) → (r1_xxreal_0 X1 X2 → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X1 X2, (v3_xxreal_0 X2 → False) → (v2_xxreal_0 X1 → 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, v3_xxreal_0 (k3_extreal1 X1) → m1_subset_1 X1 k7_numbers → False) → (∀X1, ((k3_extreal1 (k3_extreal1 X1)) = (k3_extreal1 X1) → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, (k2_xxreal_0 = X1 → False) → ((k6_xxreal_3 k1_xxreal_0 X1) = k2_xxreal_0 → False) → (r1_xxreal_0 k6_numbers X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (k2_xxreal_0 = X1 → False) → ((k6_xxreal_3 k2_xxreal_0 X1) = k1_xxreal_0 → False) → (r1_xxreal_0 k6_numbers X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (X1 = k1_xxreal_0 → False) → ((k6_xxreal_3 k1_xxreal_0 X1) = k1_xxreal_0 → False) → (r1_xxreal_0 X1 k6_numbers → False) → v1_xxreal_0 X1 → False) → (∀X1, (X1 = k1_xxreal_0 → False) → ((k6_xxreal_3 k2_xxreal_0 X1) = k2_xxreal_0 → False) → (r1_xxreal_0 X1 k6_numbers → False) → v1_xxreal_0 X1 → 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, (v2_membered X1 → False) → m1_subset_1 X1 (k1_zfmisc_1 k7_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, ((k2_supinf_2 (k2_supinf_2 X1)) = X1 → False) → m1_subset_1 X1 k7_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, ((k2_supinf_2 X1) = (k2_xxreal_3 X1) → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, (v2_xxreal_0 X1 → False) → v1_xreal_0 X1 → v2_xxreal_0 (k5_xcmplx_0 X1) → False) → (∀X1, (v2_xxreal_0 X1 → False) → v1_xreal_0 X1 → v3_xxreal_0 (k4_xcmplx_0 X1) → False) → (∀X1, (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → v2_xxreal_0 (k5_xxreal_3 X1) → False) → (∀X1, (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → v3_xxreal_0 (k2_xxreal_3 X1) → False) → (∀X1, (v3_xxreal_0 X1 → False) → v1_xreal_0 X1 → v2_xxreal_0 (k4_xcmplx_0 X1) → False) → (∀X1, (v3_xxreal_0 X1 → False) → v1_xreal_0 X1 → v3_xxreal_0 (k5_xcmplx_0 X1) → False) → (∀X1, (v3_xxreal_0 X1 → False) → v1_xxreal_0 X1 → v2_xxreal_0 (k2_xxreal_3 X1) → False) → (∀X1, (v3_xxreal_0 X1 → False) → v1_xxreal_0 X1 → v3_xxreal_0 (k5_xxreal_3 X1) → False) → (∀X2 X1, ((k5_xcmplx_0 X2) = (k5_xxreal_3 X1) → False) → X1 = X2 → v1_xcmplx_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, ((k4_xcmplx_0 X2) = (k2_xxreal_3 X1) → False) → X1 = X2 → v1_xcmplx_0 X2 → v1_xreal_0 X1 → False) → (∀X1, (m1_subset_1 (k18_complex1 X1) k1_numbers → False) → v1_xcmplx_0 X1 → False) → (∀X1, (m1_subset_1 (k17_complex1 X1) k1_numbers → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v2_xxreal_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, (v2_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, (v3_xxreal_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, (v3_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → v3_xxreal_0 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → m1_subset_1 X1 k1_numbers → False) → (∀X1, (v1_xxreal_0 X1 → False) → m1_subset_1 X1 k7_numbers → False) → (∀X1, (v6_membered X1 → False) → m1_subset_1 X1 k5_numbers → False) → (∀X1, (X1 = k2_xxreal_0 → False) → (X1 = k1_xxreal_0 → False) → (r2_hidden X1 k1_numbers → False) → v1_xxreal_0 X1 → False) → (∀X1, (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v2_xxreal_0 X1 → False) → (v1_xxreal_0 (k5_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v2_xxreal_0 X1 → False) → (v1_xcmplx_0 (k5_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, (v3_xxreal_0 X1 → False) → (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v3_xxreal_0 X1 → False) → (v1_xxreal_0 (k5_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v3_xxreal_0 X1 → False) → (v1_xcmplx_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v3_xxreal_0 X1 → False) → (v1_xcmplx_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, ((k18_complex1 (k18_complex1 X1)) = (k18_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k17_complex1 (k17_complex1 X1)) = (k17_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k16_complex1 (k16_complex1 X1)) = (k16_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v3_xxreal_0 X1 → v2_xxreal_0 X1 → False) → (∀X1, v1_xxreal_0 X1 → v3_xxreal_0 X1 → v2_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_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_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xreal_0 X1 → False) → (v3_xxreal_0 X1 → False) → (v2_xxreal_0 X1 → False) → v1_xxreal_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, ((k5_xcmplx_0 (k5_xcmplx_0 X1)) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k4_xcmplx_0 (k4_xcmplx_0 X1)) = X1 → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k2_xxreal_3 (k2_xxreal_3 X1)) = X1 → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k4_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k2_xxreal_3 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xreal_0 (k16_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v1_xreal_0 (k5_xxreal_3 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k2_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k5_xxreal_3 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xxreal_0 (k5_xxreal_3 X1) → False) → v1_xxreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k5_xcmplx_0 X1) → False) → v1_xreal_0 X1 → False) → (∀X1, (v1_xcmplx_0 (k5_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_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, ((k18_complex1 X1) = (k16_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, ((k16_complex1 X1) = (k17_complex1 X1) → False) → v1_xcmplx_0 X1 → False) → (∀X1, (v7_membered X1 → False) → v1_xboole_0 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, (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) → 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) → (esk1_0 = k1_supinf_1 → esk2_0 = k1_supinf_1 → False) → (esk1_0 = k1_supinf_1 → esk2_0 = k2_supinf_1 → False) → (esk1_0 = k2_supinf_1 → esk2_0 = k1_supinf_1 → False) → (esk1_0 = k2_supinf_1 → esk2_0 = k2_supinf_1 → False) → ((k2_extreal1 (k3_extreal1 esk1_0) (k3_extreal1 esk2_0)) = (k3_extreal1 (k2_extreal1 esk1_0 esk2_0)) → False) → (v1_finset_1 k2_numbers → False) → (v1_finset_1 k1_numbers → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk11_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 esk5_0 → False) → (v1_xboole_0 k2_numbers → False) → (v1_xboole_0 k1_numbers → False) → (v1_xboole_0 k7_numbers → False) → (v1_xreal_0 esk14_0 → False) → (v1_xreal_0 esk9_0 → False) → (v1_xreal_0 k1_xxreal_0 → False) → (v1_xreal_0 k2_xxreal_0 → False) → (esk2_0 = k6_numbers → False) → ((m2_subset_1 np__0 k1_numbers k5_numbers → False) → False) → ((m2_subset_1 k6_numbers k1_numbers k5_numbers → False) → False) → (∀X1, (m1_subset_1 (esk3_1 X1) X1 → False) → False) → ((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers) → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((r1_xxreal_0 np__0 np__0 → False) → False) → ((m1_subset_1 esk2_0 k7_numbers → False) → False) → ((m1_subset_1 esk1_0 k7_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 k1_supinf_1 k7_numbers → False) → False) → ((m1_subset_1 k2_supinf_1 k7_numbers → False) → False) → (((k3_xcmplx_0 np__0 np__0) = np__0 → False) → False) → ((v1_xboole_0 (k5_xxreal_3 k1_xxreal_0) → False) → False) → ((v1_xboole_0 (k5_xxreal_3 k2_xxreal_0) → False) → False) → ((v1_xxreal_0 (k5_xxreal_3 k1_xxreal_0) → False) → False) → ((v1_xxreal_0 (k5_xxreal_3 k2_xxreal_0) → False) → False) → ((v7_membered esk15_0 → False) → False) → ((v7_membered k4_ordinal1 → False) → False) → ((v7_membered k2_numbers → False) → False) → ((v7_membered k1_numbers → False) → False) → ((v2_xxreal_0 esk13_0 → False) → False) → ((v2_xxreal_0 esk12_0 → False) → False) → ((v2_xxreal_0 esk9_0 → False) → False) → ((v2_xxreal_0 k1_xxreal_0 → False) → False) → ((v3_xxreal_0 esk17_0 → False) → False) → ((v3_xxreal_0 esk16_0 → False) → False) → ((v3_xxreal_0 esk14_0 → False) → False) → ((v3_xxreal_0 k2_xxreal_0 → False) → False) → ((v1_xboole_0 esk19_0 → False) → False) → ((v1_xboole_0 esk18_0 → False) → False) → ((v1_xboole_0 esk6_0 → False) → False) → ((v1_xboole_0 np__0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_xreal_0 esk18_0 → False) → False) → ((v1_xreal_0 esk16_0 → False) → False) → ((v1_xreal_0 esk12_0 → False) → False) → ((v1_xreal_0 esk7_0 → False) → False) → ((v3_membered k1_numbers → False) → False) → ((v1_xxreal_0 esk19_0 → False) → False) → ((v1_xxreal_0 esk18_0 → False) → False) → ((v1_xxreal_0 esk17_0 → False) → False) → ((v1_xxreal_0 esk16_0 → False) → False) → ((v1_xxreal_0 esk14_0 → False) → False) → ((v1_xxreal_0 esk13_0 → False) → False) → ((v1_xxreal_0 esk12_0 → False) → False) → ((v1_xxreal_0 esk9_0 → False) → False) → ((v1_xxreal_0 esk8_0 → False) → False) → ((v1_xxreal_0 k1_xxreal_0 → False) → False) → ((v1_xxreal_0 k2_xxreal_0 → False) → False) → ((v2_membered k7_numbers → False) → False) → ((v1_xcmplx_0 esk18_0 → False) → False) → ((v1_xcmplx_0 esk16_0 → False) → False) → ((v1_xcmplx_0 esk12_0 → False) → False) → ((v1_membered k2_numbers → False) → False) → ((v6_membered esk15_0 → False) → False) → ((v6_membered esk10_0 → False) → False) → ((v6_membered esk5_0 → False) → False) → ((v6_membered k4_ordinal1 → False) → False) → (((k4_xcmplx_0 np__0) = np__0 → False) → False) → (((k2_xxreal_3 k2_xxreal_0) = k1_xxreal_0 → False) → False) → ((k5_numbers = k4_ordinal1 → False) → False) → ((k1_supinf_1 = k1_xxreal_0 → False) → False) → ((k2_supinf_1 = k2_xxreal_0 → False) → False) → ((k1_xboole_0 = k6_numbers → False) → False) → False
In Proofgold the corresponding term root is 35747d... and proposition id is a6ae76...
Proof:
Proof not loaded.