Theorem. (
t162_xxreal_1)
∀v1_xxreal_0 : set → prop, ∀r1_xxreal_0 : set → set → prop, ∀esk9_3 : set → set → set → set, ∀a_2_1_xxreal_1 : set → set → set, ∀k7_numbers : set, ∀m1_subset_1 : set → set → prop, ∀k3_xxreal_0 : set → set → set, ∀k2_xxreal_1 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀esk6_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀v6_membered : set → prop, ∀v4_membered : set → prop, ∀v1_membered : set → prop, ∀v1_int_1 : set → prop, ∀v2_xxreal_0 : set → prop, ∀v3_xxreal_0 : set → prop, ∀v7_membered : set → prop, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk18_0 : set, ∀esk14_0 : set, ∀esk8_1 : set → set, ∀esk19_0 : set, ∀esk16_0 : set, ∀esk22_0 : set, ∀esk11_0 : set, ∀esk13_0 : set, ∀esk12_0 : set, ∀o_0_0_xboole_0 : set, ∀esk21_0 : set, ∀esk17_0 : set, ∀esk20_0 : set, ∀esk10_0 : set, ∀esk15_0 : set, ∀k1_xboole_0 : set, ∀v1_xcmplx_0 : set → prop, ∀v1_rat_1 : set → prop, ∀v7_ordinal1 : set → prop, ∀v3_membered : set → prop, ∀v1_xreal_0 : set → prop, ∀v5_membered : set → prop, ∀k4_xxreal_0 : set → set → set, ∀esk23_2 : set → set → set, ∀v2_membered : set → prop, ∀esk5_2 : set → set → set, ∀r2_hidden : set → set → prop, ∀esk7_3 : set → set → set → set, ∀k2_xboole_0 : set → set → set, (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk7_3 X1 X2 X3) X3 → r2_hidden (esk7_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk7_3 X1 X2 X3) X3 → r2_hidden (esk7_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk7_3 X1 X2 X3) X3 → False) → (r2_hidden (esk7_3 X1 X2 X3) X2 → False) → (r2_hidden (esk7_3 X1 X2 X3) X1 → False) → False) → (∀X1 X2 X3, v1_xxreal_0 X3 → v1_xxreal_0 X1 → r2_hidden X2 (a_2_1_xxreal_1 X3 X1) → r1_xxreal_0 X1 (esk9_3 X2 X3 X1) → False) → (∀X1 X2 X3, (r1_xxreal_0 X1 (esk9_3 X2 X1 X3) → False) → v1_xxreal_0 X3 → v1_xxreal_0 X1 → r2_hidden X2 (a_2_1_xxreal_1 X1 X3) → False) → (∀X2 X1 X3, (m1_subset_1 (esk9_3 X1 X2 X3) k7_numbers → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → r2_hidden X1 (a_2_1_xxreal_1 X2 X3) → False) → (∀X1 X2, (X1 = X2 → False) → v2_membered X2 → v2_membered X1 → r2_hidden (esk5_2 X1 X2) X2 → r2_hidden (esk5_2 X1 X2) X1 → False) → (∀X2 X1 X3, ((esk9_3 X1 X2 X3) = X1 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → r2_hidden X1 (a_2_1_xxreal_1 X2 X3) → False) → (∀X2 X3 X4 X1, (r1_xxreal_0 X4 X1 → False) → (r2_hidden X2 (a_2_1_xxreal_1 X3 X4) → False) → X1 = X2 → v1_xxreal_0 X4 → v1_xxreal_0 X3 → r1_xxreal_0 X3 X1 → m1_subset_1 X1 k7_numbers → False) → (∀X2 X3 X1, (r1_xxreal_0 X3 X1 → False) → (r1_xxreal_0 X2 X1 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 (k3_xxreal_0 X2 X3) X1 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk23_2 X3 X2) → False) → (∀X2 X1 X3, v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X1 X2 → r2_hidden X2 (k2_xxreal_1 X3 X1) → False) → (∀X2 X1 X3, (r1_xxreal_0 (k4_xxreal_0 X1 X3) X2 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X3 X2 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1 X3, (r1_xxreal_0 X1 X3 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 (k4_xxreal_0 X1 X2) X3 → False) → (∀X3 X1 X2, (r1_xxreal_0 X1 X2 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r2_hidden X2 (k2_xxreal_1 X1 X3) → False) → (∀X1 X3 X2, (r1_xxreal_0 X3 X2 → False) → (r2_hidden X2 (k2_xxreal_1 X1 X3) → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X1 X2 → False) → (∀X2 X1, (X1 = X2 → False) → (r2_hidden (esk5_2 X1 X2) X2 → False) → (r2_hidden (esk5_2 X1 X2) X1 → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1 X3, v1_xxreal_0 X3 → v2_membered X2 → v2_membered X1 → r1_xboole_0 X1 X2 → r2_hidden X3 X2 → r2_hidden X3 X1 → False) → (∀X2 X1 X3, (r1_xxreal_0 (k3_xxreal_0 X2 X3) X1 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X2 X1 → False) → (∀X2 X1 X3, (r1_xxreal_0 X1 X3 → False) → v1_xxreal_0 X3 → v1_xxreal_0 X2 → v1_xxreal_0 X1 → r1_xxreal_0 X2 X3 → r1_xxreal_0 X1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X2 = (k2_xboole_0 X3 X4) → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) X1 → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk6_2 X1 X2) X2 → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (r2_hidden (esk23_2 X1 X2) X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X2 X4) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X4 X2) → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (v1_xxreal_0 (esk6_2 X1 X2) → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X1 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X2 X1) → False) → (∀X2 X1, (X1 = X2 → False) → (v1_xxreal_0 (esk5_2 X1 X2) → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v6_membered (k2_xboole_0 X1 X2) → False) → v6_membered X2 → v6_membered X1 → False) → (∀X2 X1, (v5_membered (k2_xboole_0 X1 X2) → False) → v5_membered X2 → v5_membered X1 → False) → (∀X2 X1, (v4_membered (k2_xboole_0 X1 X2) → False) → v4_membered X2 → v4_membered X1 → False) → (∀X2 X1, (v1_xreal_0 (k4_xxreal_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v1_xreal_0 (k3_xxreal_0 X1 X2) → False) → v1_xreal_0 X2 → v1_xreal_0 X1 → False) → (∀X2 X1, (v3_membered (k2_xboole_0 X1 X2) → False) → v3_membered X2 → v3_membered X1 → False) → (∀X2 X1, (v2_membered (k2_xboole_0 X1 X2) → False) → v2_membered X2 → v2_membered X1 → False) → (∀X2 X1, (v2_membered (k2_xxreal_1 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (v1_membered (k2_xboole_0 X1 X2) → False) → v1_membered X2 → v1_membered X1 → False) → (∀X2 X1, (v1_xxreal_0 (k4_xxreal_0 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (v1_xxreal_0 (k3_xxreal_0 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 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, ((a_2_1_xxreal_1 X1 X2) = (k2_xxreal_1 X1 X2) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, ((k4_xxreal_0 X1 X2) = (k4_xxreal_0 X2 X1) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, ((k3_xxreal_0 X1 X2) = (k3_xxreal_0 X2 X1) → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X1, (v1_xboole_0 (k2_xxreal_1 X1 X1) → False) → v1_xxreal_0 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 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_xcmplx_0 X2 → False) → v1_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_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, ((k4_xxreal_0 X1 X1) = X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, ((k3_xxreal_0 X1 X1) = X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X2 X1, (r1_xxreal_0 X1 X1 → False) → v1_xxreal_0 X2 → v1_xxreal_0 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → m1_subset_1 X1 k7_numbers → 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) → (∀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, (v6_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, (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, (v1_xxreal_0 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v1_xxreal_0 X1 → False) → v1_xreal_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k2_xxreal_1 (k3_xxreal_0 esk1_0 esk3_0) (k4_xxreal_0 esk2_0 esk4_0)) = (k2_xboole_0 (k2_xxreal_1 esk1_0 esk2_0) (k2_xxreal_1 esk3_0 esk4_0)) → False) → (r1_xboole_0 (k2_xxreal_1 esk1_0 esk2_0) (k2_xxreal_1 esk3_0 esk4_0) → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk15_0 → False) → (v1_xboole_0 esk14_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 k7_numbers → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → ((v3_xxreal_0 esk20_0 → False) → False) → ((v3_xxreal_0 esk19_0 → False) → False) → ((v2_xxreal_0 esk17_0 → False) → False) → ((v2_xxreal_0 esk16_0 → False) → False) → ((v7_membered esk18_0 → False) → False) → ((v1_xboole_0 esk22_0 → False) → False) → ((v1_xboole_0 esk21_0 → False) → False) → ((v1_xboole_0 esk11_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v6_membered esk18_0 → False) → False) → ((v6_membered esk14_0 → False) → False) → ((v6_membered esk10_0 → False) → False) → ((v1_xreal_0 esk21_0 → False) → False) → ((v1_xreal_0 esk19_0 → False) → False) → ((v1_xreal_0 esk16_0 → False) → False) → ((v1_xreal_0 esk12_0 → False) → False) → ((v2_membered k7_numbers → False) → False) → ((v1_xcmplx_0 esk21_0 → False) → False) → ((v1_xcmplx_0 esk19_0 → False) → False) → ((v1_xcmplx_0 esk16_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 esk19_0 → False) → False) → ((v1_xxreal_0 esk17_0 → False) → False) → ((v1_xxreal_0 esk16_0 → False) → False) → ((v1_xxreal_0 esk13_0 → False) → False) → ((v1_xxreal_0 esk4_0 → False) → False) → ((v1_xxreal_0 esk3_0 → False) → False) → ((v1_xxreal_0 esk2_0 → False) → False) → ((v1_xxreal_0 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False