Theorem. (
t39_sysrel)
∀esk15_3 : set → set → set → set, ∀k4_relat_1 : set → set, ∀esk3_2 : set → set → set, ∀esk4_2 : set → set → set, ∀k3_xboole_0 : set → set → set, ∀esk10_3 : set → set → set → set, ∀esk6_2 : set → set → set, ∀esk7_2 : set → set → set, ∀k1_xboole_0 : set, ∀esk2_0 : set, ∀v5_relat_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀m1_subset_1 : set → set → prop, ∀v3_relat_1 : set → prop, ∀esk17_0 : set, ∀esk21_2 : set → set → set, ∀esk16_1 : set → set, ∀esk18_0 : set, ∀o_0_0_xboole_0 : set, ∀esk19_0 : set, ∀esk20_0 : set, ∀v2_relat_1 : set → prop, ∀v1_xboole_0 : set → prop, ∀v4_relat_1 : set → set → prop, ∀esk1_0 : set, ∀k1_sysrel : set → set, ∀esk11_3 : set → set → set → set, ∀k6_subset_1 : set → set → set, ∀esk5_3 : set → set → set → set, ∀k9_xtuple_0 : set → set, ∀esk9_2 : set → set → set, ∀esk8_2 : set → set → set, ∀r1_tarski : set → set → prop, ∀esk13_3 : set → set → set → set, ∀esk14_3 : set → set → set → set, ∀k3_relat_1 : set → set → set, ∀v1_relat_1 : set → prop, ∀k1_tarski : set → set, ∀esk12_5 : set → set → set → set → set → set, ∀k2_tarski : set → set → set, ∀r2_hidden : set → set → prop, (∀X2 X1 X4 X5 X3, (r2_hidden (k2_tarski (k2_tarski (esk12_5 X1 X2 X3 X4 X5) X5) (k1_tarski (esk12_5 X1 X2 X3 X4 X5))) X2 → False) → X3 = (k3_relat_1 X1 X2) → v1_relat_1 X3 → r2_hidden (k2_tarski (k2_tarski X4 X5) (k1_tarski X4)) X3 → False) → (∀X3 X2 X1 X5 X4, (r2_hidden (k2_tarski (k2_tarski X1 (esk12_5 X2 X3 X4 X1 X5)) (k1_tarski X1)) X2 → False) → X4 = (k3_relat_1 X2 X3) → v1_relat_1 X4 → r2_hidden (k2_tarski (k2_tarski X1 X5) (k1_tarski X1)) X4 → False) → (∀X4 X1 X2 X3, (X3 = (k3_relat_1 X1 X2) → False) → v1_relat_1 X3 → r2_hidden (k2_tarski (k2_tarski X4 (esk14_3 X1 X2 X3)) (k1_tarski X4)) X2 → r2_hidden (k2_tarski (k2_tarski (esk13_3 X1 X2 X3) X4) (k1_tarski (esk13_3 X1 X2 X3))) X1 → r2_hidden (k2_tarski (k2_tarski (esk13_3 X1 X2 X3) (esk14_3 X1 X2 X3)) (k1_tarski (esk13_3 X1 X2 X3))) X3 → False) → (∀X2 X1 X3, (X3 = (k3_relat_1 X1 X2) → False) → (r2_hidden (k2_tarski (k2_tarski (esk13_3 X1 X2 X3) (esk14_3 X1 X2 X3)) (k1_tarski (esk13_3 X1 X2 X3))) X3 → False) → (r2_hidden (k2_tarski (k2_tarski (esk15_3 X1 X2 X3) (esk14_3 X1 X2 X3)) (k1_tarski (esk15_3 X1 X2 X3))) X2 → False) → v1_relat_1 X3 → False) → (∀X1 X2 X3, (X3 = (k3_relat_1 X1 X2) → False) → (r2_hidden (k2_tarski (k2_tarski (esk13_3 X1 X2 X3) (esk14_3 X1 X2 X3)) (k1_tarski (esk13_3 X1 X2 X3))) X3 → False) → (r2_hidden (k2_tarski (k2_tarski (esk13_3 X1 X2 X3) (esk15_3 X1 X2 X3)) (k1_tarski (esk13_3 X1 X2 X3))) X1 → False) → v1_relat_1 X3 → False) → (∀X1 X2, (X2 = (k4_relat_1 X1) → False) → (esk3_2 X1 X2) = (esk4_2 X1 X2) → v1_relat_1 X2 → r2_hidden (esk3_2 X1 X2) X1 → r2_hidden (k2_tarski (k2_tarski (esk3_2 X1 X2) (esk4_2 X1 X2)) (k1_tarski (esk3_2 X1 X2))) X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → v1_relat_1 X1 → r2_hidden (k2_tarski (k2_tarski (esk8_2 X1 X2) (esk9_2 X1 X2)) (k1_tarski (esk8_2 X1 X2))) X2 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → r2_hidden (esk10_3 X1 X2 X3) X3 → r2_hidden (esk10_3 X1 X2 X3) X2 → r2_hidden (esk10_3 X1 X2 X3) X1 → False) → (∀X3 X2 X1, (r2_hidden (k2_tarski (k2_tarski X1 (esk5_3 X3 X2 X1)) (k1_tarski X1)) X3 → False) → X2 = (k9_xtuple_0 X3) → r2_hidden X1 X2 → False) → (∀X3 X2 X1, (X2 = (k9_xtuple_0 X1) → False) → r2_hidden (esk6_2 X1 X2) X2 → r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) X3) (k1_tarski (esk6_2 X1 X2))) X1 → False) → (∀X1 X3 X2, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X2 → False) → r2_hidden (esk11_3 X1 X2 X3) X3 → r2_hidden (esk11_3 X1 X2 X3) X1 → False) → (∀X1 X2, (X2 = (k4_relat_1 X1) → False) → (r2_hidden (esk3_2 X1 X2) X1 → False) → (r2_hidden (k2_tarski (k2_tarski (esk3_2 X1 X2) (esk4_2 X1 X2)) (k1_tarski (esk3_2 X1 X2))) X2 → False) → v1_relat_1 X2 → False) → (∀X5 X3 X2 X1 X4 X6, (r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) X6 → False) → X6 = (k3_relat_1 X3 X5) → v1_relat_1 X6 → r2_hidden (k2_tarski (k2_tarski X2 X4) (k1_tarski X2)) X5 → r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3 → False) → (∀X1 X2, (X2 = (k9_xtuple_0 X1) → False) → (r2_hidden (esk6_2 X1 X2) X2 → False) → (r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) X1 → False) → False) → (∀X1 X2, (X2 = (k4_relat_1 X1) → False) → ((esk3_2 X1 X2) = (esk4_2 X1 X2) → False) → (r2_hidden (k2_tarski (k2_tarski (esk3_2 X1 X2) (esk4_2 X1 X2)) (k1_tarski (esk3_2 X1 X2))) X2 → False) → v1_relat_1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → (r2_hidden (k2_tarski (k2_tarski (esk8_2 X1 X2) (esk9_2 X1 X2)) (k1_tarski (esk8_2 X1 X2))) X1 → False) → v1_relat_1 X1 → False) → (∀X2 X3 X1, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → r2_hidden (esk11_3 X1 X2 X3) X2 → False) → (∀X1 X3 X4 X2, (r2_hidden (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) X2 → False) → v1_relat_1 X1 → r1_tarski X1 X2 → r2_hidden (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) X1 → False) → (∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2) → False) → (r2_hidden (esk10_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (esk11_3 X1 X2 X3) X1 → False) → False) → (∀X2 X1, ((k3_relat_1 (k6_subset_1 X1 (k4_relat_1 (k9_xtuple_0 X1))) X2) = k1_xboole_0 → False) → (k3_relat_1 X1 X2) = X2 → (k3_relat_1 (k6_subset_1 X1 (k4_relat_1 (k9_xtuple_0 X1))) X1) = k1_xboole_0 → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X1 X2, ((k3_relat_1 X1 (k6_subset_1 X2 (k4_relat_1 (k9_xtuple_0 X2)))) = k1_xboole_0 → False) → (k3_relat_1 X1 X2) = X1 → (k3_relat_1 X2 (k6_subset_1 X2 (k4_relat_1 (k9_xtuple_0 X2)))) = k1_xboole_0 → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X4 X3 X1 X2, (r2_hidden X1 X2 → False) → X4 = (k4_relat_1 X2) → v1_relat_1 X4 → r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X4 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k9_xtuple_0 X3) → r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3 → False) → (∀X4 X3 X1 X2, (X1 = X2 → False) → X3 = (k4_relat_1 X4) → v1_relat_1 X3 → r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X4 → False) → X1 = X3 → X4 = (k4_relat_1 X2) → v1_relat_1 X4 → r2_hidden X1 X2 → False) → (((k3_relat_1 esk2_0 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0)))) = k1_xboole_0 → False) → ((k3_relat_1 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0))) esk2_0) = k1_xboole_0 → False) → False) → (((k3_relat_1 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0))) esk2_0) = k1_xboole_0 → False) → r1_tarski (k1_sysrel esk1_0) (k1_sysrel esk2_0) → False) → (((k3_relat_1 esk2_0 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0)))) = k1_xboole_0 → False) → r1_tarski (k1_sysrel esk1_0) (k1_sysrel esk2_0) → False) → (∀X2 X3 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_xboole_0 X2 X3) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X1 X3 X2, (v5_relat_1 (k3_relat_1 X1 X2) X3 → False) → v1_relat_1 X2 → v1_relat_1 X1 → v5_relat_1 X2 X3 → False) → (∀X1 X3 X2, (v4_relat_1 (k3_relat_1 X1 X2) X3 → False) → v1_relat_1 X2 → v1_relat_1 X1 → v4_relat_1 X1 X3 → False) → (∀X1 X3 X2, (v5_relat_1 X3 X2 → False) → v1_relat_1 X1 → v5_relat_1 X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X1 X3 X2, (v4_relat_1 X3 X2 → False) → v1_relat_1 X1 → v4_relat_1 X1 X2 → m1_subset_1 X3 (k1_zfmisc_1 X1) → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X4 = (k6_subset_1 X2 X3) → r2_hidden X1 X2 → False) → (((k3_relat_1 esk1_0 esk2_0) = esk1_0 → False) → ((k3_relat_1 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0))) esk2_0) = k1_xboole_0 → False) → False) → (((k3_relat_1 esk2_0 esk1_0) = esk1_0 → False) → ((k3_relat_1 esk2_0 (k6_subset_1 esk2_0 (k4_relat_1 (k9_xtuple_0 esk2_0)))) = k1_xboole_0 → False) → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X4 X3 X2 X1, X3 = (k6_subset_1 X4 X2) → r2_hidden X1 X3 → r2_hidden X1 X2 → False) → (∀X3 X2 X1, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v5_relat_1 X2 X3 → False) → (∀X3 X2 X1, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v4_relat_1 X1 X3 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X2 X4) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k3_xboole_0 X4 X2) → r2_hidden X1 X3 → False) → (∀X3 X4 X1 X2, (r2_hidden X1 X2 → False) → X3 = (k6_subset_1 X2 X4) → r2_hidden X1 X3 → False) → (∀X1 X2, (v2_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v2_relat_1 X2 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_relat_1 X1 → v2_relat_1 X2 → 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) → (∀X1 X2, (v1_xboole_0 (k3_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_xboole_0 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X1 → v1_xboole_0 X2 → False) → (∀X2 X1, (v1_relat_1 (k3_relat_1 X1 X2) → False) → v1_relat_1 X2 → v1_xboole_0 X1 → False) → (∀X1 X2, (v1_relat_1 X2 → False) → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (((k3_relat_1 esk2_0 esk1_0) = esk1_0 → False) → r1_tarski (k1_sysrel esk1_0) (k1_sysrel esk2_0) → False) → (((k3_relat_1 esk1_0 esk2_0) = esk1_0 → False) → r1_tarski (k1_sysrel esk1_0) (k1_sysrel esk2_0) → False) → (∀X1, ((k3_xboole_0 X1 (k4_relat_1 (k9_xtuple_0 X1))) = (k1_sysrel X1) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X2 → v5_relat_1 X1 X2 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X2 → v4_relat_1 X1 X2 → False) → (∀X2 X1, (v1_relat_1 (k3_xboole_0 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (v1_relat_1 (k6_subset_1 X1 X2) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_relat_1 X1 → v1_xboole_0 (k9_xtuple_0 X1) → False) → (((k3_relat_1 esk1_0 esk2_0) = esk1_0 → False) → ((k3_relat_1 esk2_0 esk1_0) = esk1_0 → False) → False) → (∀X1, (v2_relat_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v3_relat_1 X1 → False) → v1_relat_1 X1 → v1_xboole_0 X1 → False) → (∀X1, (v1_xboole_0 (k9_xtuple_0 X1) → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 (k1_sysrel X1) → False) → v1_relat_1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_relat_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X1 X2, v1_xboole_0 (k2_tarski X1 X2) → False) → (r1_tarski (k1_sysrel esk1_0) (k1_sysrel esk2_0) → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v1_xboole_0 esk20_0 → False) → (v1_xboole_0 esk17_0 → False) → (∀X1 X2 X3 X4, (v1_relat_1 (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_tarski (k2_tarski X3 X4) (k1_tarski X3))) → False) → False) → (∀X1 X2, (v1_relat_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) → False) → False) → (∀X1 X2, (m1_subset_1 (k6_subset_1 X1 X2) (k1_zfmisc_1 X1) → False) → False) → (∀X2 X1, (v5_relat_1 (esk21_2 X1 X2) X2 → False) → False) → (∀X1 X2, (v4_relat_1 (esk21_2 X1 X2) X1 → False) → False) → (∀X1 X2, (v1_relat_1 (esk21_2 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (k3_relat_1 X1 X2) → False) → False) → (∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → False) → False) → (∀X1, (v5_relat_1 (k4_relat_1 X1) X1 → False) → False) → (∀X1, (v4_relat_1 (k4_relat_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 (esk16_1 X1) X1 → False) → False) → (∀X1, ((k3_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k6_subset_1 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, ((k6_subset_1 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → (∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0 → False) → False) → (∀X1, ((k9_xtuple_0 (k4_relat_1 X1)) = X1 → False) → False) → (∀X1, (v1_relat_1 (k4_relat_1 X1) → False) → False) → (∀X1, (v1_relat_1 (k4_relat_1 X1) → False) → False) → ((v2_relat_1 esk19_0 → False) → False) → ((v1_xboole_0 esk18_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v1_relat_1 esk19_0 → False) → False) → ((v1_relat_1 esk17_0 → False) → False) → ((v1_relat_1 esk2_0 → False) → False) → ((v1_relat_1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False