Theorem. (
t111_zfmisc_1)
∀esk9_3 : set → set → set → set, ∀esk10_3 : set → set → set → set, ∀esk8_3 : set → set → set → set, ∀k2_xboole_0 : set → set → set, ∀esk12_3 : set → set → set → set, ∀esk13_3 : set → set → set → set, ∀esk17_1 : set → set, ∀esk16_1 : set → set, ∀esk20_1 : set → set, ∀esk4_2 : set → set → set, ∀r1_tarski : set → set → prop, ∀esk11_2 : set → set → set, ∀r1_xboole_0 : set → set → prop, ∀esk24_2 : set → set → set, ∀v1_xboole_0 : set → prop, ∀esk23_1 : set → set, ∀k1_xboole_0 : set, ∀esk25_1 : set → set, ∀esk19_0 : set, ∀o_0_0_xboole_0 : set, ∀esk18_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk1_0 : set, ∀esk22_2 : set → set → set, ∀esk21_2 : set → set → set, ∀esk15_2 : set → set → set, ∀esk14_2 : set → set → set, ∀k3_tarski : set → set, ∀esk5_3 : set → set → set → set, ∀k1_tarski : set → set, ∀esk6_4 : set → set → set → set → set, ∀esk7_4 : set → set → set → set → set, ∀k2_tarski : set → set → set, ∀k2_zfmisc_1 : set → set → set, ∀r2_hidden : set → set → prop, (∀X3 X2 X4 X1, ((k2_tarski (k2_tarski (esk6_4 X2 X3 X4 X1) (esk7_4 X2 X3 X4 X1)) (k1_tarski (esk6_4 X2 X3 X4 X1))) = X1 → False) → X4 = (k2_zfmisc_1 X2 X3) → r2_hidden X1 X4 → False) → (∀X3 X2 X1, (X3 = (k2_zfmisc_1 X1 X2) → False) → ((k2_tarski (k2_tarski (esk9_3 X1 X2 X3) (esk10_3 X1 X2 X3)) (k1_tarski (esk9_3 X1 X2 X3))) = (esk8_3 X1 X2 X3) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → False) → (∀X2 X1 X3 X4, (r2_hidden (esk7_4 X1 X2 X3 X4) X2 → False) → X3 = (k2_zfmisc_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk6_4 X1 X2 X3 X4) X1 → False) → X3 = (k2_zfmisc_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X5 X4 X1 X2 X3, (X3 = (k2_zfmisc_1 X1 X2) → False) → (esk8_3 X1 X2 X3) = (k2_tarski (k2_tarski X4 X5) (k1_tarski X4)) → r2_hidden X5 X2 → r2_hidden X4 X1 → r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk12_3 X1 X2 X3) X3 → r2_hidden (esk12_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk12_3 X1 X2 X3) X3 → r2_hidden (esk12_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk12_3 X1 X2 X3) X3 → False) → (r2_hidden (esk12_3 X1 X2 X3) X2 → False) → (r2_hidden (esk12_3 X1 X2 X3) X1 → False) → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → (esk5_3 X1 X2 X3) = X1 → r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → (esk5_3 X1 X2 X3) = X2 → r2_hidden (esk5_3 X1 X2 X3) X3 → False) → (∀X2 X3 X1, (X3 = (k2_zfmisc_1 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk10_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k2_zfmisc_1 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk9_3 X1 X2 X3) X1 → False) → False) → (∀X3 X2 X1, (X3 = (k2_tarski X1 X2) → False) → ((esk5_3 X1 X2 X3) = X2 → False) → ((esk5_3 X1 X2 X3) = X1 → False) → (r2_hidden (esk5_3 X1 X2 X3) X3 → False) → False) → (∀X4 X2 X3 X1 X5 X6, (r2_hidden X5 X6 → False) → X6 = (k2_zfmisc_1 X2 X4) → X5 = (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) → r2_hidden X3 X4 → r2_hidden X1 X2 → False) → (∀X3 X2 X1, (X2 = (k3_tarski X1) → False) → r2_hidden X3 X1 → r2_hidden (esk14_2 X1 X2) X3 → r2_hidden (esk14_2 X1 X2) X2 → False) → (∀X1 X2 X3, (r2_hidden (esk13_3 X1 X2 X3) X1 → False) → X2 = (k3_tarski X1) → r2_hidden X3 X2 → False) → (∀X2 X3 X1, (r2_hidden X1 (esk13_3 X2 X3 X1) → False) → X3 = (k3_tarski X2) → r2_hidden X1 X3 → False) → (∀X2 X3 X1, ((k2_tarski (k2_tarski (esk16_1 X1) (esk17_1 X1)) (k1_tarski (esk16_1 X1))) = X1 → False) → r2_hidden X1 (k2_zfmisc_1 X2 X3) → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk14_2 X1 X2) X2 → False) → (r2_hidden (esk14_2 X1 X2) (esk15_2 X1 X2) → False) → False) → (∀X3 X4 X1 X2, (r2_hidden X1 (esk20_1 X2) → False) → X1 = X3 → r2_hidden X4 X3 → r2_hidden X4 X2 → r2_hidden X1 (k3_tarski X2) → False) → (∀X1 X2, (r2_hidden (esk22_2 X1 X2) (esk21_2 X1 X2) → False) → r2_hidden X2 (esk20_1 X1) → False) → (∀X2 X1, (X2 = (k1_tarski X1) → False) → (esk4_2 X1 X2) = X1 → r2_hidden (esk4_2 X1 X2) X2 → False) → (∀X1 X2, (X2 = (k3_tarski X1) → False) → (r2_hidden (esk14_2 X1 X2) X2 → False) → (r2_hidden (esk15_2 X1 X2) X1 → False) → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk11_2 X1 X2) 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) → (∀X1 X2, (r2_hidden (esk22_2 X1 X2) X1 → False) → r2_hidden X2 (esk20_1 X1) → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → X4 = (k3_tarski X3) → r2_hidden X2 X3 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, r2_hidden X1 X3 → r2_hidden X1 X2 → r1_xboole_0 X2 X3 → False) → ((r1_tarski esk1_0 (k2_zfmisc_1 esk1_0 esk2_0) → False) → (r1_tarski esk1_0 (k2_zfmisc_1 esk3_0 esk1_0) → False) → 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, (X2 = (k1_tarski X1) → False) → ((esk4_2 X1 X2) = X1 → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r1_tarski X1 X2 → r2_hidden X3 X1 → False) → (∀X1 X2, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk24_2 X1 X2) X1 → False) → False) → (∀X2 X1, (r1_xboole_0 X1 X2 → False) → (r2_hidden (esk24_2 X1 X2) X2 → False) → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk11_2 X1 X2) X1 → False) → False) → (∀X2 X1, (r2_hidden X1 (k3_tarski X2) → False) → r2_hidden X1 (esk20_1 X2) → 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) → (∀X3 X2 X1 X4, (X1 = X4 → False) → (X1 = X3 → False) → X2 = (k2_tarski X3 X4) → r2_hidden X1 X2 → False) → (∀X2 X1, ((esk21_2 X2 X1) = X1 → False) → r2_hidden X1 (esk20_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_tarski X1 (k3_tarski X2) → False) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k2_tarski X2 X4) → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k2_tarski X4 X2) → False) → (∀X2 X1, (r1_xboole_0 X2 X1 → False) → r1_xboole_0 X1 X2 → False) → (∀X2 X1 X3, (X1 = X3 → False) → X2 = (k1_tarski X3) → r2_hidden X1 X2 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X1 = X2 → X3 = (k1_tarski X2) → False) → (∀X1, (v1_xboole_0 X1 → False) → (r1_xboole_0 (esk23_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk23_1 X1) X1 → False) → False) → (∀X1, (X1 = k1_xboole_0 → False) → (r2_hidden (esk25_1 X1) X1 → False) → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (∀X2 X1, v1_xboole_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) → False) → (∀X1 X2, v1_xboole_0 (k2_tarski X1 X2) → False) → (∀X1, v1_xboole_0 (k1_tarski X1) → False) → (v1_xboole_0 esk19_0 → False) → (esk1_0 = k1_xboole_0 → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1) → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → 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) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False