Theorem. (
t30_setfam_1)
∀esk8_3 : set → set → set → set, ∀esk4_2 : set → set → set, ∀esk5_2 : set → set → set, ∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀v1_xboole_0 : set → prop, ∀v1_subset_1 : set → set → prop, ∀esk15_1 : set → set, ∀esk6_1 : set → set, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk17_1 : set → set, ∀o_1_0_setfam_1 : set → set, ∀esk16_0 : set, ∀o_0_0_xboole_0 : set, ∀esk14_1 : set → set, ∀esk18_0 : set, ∀esk19_1 : set → set, ∀esk20_1 : set → set, ∀esk7_2 : set → set → set, ∀r1_tarski : set → set → prop, ∀esk3_3 : set → set → set → set, ∀k1_setfam_1 : set → set, ∀k1_xboole_0 : set, ∀esk11_3 : set → set → set → set, ∀esk12_3 : set → set → set → set, ∀esk13_3 : set → set → set → set, ∀esk10_4 : set → set → set → set → set, ∀esk9_4 : set → set → set → set → set, ∀k6_subset_1 : set → set → set, ∀k4_setfam_1 : set → set → set, ∀r2_hidden : set → set → prop, (∀X3 X2 X4 X1, ((k6_subset_1 (esk9_4 X2 X3 X4 X1) (esk10_4 X2 X3 X4 X1)) = X1 → False) → X4 = (k4_setfam_1 X2 X3) → r2_hidden X1 X4 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk10_4 X1 X2 X3 X4) X2 → False) → X3 = (k4_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X2 X1 X3 X4, (r2_hidden (esk9_4 X1 X2 X3 X4) X1 → False) → X3 = (k4_setfam_1 X1 X2) → r2_hidden X4 X3 → False) → (∀X1 X3 X2, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X2 → False) → r2_hidden (esk8_3 X1 X2 X3) X3 → r2_hidden (esk8_3 X1 X2 X3) X1 → False) → (∀X3 X2 X1, (X3 = (k4_setfam_1 X1 X2) → False) → ((k6_subset_1 (esk12_3 X1 X2 X3) (esk13_3 X1 X2 X3)) = (esk11_3 X1 X2 X3) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → False) → (∀X5 X4 X1 X2 X3, (X3 = (k4_setfam_1 X1 X2) → False) → (esk11_3 X1 X2 X3) = (k6_subset_1 X4 X5) → r2_hidden X5 X2 → r2_hidden X4 X1 → r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (∀X2 X3 X1, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → r2_hidden (esk8_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k6_subset_1 X1 X2) → False) → (r2_hidden (esk8_3 X1 X2 X3) X3 → False) → (r2_hidden (esk8_3 X1 X2 X3) X1 → False) → False) → (∀X2 X3 X1, (X3 = (k4_setfam_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (esk13_3 X1 X2 X3) X2 → False) → False) → (∀X1 X3 X2, (X3 = (k4_setfam_1 X1 X2) → False) → (r2_hidden (esk11_3 X1 X2 X3) X3 → False) → (r2_hidden (esk12_3 X1 X2 X3) X1 → False) → False) → (∀X3 X1 X2, (X2 = k1_xboole_0 → False) → (r2_hidden X1 X3 → False) → X3 = (k1_setfam_1 X2) → r2_hidden X1 (esk3_3 X2 X3 X1) → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → r2_hidden (esk4_2 X1 X2) X2 → r2_hidden (esk4_2 X1 X2) (esk5_2 X1 X2) → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (r2_hidden X3 X2 → False) → (r2_hidden (esk3_3 X1 X2 X3) X1 → False) → X2 = (k1_setfam_1 X1) → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → (r2_hidden (esk5_2 X1 X2) X1 → False) → r2_hidden (esk4_2 X1 X2) X2 → False) → (∀X2 X3 X1, (X1 = k1_xboole_0 → False) → (X2 = (k1_setfam_1 X1) → False) → (r2_hidden (esk4_2 X1 X2) X3 → False) → (r2_hidden (esk4_2 X1 X2) X2 → False) → r2_hidden X3 X1 → False) → (∀X4 X2 X1 X3 X5 X6, (r2_hidden X5 X6 → False) → X6 = (k4_setfam_1 X2 X4) → X5 = (k6_subset_1 X1 X3) → r2_hidden X3 X4 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → r2_hidden (esk7_2 X1 X2) X2 → 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) → (∀X3 X1 X2 X4, (X4 = k1_xboole_0 → False) → (r2_hidden X1 X3 → False) → X2 = (k1_setfam_1 X4) → r2_hidden X3 X4 → r2_hidden X1 X2 → 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) → (∀X2 X1, v1_xboole_0 X1 → v1_subset_1 X2 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → 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 = (k6_subset_1 X2 X4) → r2_hidden X1 X3 → False) → (∀X1 X3 X2, (r2_hidden X3 X2 → False) → r1_tarski X1 X2 → r2_hidden X3 X1 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → (v1_subset_1 X2 X1 → False) → v1_xboole_0 X2 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → (r2_hidden (esk7_2 X1 X2) X1 → False) → 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 X2 → False) → v1_xboole_0 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) → (∀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, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X2 X1, v1_xboole_0 X1 → r2_hidden X2 X1 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_subset_1 (esk20_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (r2_hidden (esk6_1 X1) X1 → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk15_1 X1) → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X2 X1, (X1 = k1_xboole_0 → False) → X2 = k1_xboole_0 → X1 = (k1_setfam_1 X2) → False) → (∀X2 X1, (X1 = (k1_setfam_1 X2) → False) → X2 = k1_xboole_0 → X1 = k1_xboole_0 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (r1_tarski (k1_setfam_1 (k4_setfam_1 esk1_0 esk2_0)) (k6_subset_1 (k1_setfam_1 esk1_0) (k1_setfam_1 esk2_0)) → False) → (∀X1, v1_subset_1 (esk19_1 X1) X1 → False) → (∀X1, v1_xboole_0 (k1_zfmisc_1 X1) → False) → (v1_xboole_0 esk18_0 → False) → (∀X1 X2, (m1_subset_1 (k6_subset_1 X1 X2) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (m1_subset_1 (esk14_1 X1) X1 → False) → False) → (∀X1, (m1_subset_1 (o_1_0_setfam_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k6_subset_1 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, (r1_tarski k1_xboole_0 X1 → False) → False) → (∀X1, ((k6_subset_1 k1_xboole_0 X1) = k1_xboole_0 → False) → False) → (∀X1, (v1_xboole_0 (esk17_1 X1) → False) → False) → ((v1_xboole_0 esk16_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