Theorem. (l32_interva1)
∀k2_setfam_1 : setsetset, ∀k2_xboole_0 : setsetset, ∀esk6_4 : setsetsetsetset, ∀esk7_4 : setsetsetsetset, ∀esk15_3 : setsetsetset, ∀esk14_3 : setsetsetset, ∀esk13_3 : setsetsetset, ∀m1_subset_1 : setsetprop, ∀k1_zfmisc_1 : setset, ∀esk17_1 : setset, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk19_1 : setset, ∀esk16_1 : setset, ∀o_0_0_xboole_0 : set, ∀esk18_0 : set, ∀esk1_0 : set, ∀esk20_0 : set, ∀esk21_1 : setset, ∀k1_xboole_0 : set, ∀esk22_1 : setset, ∀v1_subset_1 : setsetprop, ∀v1_xboole_0 : setprop, ∀esk5_2 : setsetset, ∀r1_tarski : setsetprop, ∀esk8_3 : setsetsetset, ∀esk9_3 : setsetsetset, ∀esk10_3 : setsetsetset, ∀esk12_4 : setsetsetsetset, ∀esk11_4 : setsetsetsetset, ∀k3_xboole_0 : setsetset, ∀k3_setfam_1 : setsetset, ∀r2_hidden : setsetprop, (∀X3 X2 X4 X1, ((k3_xboole_0 (esk11_4 X2 X3 X4 X1) (esk12_4 X2 X3 X4 X1)) = X1False)X4 = (k3_setfam_1 X2 X3)r2_hidden X1 X4False)(∀X3 X2 X4 X1, ((k2_xboole_0 (esk6_4 X2 X3 X4 X1) (esk7_4 X2 X3 X4 X1)) = X1False)X4 = (k2_setfam_1 X2 X3)r2_hidden X1 X4False)(∀X2 X1 X3 X4, (r2_hidden (esk12_4 X1 X2 X3 X4) X2False)X3 = (k3_setfam_1 X1 X2)r2_hidden X4 X3False)(∀X2 X1 X3 X4, (r2_hidden (esk11_4 X1 X2 X3 X4) X1False)X3 = (k3_setfam_1 X1 X2)r2_hidden X4 X3False)(∀X2 X1 X3 X4, (r2_hidden (esk7_4 X1 X2 X3 X4) X2False)X3 = (k2_setfam_1 X1 X2)r2_hidden X4 X3False)(∀X2 X1 X3 X4, (r2_hidden (esk6_4 X1 X2 X3 X4) X1False)X3 = (k2_setfam_1 X1 X2)r2_hidden X4 X3False)(∀X3 X2 X1, (X3 = (k2_setfam_1 X1 X2)False)((k2_xboole_0 (esk9_3 X1 X2 X3) (esk10_3 X1 X2 X3)) = (esk8_3 X1 X2 X3)False)(r2_hidden (esk8_3 X1 X2 X3) X3False)False)(∀X3 X2 X1, (X3 = (k3_setfam_1 X1 X2)False)((k3_xboole_0 (esk14_3 X1 X2 X3) (esk15_3 X1 X2 X3)) = (esk13_3 X1 X2 X3)False)(r2_hidden (esk13_3 X1 X2 X3) X3False)False)(∀X5 X4 X1 X2 X3, (X3 = (k2_setfam_1 X1 X2)False)(esk8_3 X1 X2 X3) = (k2_xboole_0 X4 X5)r2_hidden X5 X2r2_hidden X4 X1r2_hidden (esk8_3 X1 X2 X3) X3False)(∀X5 X4 X1 X2 X3, (X3 = (k3_setfam_1 X1 X2)False)(esk13_3 X1 X2 X3) = (k3_xboole_0 X4 X5)r2_hidden X5 X2r2_hidden X4 X1r2_hidden (esk13_3 X1 X2 X3) X3False)(∀X2 X3 X1, (X3 = (k2_setfam_1 X1 X2)False)(r2_hidden (esk8_3 X1 X2 X3) X3False)(r2_hidden (esk10_3 X1 X2 X3) X2False)False)(∀X1 X3 X2, (X3 = (k2_setfam_1 X1 X2)False)(r2_hidden (esk8_3 X1 X2 X3) X3False)(r2_hidden (esk9_3 X1 X2 X3) X1False)False)(∀X2 X3 X1, (X3 = (k3_setfam_1 X1 X2)False)(r2_hidden (esk13_3 X1 X2 X3) X3False)(r2_hidden (esk15_3 X1 X2 X3) X2False)False)(∀X1 X3 X2, (X3 = (k3_setfam_1 X1 X2)False)(r2_hidden (esk13_3 X1 X2 X3) X3False)(r2_hidden (esk14_3 X1 X2 X3) X1False)False)(∀X4 X2 X1 X3 X5 X6, (r2_hidden X5 X6False)X6 = (k2_setfam_1 X2 X4)X5 = (k2_xboole_0 X1 X3)r2_hidden X3 X4r2_hidden X1 X2False)(∀X4 X2 X1 X3 X5 X6, (r2_hidden X5 X6False)X6 = (k3_setfam_1 X2 X4)X5 = (k3_xboole_0 X1 X3)r2_hidden X3 X4r2_hidden X1 X2False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk5_2 X1 X2) X2False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X2 X1, v1_xboole_0 X1v1_subset_1 X2 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X1 X3 X2, (r2_hidden X3 X2False)r1_tarski X1 X2r2_hidden X3 X1False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (v1_xboole_0 X1False)(v1_subset_1 X2 X1False)v1_xboole_0 X2m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk5_2 X1 X2) X1False)False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X1 X2)False)(∀X2 X1, (v1_xboole_0 X1False)v1_xboole_0 (k2_xboole_0 X2 X1)False)(∀X2 X1, (r1_tarski X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk22_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v1_xboole_0 X1False)(v1_subset_1 (esk22_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk17_1 X1)False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(r1_tarski (k2_setfam_1 esk2_0 (k3_setfam_1 esk3_0 esk4_0)) (k3_setfam_1 (k2_setfam_1 esk2_0 esk3_0) (k2_setfam_1 esk2_0 esk4_0))False)(∀X1, v1_subset_1 (esk21_1 X1) X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk20_0False)(∀X2 X3 X1, ((k3_xboole_0 (k2_xboole_0 X1 X2) (k2_xboole_0 X1 X3)) = (k2_xboole_0 X1 (k3_xboole_0 X2 X3))False)False)(∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1)False)False)(∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1)False)False)(∀X2 X1, ((k2_setfam_1 X1 X2) = (k2_setfam_1 X2 X1)False)False)(∀X2 X1, ((k3_setfam_1 X1 X2) = (k3_setfam_1 X2 X1)False)False)(∀X1, (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 X1)False)False)((m1_subset_1 esk4_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0))False)False)((m1_subset_1 esk3_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0))False)False)((m1_subset_1 esk2_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0))False)False)(∀X1, (m1_subset_1 (esk16_1 X1) X1False)False)(∀X1, ((k3_xboole_0 X1 X1) = X1False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1False)False)(∀X1, ((k3_xboole_0 X1 k1_xboole_0) = k1_xboole_0False)False)(∀X1, (v1_xboole_0 (esk19_1 X1)False)False)((v1_xboole_0 esk18_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((v1_xboole_0 k1_xboole_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.