Theorem. (t33_setfam_1)
∀k4_xboole_0 : setsetset, ∀esk10_3 : setsetsetset, ∀esk4_2 : setsetset, ∀esk5_2 : setsetset, ∀k3_tarski : setset, ∀esk8_2 : setsetset, ∀esk9_2 : setsetset, ∀k5_setfam_1 : setsetset, ∀r1_tarski : setsetprop, ∀esk6_2 : setsetset, ∀v1_xboole_0 : setprop, ∀v1_subset_1 : setsetprop, ∀esk13_1 : setset, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk16_0 : set, ∀o_0_0_xboole_0 : set, ∀esk14_0 : set, ∀esk12_1 : setset, ∀esk15_1 : setset, ∀esk17_1 : setset, ∀esk18_1 : setset, ∀k6_setfam_1 : setsetset, ∀esk7_3 : setsetsetset, ∀k7_subset_1 : setsetsetset, ∀esk3_3 : setsetsetset, ∀k1_setfam_1 : setset, ∀k1_xboole_0 : set, ∀k1_zfmisc_1 : setset, ∀m1_subset_1 : setsetprop, ∀esk11_3 : setsetsetset, ∀r2_hidden : setsetprop, ∀k3_subset_1 : setsetset, ∀k7_setfam_1 : setsetset, (∀X2 X3 X1, (X3 = (k7_setfam_1 X1 X2)False)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1))m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))r2_hidden (esk11_3 X1 X2 X3) X3r2_hidden (k3_subset_1 X1 (esk11_3 X1 X2 X3)) X2False)(∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk10_3 X1 X2 X3) X2False)r2_hidden (esk10_3 X1 X2 X3) X3r2_hidden (esk10_3 X1 X2 X3) X1False)(∀X3 X1 X2, (X3 = (k7_setfam_1 X1 X2)False)(r2_hidden (esk11_3 X1 X2 X3) X3False)(r2_hidden (k3_subset_1 X1 (esk11_3 X1 X2 X3)) X2False)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1))m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X2 X3 X1, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk10_3 X1 X2 X3) X3False)r2_hidden (esk10_3 X1 X2 X3) X2False)(∀X1 X3 X2, (X3 = (k4_xboole_0 X1 X2)False)(r2_hidden (esk10_3 X1 X2 X3) X3False)(r2_hidden (esk10_3 X1 X2 X3) X1False)False)(∀X3 X1 X2, (X3 = (k7_setfam_1 X1 X2)False)(m1_subset_1 (esk11_3 X1 X2 X3) (k1_zfmisc_1 X1)False)m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1))m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X3 X1 X2 X4, (r2_hidden X2 X4False)X4 = (k7_setfam_1 X1 X3)m1_subset_1 X2 (k1_zfmisc_1 X1)r2_hidden (k3_subset_1 X1 X2) X3m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X1))m1_subset_1 X3 (k1_zfmisc_1 (k1_zfmisc_1 X1))False)(∀X2 X1 X3 X4, (r2_hidden (k3_subset_1 X3 X1) X4False)X2 = (k7_setfam_1 X3 X4)r2_hidden X1 X2m1_subset_1 X1 (k1_zfmisc_1 X3)m1_subset_1 X4 (k1_zfmisc_1 (k1_zfmisc_1 X3))m1_subset_1 X2 (k1_zfmisc_1 (k1_zfmisc_1 X3))False)(∀X3 X1 X2, (X2 = k1_xboole_0False)(r2_hidden X1 X3False)X3 = (k1_setfam_1 X2)r2_hidden X1 (esk3_3 X2 X3 X1)False)(∀X2 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)r2_hidden (esk4_2 X1 X2) X2r2_hidden (esk4_2 X1 X2) (esk5_2 X1 X2)False)(∀X3 X2 X1, (m1_subset_1 (k7_subset_1 X2 X1 X3) (k1_zfmisc_1 X2)False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X3 X2 X1, (X2 = (k3_tarski X1)False)r2_hidden X3 X1r2_hidden (esk8_2 X1 X2) X3r2_hidden (esk8_2 X1 X2) X2False)(∀X1 X2 X3, (r2_hidden (esk7_3 X1 X2 X3) X1False)X2 = (k3_tarski X1)r2_hidden X3 X2False)(∀X2 X3 X1, (r2_hidden X1 (esk7_3 X2 X3 X1)False)X3 = (k3_tarski X2)r2_hidden X1 X3False)(∀X2 X3 X1, (X1 = k1_xboole_0False)(r2_hidden X3 X2False)(r2_hidden (esk3_3 X1 X2 X3) X1False)X2 = (k1_setfam_1 X1)False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk8_2 X1 X2) X2False)(r2_hidden (esk8_2 X1 X2) (esk9_2 X1 X2)False)False)(∀X2 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)(r2_hidden (esk5_2 X1 X2) X1False)r2_hidden (esk4_2 X1 X2) X2False)(∀X2 X3 X1, (X1 = k1_xboole_0False)(X2 = (k1_setfam_1 X1)False)(r2_hidden (esk4_2 X1 X2) X3False)(r2_hidden (esk4_2 X1 X2) X2False)r2_hidden X3 X1False)(∀X2 X1, (m1_subset_1 (k7_setfam_1 X2 X1) (k1_zfmisc_1 (k1_zfmisc_1 X2))False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X3 X2 X1, ((k7_subset_1 X2 X1 X3) = (k4_xboole_0 X1 X3)False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, (m1_subset_1 (k6_setfam_1 X2 X1) (k1_zfmisc_1 X2)False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X2 X1, (m1_subset_1 (k5_setfam_1 X2 X1) (k1_zfmisc_1 X2)False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X2 X1, ((k7_setfam_1 X2 (k7_setfam_1 X2 X1)) = X1False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X1 X2, (X2 = (k3_tarski X1)False)(r2_hidden (esk8_2 X1 X2) X2False)(r2_hidden (esk9_2 X1 X2) X1False)False)(∀X2 X1, (m1_subset_1 (k3_subset_1 X2 X1) (k1_zfmisc_1 X2)False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk6_2 X1 X2) X2False)(∀X2 X1, (X1 = k1_xboole_0False)(k7_setfam_1 X2 X1) = k1_xboole_0m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)(r2_hidden X1 X3False)X4 = (k4_xboole_0 X2 X3)r2_hidden X1 X2False)(∀X2 X1, ((k3_subset_1 X2 (k3_subset_1 X2 X1)) = X1False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X3 X1 X2 X4, (X4 = k1_xboole_0False)(r2_hidden X1 X3False)X2 = (k1_setfam_1 X4)r2_hidden X3 X4r2_hidden X1 X2False)(∀X2 X1, ((k6_setfam_1 X2 X1) = (k1_setfam_1 X1)False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X2 X1, ((k5_setfam_1 X2 X1) = (k3_tarski X1)False)m1_subset_1 X1 (k1_zfmisc_1 (k1_zfmisc_1 X2))False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X4 X3 X2 X1, X3 = (k4_xboole_0 X4 X2)r2_hidden X1 X3r2_hidden X1 X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)X4 = (k3_tarski X3)r2_hidden X2 X3r2_hidden X1 X2False)(∀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)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k4_xboole_0 X2 X4)r2_hidden X1 X3False)(∀X2 X1, ((k3_subset_1 X2 X1) = (k4_xboole_0 X2 X1)False)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X1 X3 X2, (r2_hidden X3 X2False)r2_hidden X3 X1r1_tarski X1 X2False)(∀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 (esk6_2 X1 X2) X1False)False)(∀X2 X1, (X1 = X2False)r1_tarski X2 X1r1_tarski X1 X2False)(∀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 (esk18_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (v1_xboole_0 X1False)(m1_subset_1 (esk13_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 (esk18_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk13_1 X1)False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X2 X1, (r1_tarski X1 X2False)X1 = X2False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X2 X1, (X1 = k1_xboole_0False)X2 = k1_xboole_0X1 = (k1_setfam_1 X2)False)(∀X2 X1, (X1 = (k1_setfam_1 X2)False)X2 = k1_xboole_0X1 = k1_xboole_0False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)((k7_subset_1 esk1_0 esk1_0 (k5_setfam_1 esk1_0 esk2_0)) = (k6_setfam_1 esk1_0 (k7_setfam_1 esk1_0 esk2_0))False)(∀X1, v1_subset_1 (esk17_1 X1) X1False)(∀X1, v1_subset_1 X1 X1False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk16_0False)(esk2_0 = k1_xboole_0False)(∀X1, (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1)False)False)((m1_subset_1 esk2_0 (k1_zfmisc_1 (k1_zfmisc_1 esk1_0))False)False)(∀X1, (m1_subset_1 (esk12_1 X1) X1False)False)(∀X1, (m1_subset_1 X1 (k1_zfmisc_1 X1)False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, ((k4_xboole_0 X1 k1_xboole_0) = X1False)False)(∀X1, ((k4_xboole_0 k1_xboole_0 X1) = k1_xboole_0False)False)(∀X1, (v1_xboole_0 (esk15_1 X1)False)False)((v1_xboole_0 esk14_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.