Theorem. (t1_partfun1)
∀esk24_2 : setsetset, ∀v1_funct_1 : setprop, ∀k9_xtuple_0 : setset, ∀k2_xboole_0 : setsetset, ∀esk21_2 : setsetset, ∀esk23_2 : setsetset, ∀esk3_3 : setsetsetset, ∀k1_funct_1 : setsetset, ∀v1_xboole_0 : setprop, ∀m1_subset_1 : setsetprop, ∀v2_relat_1 : setprop, ∀v3_relat_1 : setprop, ∀v1_zfmisc_1 : setprop, ∀v3_funct_1 : setprop, ∀esk19_0 : set, ∀esk18_0 : set, ∀esk12_0 : set, ∀esk17_0 : set, ∀esk14_0 : set, ∀o_0_0_xboole_0 : set, ∀esk11_0 : set, ∀esk13_0 : set, ∀esk15_0 : set, ∀esk10_1 : setset, ∀esk16_0 : set, ∀esk20_0 : set, ∀k1_xboole_0 : set, ∀v2_funct_1 : setprop, ∀v4_funct_1 : setprop, ∀esk2_0 : set, ∀esk1_0 : set, ∀esk8_3 : setsetsetset, ∀esk5_2 : setsetset, ∀esk4_2 : setsetset, ∀esk9_3 : setsetsetset, ∀k3_xboole_0 : setsetset, ∀esk22_2 : setsetset, ∀v1_relat_1 : setprop, ∀k1_tarski : setset, ∀esk6_2 : setsetset, ∀esk7_2 : setsetset, ∀k2_tarski : setsetset, ∀r2_hidden : setsetprop, (∀X1 X2, (X1 = X2False)v1_relat_1 X2v1_relat_1 X1r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) X2r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) X1False)(∀X1 X4 X3 X2, (r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X2 X3) (esk23_2 X2 X3)) (k1_tarski (esk21_2 X2 X3))) (k2_xboole_0 X2 X3)False)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (k2_xboole_0 X2 X3)False)(∀X1 X4 X3 X2, (r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X2 X3) (esk22_2 X2 X3)) (k1_tarski (esk21_2 X2 X3))) (k2_xboole_0 X2 X3)False)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (k2_xboole_0 X2 X3)False)(∀X2 X1, (X1 = X2False)(r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) X2False)(r2_hidden (k2_tarski (k2_tarski (esk6_2 X1 X2) (esk7_2 X1 X2)) (k1_tarski (esk6_2 X1 X2))) X1False)v1_relat_1 X2v1_relat_1 X1False)(∀X1 X2 X4 X3, (r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_xboole_0 X3 X4)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X3 X4) (esk23_2 X3 X4)) (k1_tarski (esk21_2 X3 X4))) (k2_xboole_0 X3 X4)False)v1_relat_1 X4v1_relat_1 X3v1_funct_1 X4v1_funct_1 X3r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (esk24_2 X3 X4)False)(∀X1 X2 X4 X3, (r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_xboole_0 X3 X4)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X3 X4) (esk22_2 X3 X4)) (k1_tarski (esk21_2 X3 X4))) (k2_xboole_0 X3 X4)False)v1_relat_1 X4v1_relat_1 X3v1_funct_1 X4v1_funct_1 X3r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (esk24_2 X3 X4)False)(∀X4 X2 X3 X1, (r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X2 X3) (esk23_2 X2 X3)) (k1_tarski (esk21_2 X2 X3))) (k2_xboole_0 X2 X3)False)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(∀X4 X2 X3 X1, (r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X2 X3) (esk22_2 X2 X3)) (k1_tarski (esk21_2 X2 X3))) (k2_xboole_0 X2 X3)False)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)r2_hidden (esk9_3 X1 X2 X3) X3r2_hidden (esk9_3 X1 X2 X3) X2r2_hidden (esk9_3 X1 X2 X3) X1False)(∀X3 X2 X1, (r2_hidden (k2_tarski (k2_tarski X1 (esk3_3 X3 X2 X1)) (k1_tarski X1)) X3False)X2 = (k9_xtuple_0 X3)r2_hidden X1 X2False)(∀X3 X2 X1, (X2 = (k9_xtuple_0 X1)False)r2_hidden (esk4_2 X1 X2) X2r2_hidden (k2_tarski (k2_tarski (esk4_2 X1 X2) X3) (k1_tarski (esk4_2 X1 X2))) X1False)(∀X1 X4 X3 X2, (r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(esk23_2 X2 X3) = (esk22_2 X2 X3)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (k2_xboole_0 X2 X3)False)(∀X1 X2, (v1_funct_1 (esk24_2 X1 X2)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X1 X2) (esk23_2 X1 X2)) (k1_tarski (esk21_2 X1 X2))) (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_funct_1 (esk24_2 X1 X2)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X1 X2) (esk22_2 X1 X2)) (k1_tarski (esk21_2 X1 X2))) (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_relat_1 (esk24_2 X1 X2)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X1 X2) (esk23_2 X1 X2)) (k1_tarski (esk21_2 X1 X2))) (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_relat_1 (esk24_2 X1 X2)False)(r2_hidden (k2_tarski (k2_tarski (esk21_2 X1 X2) (esk22_2 X1 X2)) (k1_tarski (esk21_2 X1 X2))) (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (X2 = (k9_xtuple_0 X1)False)(r2_hidden (esk4_2 X1 X2) X2False)(r2_hidden (k2_tarski (k2_tarski (esk4_2 X1 X2) (esk5_2 X1 X2)) (k1_tarski (esk4_2 X1 X2))) X1False)False)(∀X1 X2 X4 X3, (r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (k2_xboole_0 X3 X4)False)(esk23_2 X3 X4) = (esk22_2 X3 X4)v1_relat_1 X4v1_relat_1 X3v1_funct_1 X4v1_funct_1 X3r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) (esk24_2 X3 X4)False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk8_3 X1 X2 X3) X3r2_hidden (esk8_3 X1 X2 X3) X1False)(∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk8_3 X1 X2 X3) X3r2_hidden (esk8_3 X1 X2 X3) X2False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)(r2_hidden (esk8_3 X1 X2 X3) X3False)(r2_hidden (esk8_3 X1 X2 X3) X2False)(r2_hidden (esk8_3 X1 X2 X3) X1False)False)(∀X4 X2 X3 X1, (r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))False)(esk23_2 X2 X3) = (esk22_2 X2 X3)v1_relat_1 X3v1_relat_1 X2v1_funct_1 X3v1_funct_1 X2r2_hidden (k2_tarski (k2_tarski X1 X4) (k1_tarski X1)) (esk24_2 X2 X3)False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk9_3 X1 X2 X3) X3False)(r2_hidden (esk9_3 X1 X2 X3) X1False)False)(∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk9_3 X1 X2 X3) X3False)(r2_hidden (esk9_3 X1 X2 X3) X2False)False)(∀X3 X1 X2, (r2_hidden X1 (k9_xtuple_0 X2)False)v1_relat_1 X2v1_funct_1 X2r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X2False)(∀X1 X3 X2, (X1 = (k1_funct_1 X2 X3)False)v1_relat_1 X2v1_funct_1 X2r2_hidden (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)X4 = (k9_xtuple_0 X3)r2_hidden (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3False)(∀X3 X1 X2, (r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X2False)X3 = (k1_funct_1 X2 X1)v1_relat_1 X2v1_funct_1 X2r2_hidden X1 (k9_xtuple_0 X2)False)(∀X1, ((k1_funct_1 esk2_0 X1) = (k1_funct_1 esk1_0 X1)False)r2_hidden X1 (k3_xboole_0 (k9_xtuple_0 esk1_0) (k9_xtuple_0 esk2_0))False)(∀X2 X1, (v1_xboole_0 X1False)v1_relat_1 X1v1_funct_1 X1v2_relat_1 X1v1_xboole_0 (k1_funct_1 X1 X2)m1_subset_1 X2 (k9_xtuple_0 X1)False)(∀X1 X2, (v1_funct_1 (esk24_2 X1 X2)False)(esk23_2 X1 X2) = (esk22_2 X1 X2)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_relat_1 (esk24_2 X1 X2)False)(esk23_2 X1 X2) = (esk22_2 X1 X2)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X2 X3 X1 X4, (r2_hidden X1 X4False)X4 = (k3_xboole_0 X2 X3)r2_hidden X1 X3r2_hidden X1 X2False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)(r2_hidden X1 X3False)X2 = (k2_xboole_0 X3 X4)r2_hidden X1 X2False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k3_xboole_0 X2 X4)r2_hidden X1 X3False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)X3 = (k3_xboole_0 X4 X2)r2_hidden X1 X3False)(∀X2 X4 X1 X3, (r2_hidden X1 X3False)X3 = (k2_xboole_0 X2 X4)r2_hidden X1 X2False)(∀X2 X4 X1 X3, (r2_hidden X1 X3False)X3 = (k2_xboole_0 X4 X2)r2_hidden X1 X2False)(∀X1 X2, (v4_funct_1 (k2_tarski X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀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, (v1_xboole_0 (k1_funct_1 X1 X2)False)v1_relat_1 X1v1_funct_1 X1v3_relat_1 X1False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X2 X1, (v1_relat_1 (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X2 X1, (v1_relat_1 (k3_xboole_0 X1 X2)False)v1_relat_1 X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, (v1_zfmisc_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_zfmisc_1 (k9_xtuple_0 X1)False)(∀X2 X1, (v1_funct_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X2 X1, (v1_relat_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X1, (k2_xboole_0 esk1_0 esk2_0) = X1v1_relat_1 X1v1_funct_1 X1False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v1_xboole_0 X1False)v1_relat_1 X1v1_xboole_0 (k9_xtuple_0 X1)False)(∀X1, (v3_funct_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_xboole_0 X1False)(∀X1, (v2_funct_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_xboole_0 X1False)(∀X1, (v4_funct_1 (k1_tarski X1)False)v1_relat_1 X1v1_funct_1 X1False)(∀X1, (v1_zfmisc_1 (k9_xtuple_0 X1)False)v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v2_relat_1 X1False)v1_relat_1 X1v1_xboole_0 X1False)(∀X1, (v3_relat_1 X1False)v1_relat_1 X1v1_xboole_0 X1False)(∀X1, (v1_xboole_0 (k9_xtuple_0 X1)False)v1_xboole_0 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v4_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v1_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v1_relat_1 X1False)v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(∀X1 X2, v1_xboole_0 (k2_tarski X1 X2)False)(∀X1, v1_xboole_0 (k1_tarski X1)False)(v3_funct_1 esk19_0False)(v1_xboole_0 esk20_0False)(v1_xboole_0 esk18_0False)(v1_xboole_0 esk16_0False)(v1_xboole_0 esk12_0False)(∀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_funct_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)))False)False)(∀X1 X2, (v1_relat_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)))False)False)(∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1)False)False)(∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1)False)False)(∀X2 X1, ((k3_xboole_0 X1 X2) = (k3_xboole_0 X2 X1)False)False)(∀X1, (m1_subset_1 (esk10_1 X1) X1False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, ((k3_xboole_0 X1 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)((v4_funct_1 esk20_0False)False)((v2_relat_1 esk18_0False)False)((v2_relat_1 esk17_0False)False)((v2_relat_1 esk15_0False)False)((v2_funct_1 esk14_0False)False)((v1_xboole_0 esk13_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((v1_xboole_0 k1_xboole_0False)False)((v1_funct_1 esk19_0False)False)((v1_funct_1 esk18_0False)False)((v1_funct_1 esk17_0False)False)((v1_funct_1 esk14_0False)False)((v1_funct_1 esk11_0False)False)((v1_funct_1 esk2_0False)False)((v1_funct_1 esk1_0False)False)((v1_relat_1 esk19_0False)False)((v1_relat_1 esk18_0False)False)((v1_relat_1 esk17_0False)False)((v1_relat_1 esk15_0False)False)((v1_relat_1 esk14_0False)False)((v1_relat_1 esk12_0False)False)((v1_relat_1 esk11_0False)False)((v1_relat_1 esk2_0False)False)((v1_relat_1 esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.