Theorem. (t5_yellow12)
∀k10_xtuple_0 : setset, ∀v1_xboole_0 : setprop, ∀v1_funct_2 : setsetsetprop, ∀k7_relat_1 : setsetset, ∀v1_funct_1 : setprop, ∀v4_relat_1 : setsetprop, ∀esk11_4 : setsetsetsetset, ∀esk12_3 : setsetsetset, ∀esk13_3 : setsetsetset, ∀k1_binop_1 : setsetsetset, ∀esk17_1 : setset, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk21_1 : setset, ∀esk16_2 : setsetset, ∀esk19_1 : setset, ∀esk18_0 : set, ∀o_0_0_xboole_0 : set, ∀esk14_1 : setset, ∀esk15_2 : setsetset, ∀esk20_0 : set, ∀k1_xboole_0 : set, ∀esk22_1 : setset, ∀v1_subset_1 : setsetprop, ∀esk10_2 : setsetset, ∀r1_tarski : setsetprop, ∀k1_funct_1 : setsetset, ∀v5_relat_1 : setsetprop, ∀v1_partfun1 : setsetprop, ∀esk7_3 : setsetsetset, ∀esk9_3 : setsetsetset, ∀esk8_3 : setsetsetset, ∀r2_hidden : setsetprop, ∀k2_tarski : setsetset, ∀esk6_4 : setsetsetsetset, ∀esk5_4 : setsetsetsetset, ∀k1_tarski : setset, ∀k1_zfmisc_1 : setset, ∀k13_funct_3 : setsetset, ∀k9_funct_3 : setsetset, ∀k10_funct_3 : setsetset, ∀m1_subset_1 : setsetprop, ∀v1_relat_1 : setprop, ∀k9_xtuple_0 : setset, (∀X4 X2 X3 X1, (v1_relat_1 (k9_xtuple_0 X1)False)m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))) X4) (k9_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))) X4))))False)(∀X2 X4 X3 X1, (v1_relat_1 (k10_xtuple_0 X1)False)m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X3 X4) (k9_funct_3 X3 X4)))) (k9_funct_3 X2 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X3 X4) (k9_funct_3 X3 X4)))))))False)(∀X3 X2 X4 X1, ((k2_tarski (k2_tarski (esk5_4 X2 X3 X4 X1) (esk6_4 X2 X3 X4 X1)) (k1_tarski (esk5_4 X2 X3 X4 X1))) = X1False)X4 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3)))r2_hidden X1 X4False)(∀X2 X3 X1 X4, (v1_xboole_0 X4False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_funct_1 X3v1_funct_2 X3 X1 X2v1_xboole_0 (k7_relat_1 X3 X4)m1_subset_1 X4 (k1_zfmisc_1 X1)m1_subset_1 X3 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))))False)(∀X3 X2 X1, (X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))False)((k2_tarski (k2_tarski (esk8_3 X1 X2 X3) (esk9_3 X1 X2 X3)) (k1_tarski (esk8_3 X1 X2 X3))) = (esk7_3 X1 X2 X3)False)(r2_hidden (esk7_3 X1 X2 X3) X3False)False)(∀X2 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)v1_xboole_0 X1v1_funct_1 X1v1_funct_2 X1 X2 X3m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))))False)(∀X3 X2 X1, (v1_partfun1 X2 X1False)v1_xboole_0 X1v1_funct_2 X2 X1 X3m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X3) (k9_funct_3 X1 X3))))False)(∀X3 X2 X1, (v1_xboole_0 X1False)(v1_partfun1 X2 X3False)v1_funct_2 X2 X3 X1m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X3 X1) (k9_funct_3 X3 X1))))False)(∀X2 X1, (v1_partfun1 X1 X2False)v1_funct_2 X1 X2 X2m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X2) (k9_funct_3 X2 X2))))False)(∀X3 X1 X2, (v1_funct_2 X1 X2 X3False)v1_partfun1 X1 X2m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))))False)(∀X3 X1 X2, (v5_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X3 X2) (k9_funct_3 X3 X2))))False)(∀X3 X1 X2, (v4_relat_1 X1 X2False)m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X3) (k9_funct_3 X1 X3))))False)(∀X1 X3 X2, (v1_xboole_0 X2False)v1_xboole_0 X1m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X3 X1) (k9_funct_3 X3 X1))))False)(∀X3 X2 X1, (v1_relat_1 X1False)m1_subset_1 X1 (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X3) (k9_funct_3 X2 X3))))False)(∀X2 X1 X3 X4, (r2_hidden (esk6_4 X1 X2 X3 X4) X2False)X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))r2_hidden X4 X3False)(∀X2 X1 X3 X4, (r2_hidden (esk5_4 X1 X2 X3 X4) X1False)X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))r2_hidden X4 X3False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X4) (k9_funct_3 X2 X4)))False)(∀X3 X4 X1 X2, (r2_hidden X1 X2False)r2_hidden (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X4 X2) (k9_funct_3 X4 X2)))False)(∀X2 X3 X4 X1, (r2_hidden (esk11_4 X1 X2 X3 X4) (k9_xtuple_0 X1)False)X3 = (k7_relat_1 X1 X2)v1_relat_1 X1v1_funct_1 X1r2_hidden X4 X3False)(∀X3 X4 X1 X2, ((k1_funct_1 X2 (esk11_4 X2 X3 X4 X1)) = X1False)X4 = (k7_relat_1 X2 X3)v1_relat_1 X2v1_funct_1 X2r2_hidden X1 X4False)(∀X2 X3 X4 X1, (r2_hidden (esk11_4 X1 X2 X3 X4) X2False)X3 = (k7_relat_1 X1 X2)v1_relat_1 X1v1_funct_1 X1r2_hidden X4 X3False)(∀X5 X4 X1 X2 X3, (X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))False)(esk7_3 X1 X2 X3) = (k2_tarski (k2_tarski X4 X5) (k1_tarski X4))r2_hidden X5 X2r2_hidden X4 X1r2_hidden (esk7_3 X1 X2 X3) X3False)(∀X1 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_xboole_0 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))False)(∀X4 X3 X2 X1, (r2_hidden (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X4) (k9_funct_3 X2 X4)))False)r2_hidden X3 X4r2_hidden X1 X2False)(∀X4 X1 X2 X3, (X3 = (k7_relat_1 X1 X2)False)(esk12_3 X1 X2 X3) = (k1_funct_1 X1 X4)v1_relat_1 X1v1_funct_1 X1r2_hidden X4 X2r2_hidden X4 (k9_xtuple_0 X1)r2_hidden (esk12_3 X1 X2 X3) X3False)(∀X2 X3 X1, (X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))False)(r2_hidden (esk7_3 X1 X2 X3) X3False)(r2_hidden (esk9_3 X1 X2 X3) X2False)False)(∀X1 X3 X2, (X3 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2)))False)(r2_hidden (esk7_3 X1 X2 X3) X3False)(r2_hidden (esk8_3 X1 X2 X3) X1False)False)(∀X1 X3 X2 X4 X5 X6, (r2_hidden X5 X6False)X5 = (k2_tarski (k2_tarski X1 X3) (k1_tarski X1))X6 = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X4) (k9_funct_3 X2 X4)))r2_hidden X3 X4r2_hidden X1 X2False)(∀X3 X2 X1, (X3 = (k7_relat_1 X1 X2)False)((k1_funct_1 X1 (esk13_3 X1 X2 X3)) = (esk12_3 X1 X2 X3)False)(r2_hidden (esk12_3 X1 X2 X3) X3False)v1_relat_1 X1v1_funct_1 X1False)(∀X3 X2 X1, (X3 = (k7_relat_1 X1 X2)False)(r2_hidden (esk12_3 X1 X2 X3) X3False)(r2_hidden (esk13_3 X1 X2 X3) (k9_xtuple_0 X1)False)v1_relat_1 X1v1_funct_1 X1False)(∀X4 X3 X2 X1, ((k1_binop_1 (k13_funct_3 (k10_funct_3 X2 X4) (k9_funct_3 X2 X4)) X1 X3) = (k2_tarski (k2_tarski X3 X1) (k1_tarski X3))False)r2_hidden X3 X4r2_hidden X1 X2False)(∀X2 X3 X1, (X3 = (k7_relat_1 X1 X2)False)(r2_hidden (esk12_3 X1 X2 X3) X3False)(r2_hidden (esk13_3 X1 X2 X3) X2False)v1_relat_1 X1v1_funct_1 X1False)(∀X3 X2 X1, ((k1_funct_1 X1 (k2_tarski (k2_tarski X2 X3) (k1_tarski X2))) = (k1_binop_1 X1 X2 X3)False)v1_relat_1 X1v1_funct_1 X1False)(∀X3 X2 X1 X4 X5, (r2_hidden X4 X5False)X5 = (k7_relat_1 X2 X3)X4 = (k1_funct_1 X2 X1)v1_relat_1 X2v1_funct_1 X2r2_hidden X1 X3r2_hidden X1 (k9_xtuple_0 X2)False)(∀X1 X2, (v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_relat_1 X1v1_xboole_0 (k7_relat_1 X1 X2)m1_subset_1 X2 (k1_zfmisc_1 (k9_xtuple_0 X1))False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk10_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)(∀X1 X2, (v1_funct_1 (k13_funct_3 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_relat_1 (k13_funct_3 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 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 (esk10_2 X1 X2) X1False)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 (k7_relat_1 (k13_funct_3 (k10_funct_3 esk1_0 esk2_0) (k9_funct_3 esk1_0 esk2_0)) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 esk3_0 esk4_0) (k9_funct_3 esk3_0 esk4_0)))) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 esk4_0 esk3_0) (k9_funct_3 esk4_0 esk3_0)))False)(∀X1 X2, v1_xboole_0 (k2_tarski X1 X2)False)(∀X1, v1_subset_1 (esk21_1 X1) X1False)(∀X1, v1_xboole_0 (k1_tarski X1)False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk20_0False)(∀X1 X2, (m1_subset_1 (k9_funct_3 X1 X2) (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X1) (k9_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X1))))False)False)(∀X2 X1, (m1_subset_1 (k10_funct_3 X1 X2) (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X2) (k9_funct_3 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X2))))False)False)(∀X2 X1, (m1_subset_1 (esk16_2 X1 X2) (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))))False)False)(∀X2 X1, (m1_subset_1 (esk15_2 X1 X2) (k1_zfmisc_1 (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))))False)False)(∀X1 X2, (v1_funct_2 (k9_funct_3 X1 X2) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X1False)False)(∀X2 X1, (v1_funct_2 (k10_funct_3 X1 X2) (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) X2False)False)(∀X2 X1, ((k10_xtuple_0 (k13_funct_3 (k10_funct_3 X1 X2) (k9_funct_3 X1 X2))) = (k9_xtuple_0 (k13_funct_3 (k10_funct_3 X2 X1) (k9_funct_3 X2 X1)))False)False)(∀X2 X1, (v1_funct_2 (esk15_2 X1 X2) X1 X2False)False)(∀X2 X1, (v5_relat_1 (esk16_2 X1 X2) X2False)False)(∀X2 X1, (v5_relat_1 (esk15_2 X1 X2) X2False)False)(∀X1 X2, (v4_relat_1 (esk16_2 X1 X2) X1False)False)(∀X1 X2, (v4_relat_1 (esk15_2 X1 X2) X1False)False)(∀X1 X2, (v1_funct_1 (esk15_2 X1 X2)False)False)(∀X1 X2, (v1_funct_1 (k9_funct_3 X1 X2)False)False)(∀X1 X2, (v1_funct_1 (k9_funct_3 X1 X2)False)False)(∀X1 X2, (v1_funct_1 (k10_funct_3 X1 X2)False)False)(∀X1 X2, (v1_funct_1 (k10_funct_3 X1 X2)False)False)(∀X1 X2, (v1_xboole_0 (esk16_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk16_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (esk15_2 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (k9_funct_3 X1 X2)False)False)(∀X1 X2, (v1_relat_1 (k10_funct_3 X1 X2)False)False)(∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski 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)(∀X1, (m1_subset_1 (esk14_1 X1) X1False)False)(∀X1, (r1_tarski X1 X1False)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.