Theorem. (t1_algspec1)
∀r2_hidden : setsetprop, ∀k3_xboole_0 : setsetset, ∀esk6_3 : setsetsetset, ∀v1_xboole_0 : setprop, ∀m1_subset_1 : setsetprop, ∀v2_relat_1 : setprop, ∀k1_zfmisc_1 : setset, ∀v4_funct_1 : setprop, ∀k5_numbers : set, ∀v2_finseq_1 : setprop, ∀v3_funct_1 : setprop, ∀v1_finset_1 : setprop, ∀esk1_0 : set, ∀esk2_0 : set, ∀esk3_0 : set, ∀esk11_0 : set, ∀esk21_0 : set, ∀esk18_0 : set, ∀esk14_0 : set, ∀esk7_1 : setset, ∀esk16_0 : set, ∀esk12_0 : set, ∀o_0_0_xboole_0 : set, ∀k4_ordinal1 : set, ∀esk8_0 : set, ∀esk10_0 : set, ∀esk13_0 : set, ∀esk15_0 : set, ∀k1_numbers : set, ∀esk23_1 : setset, ∀esk9_0 : set, ∀esk17_0 : set, ∀esk19_0 : set, ∀esk22_0 : set, ∀esk20_0 : set, ∀k1_xboole_0 : set, ∀v2_funct_1 : setprop, ∀v1_finseq_1 : setprop, ∀v1_zfmisc_1 : setprop, ∀v3_finseq_1 : setprop, ∀r1_tarski : setsetprop, ∀v3_relat_1 : setprop, ∀v4_relat_1 : setsetprop, ∀esk24_2 : setsetset, ∀esk5_3 : setsetsetset, ∀k9_xtuple_0 : setset, ∀k2_xboole_0 : setsetset, ∀v1_relat_1 : setprop, ∀v1_funct_1 : setprop, ∀esk4_3 : setsetsetset, ∀k1_funct_1 : setsetset, ∀k1_funct_4 : setsetset, (∀X2 X1 X3, (X1 = (k1_funct_4 X2 X3)False)(k9_xtuple_0 X1) = (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))(k1_funct_1 X1 (esk4_3 X2 X3 X1)) = (k1_funct_1 X3 (esk4_3 X2 X3 X1))(k1_funct_1 X1 (esk4_3 X2 X3 X1)) = (k1_funct_1 X2 (esk4_3 X2 X3 X1))v1_relat_1 X3v1_relat_1 X2v1_relat_1 X1v1_funct_1 X3v1_funct_1 X2v1_funct_1 X1False)(∀X2 X1 X3, (X3 = (k1_funct_4 X1 X2)False)(k9_xtuple_0 X3) = (k2_xboole_0 (k9_xtuple_0 X1) (k9_xtuple_0 X2))(k1_funct_1 X2 (esk4_3 X1 X2 X3)) = (k1_funct_1 X3 (esk4_3 X1 X2 X3))v1_relat_1 X3v1_relat_1 X2v1_relat_1 X1v1_funct_1 X3v1_funct_1 X2v1_funct_1 X1r2_hidden (esk4_3 X1 X2 X3) (k9_xtuple_0 X2)False)(∀X2 X1 X3, (X1 = (k1_funct_4 X2 X3)False)(r2_hidden (esk4_3 X2 X3 X1) (k9_xtuple_0 X3)False)(k9_xtuple_0 X1) = (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))(k1_funct_1 X1 (esk4_3 X2 X3 X1)) = (k1_funct_1 X2 (esk4_3 X2 X3 X1))v1_relat_1 X3v1_relat_1 X2v1_relat_1 X1v1_funct_1 X3v1_funct_1 X2v1_funct_1 X1False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)r2_hidden (esk6_3 X1 X2 X3) X3r2_hidden (esk6_3 X1 X2 X3) X2r2_hidden (esk6_3 X1 X2 X3) X1False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk5_3 X1 X2 X3) X3r2_hidden (esk5_3 X1 X2 X3) X1False)(∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2)False)r2_hidden (esk5_3 X1 X2 X3) X3r2_hidden (esk5_3 X1 X2 X3) X2False)(∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2)False)(r2_hidden (esk5_3 X1 X2 X3) X3False)(r2_hidden (esk5_3 X1 X2 X3) X2False)(r2_hidden (esk5_3 X1 X2 X3) X1False)False)(∀X2 X1 X3, (X3 = (k1_funct_4 X1 X2)False)(r2_hidden (esk4_3 X1 X2 X3) (k2_xboole_0 (k9_xtuple_0 X1) (k9_xtuple_0 X2))False)(k9_xtuple_0 X3) = (k2_xboole_0 (k9_xtuple_0 X1) (k9_xtuple_0 X2))v1_relat_1 X3v1_relat_1 X2v1_relat_1 X1v1_funct_1 X3v1_funct_1 X2v1_funct_1 X1False)(∀X1 X3 X2, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk6_3 X1 X2 X3) X3False)(r2_hidden (esk6_3 X1 X2 X3) X1False)False)(∀X2 X3 X1, (X3 = (k3_xboole_0 X1 X2)False)(r2_hidden (esk6_3 X1 X2 X3) X3False)(r2_hidden (esk6_3 X1 X2 X3) X2False)False)(∀X4 X2 X1 X3, ((k1_funct_1 X2 X1) = (k1_funct_1 X3 X1)False)X3 = (k1_funct_4 X4 X2)v1_relat_1 X4v1_relat_1 X3v1_relat_1 X2v1_funct_1 X4v1_funct_1 X3v1_funct_1 X2r2_hidden X1 (k9_xtuple_0 X2)r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X4) (k9_xtuple_0 X2))False)(∀X2 X3 X1 X4, ((k1_funct_1 X3 X1) = (k1_funct_1 X4 X1)False)(r2_hidden X1 (k9_xtuple_0 X2)False)X3 = (k1_funct_4 X4 X2)v1_relat_1 X4v1_relat_1 X3v1_relat_1 X2v1_funct_1 X4v1_funct_1 X3v1_funct_1 X2r2_hidden X1 (k2_xboole_0 (k9_xtuple_0 X4) (k9_xtuple_0 X2))False)(∀X1 X2, (X1 = X2False)(k9_xtuple_0 X1) = (k9_xtuple_0 X2)(k1_funct_1 X1 (esk24_2 X1 X2)) = (k1_funct_1 X2 (esk24_2 X1 X2))v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X3 X2, ((k1_funct_1 (k1_funct_4 X2 X1) X3) = (k1_funct_1 X1 X3)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1r2_hidden X3 (k9_xtuple_0 X1)False)(∀X1 X3 X2, (v4_relat_1 (k1_funct_4 X1 X2) X3False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v4_relat_1 X2 X3v4_relat_1 X1 X3False)(∀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)(∀X3 X2 X1, (v1_funct_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v4_relat_1 X2 X3v4_relat_1 X1 X3False)(∀X3 X2 X1, (v1_relat_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v4_relat_1 X2 X3v4_relat_1 X1 X3False)(∀X3 X1 X2, ((k1_funct_1 (k1_funct_4 X2 X1) X3) = (k1_funct_1 X2 X3)False)(r2_hidden X3 (k9_xtuple_0 X1)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2 X3, (v4_relat_1 (k2_xboole_0 X1 X3) X2False)v1_relat_1 X3v1_relat_1 X1v4_relat_1 X3 X2v4_relat_1 X1 X2False)(∀X2 X1 X3, ((k9_xtuple_0 X1) = (k2_xboole_0 (k9_xtuple_0 X2) (k9_xtuple_0 X3))False)X1 = (k1_funct_4 X2 X3)v1_relat_1 X3v1_relat_1 X2v1_relat_1 X1v1_funct_1 X3v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (X1 = X2False)(r2_hidden (esk24_2 X1 X2) (k9_xtuple_0 X1)False)(k9_xtuple_0 X1) = (k9_xtuple_0 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)(∀X1 X2, ((k1_funct_4 (k1_funct_4 X1 X2) X2) = (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X2 X1, (v1_xboole_0 X1False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v1_xboole_0 (k1_funct_4 X1 X2)False)(∀X1 X2, (v1_xboole_0 X2False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v1_xboole_0 (k1_funct_4 X1 X2)False)(∀X1 X2 X3, (v4_relat_1 (k3_xboole_0 X1 X3) X2False)v1_relat_1 X3v1_relat_1 X1v4_relat_1 X1 X2False)(∀X1 X3 X2, (v4_relat_1 X3 X2False)v1_relat_1 X1v4_relat_1 X1 X2m1_subset_1 X3 (k1_zfmisc_1 X1)False)(∀X3 X2 X1 X4, (r2_hidden X1 X4False)(r2_hidden X1 X3False)X2 = (k2_xboole_0 X3 X4)r2_hidden X1 X2False)(∀X1 X2, (v2_relat_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v2_relat_1 X2v2_relat_1 X1False)(∀X1 X2, (v1_funct_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v2_relat_1 X2v2_relat_1 X1False)(∀X1 X2, (v1_relat_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v2_relat_1 X2v2_relat_1 X1False)(∀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 X1False)(v1_funct_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X2 X1, (v1_xboole_0 X1False)(v1_relat_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_xboole_0 X2False)(v1_funct_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_xboole_0 X2False)(v1_relat_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀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 = (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, (v1_funct_1 (k1_funct_4 X1 X2)False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀X1 X2, (v1_relat_1 (k1_funct_4 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)(∀X1 X2, (v1_funct_1 X2False)v1_relat_1 X1v1_funct_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, ((k1_funct_4 X1 X2) = X1False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v1_xboole_0 X2False)(∀X1 X2, ((k1_funct_4 X2 X1) = X1False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1v1_xboole_0 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)(∀X2 X1, (v1_relat_1 (k2_xboole_0 X1 X2)False)v1_relat_1 X2v1_relat_1 X1False)(∀X1 X2, (v4_funct_1 X2False)v4_funct_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v3_finseq_1 X2False)v3_finseq_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X1 X2, (v1_relat_1 X2False)v1_relat_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀X2 X1, ((k1_funct_4 X1 X1) = X1False)v1_relat_1 X2v1_relat_1 X1v1_funct_1 X2v1_funct_1 X1False)(∀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, (v1_xboole_0 X1False)v1_relat_1 X1v1_xboole_0 X2v4_relat_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)(∀X1, (v4_relat_1 X1 k5_numbersFalse)v1_relat_1 X1v1_funct_1 X1v2_finseq_1 X1False)(∀X1, (v4_relat_1 X1 k5_numbersFalse)v1_relat_1 X1v1_funct_1 X1v1_finseq_1 X1False)(∀X1 X2, (v1_finseq_1 X2False)v3_finseq_1 X1m1_subset_1 X2 X1False)(∀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 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, (v2_finseq_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_finseq_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_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, (v1_finset_1 X1False)v1_relat_1 X1v1_funct_1 X1v1_finseq_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_finseq_1 X1False)v1_relat_1 X1v1_xboole_0 X1False)(∀X1, (v1_finseq_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, (v4_funct_1 X1False)v3_finseq_1 X1False)(∀X1, (v3_finseq_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)((k1_funct_4 (k1_funct_4 esk2_0 esk1_0) esk3_0) = (k1_funct_4 (k1_funct_4 esk1_0 esk2_0) esk3_0)False)(v3_funct_1 esk20_0False)(v3_relat_1 esk11_0False)(v1_xboole_0 esk22_0False)(v1_xboole_0 esk21_0False)(v1_xboole_0 esk19_0False)(v1_xboole_0 esk18_0False)(v1_xboole_0 esk17_0False)(v1_xboole_0 esk14_0False)(v1_xboole_0 esk9_0False)((r1_tarski (k3_xboole_0 (k9_xtuple_0 esk1_0) (k9_xtuple_0 esk2_0)) (k9_xtuple_0 esk3_0)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, (v4_relat_1 (esk23_1 X1) X1False)False)(∀X1, (m1_subset_1 (esk7_1 X1) X1False)False)((m1_subset_1 k5_numbers (k1_zfmisc_1 k1_numbers)False)False)(∀X1, ((k2_xboole_0 X1 X1) = X1False)False)(∀X1, ((k3_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)((v4_relat_1 esk19_0 k5_numbersFalse)False)((v4_relat_1 esk17_0 k5_numbersFalse)False)(∀X1, (v2_relat_1 (esk23_1 X1)False)False)(∀X1, (v1_funct_1 (esk23_1 X1)False)False)(∀X1, (v1_relat_1 (esk23_1 X1)False)False)((v4_funct_1 esk21_0False)False)((v2_finseq_1 esk19_0False)False)((v2_finseq_1 esk17_0False)False)((v2_finseq_1 esk15_0False)False)((v2_relat_1 esk19_0False)False)((v2_relat_1 esk18_0False)False)((v2_relat_1 esk16_0False)False)((v2_relat_1 esk13_0False)False)((v2_funct_1 esk12_0False)False)((v1_finset_1 esk19_0False)False)((v1_finset_1 esk17_0False)False)((v1_xboole_0 esk10_0False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((v1_xboole_0 k1_xboole_0False)False)((v1_finseq_1 esk19_0False)False)((v1_finseq_1 esk17_0False)False)((v3_finseq_1 esk22_0False)False)((v1_funct_1 esk20_0False)False)((v1_funct_1 esk19_0False)False)((v1_funct_1 esk18_0False)False)((v1_funct_1 esk17_0False)False)((v1_funct_1 esk16_0False)False)((v1_funct_1 esk15_0False)False)((v1_funct_1 esk12_0False)False)((v1_funct_1 esk11_0False)False)((v1_funct_1 esk8_0False)False)((v1_funct_1 esk3_0False)False)((v1_funct_1 esk2_0False)False)((v1_funct_1 esk1_0False)False)((v1_relat_1 esk20_0False)False)((v1_relat_1 esk19_0False)False)((v1_relat_1 esk18_0False)False)((v1_relat_1 esk17_0False)False)((v1_relat_1 esk16_0False)False)((v1_relat_1 esk15_0False)False)((v1_relat_1 esk13_0False)False)((v1_relat_1 esk12_0False)False)((v1_relat_1 esk11_0False)False)((v1_relat_1 esk9_0False)False)((v1_relat_1 esk8_0False)False)((v1_relat_1 esk3_0False)False)((v1_relat_1 esk2_0False)False)((v1_relat_1 esk1_0False)False)((k5_numbers = k4_ordinal1False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.