Theorem. (t24_domain_1)
∀v2_xtuple_0 : setprop, ∀k2_xtuple_0 : setset, ∀k1_xtuple_0 : setset, ∀k2_mcart_1 : setsetsetsetset, ∀v1_xtuple_0 : setprop, ∀r1_tarski : setsetprop, ∀esk7_2 : setsetset, ∀esk21_1 : setset, ∀v3_relat_1 : setprop, ∀esk18_0 : set, ∀esk17_1 : setset, ∀esk15_0 : set, ∀esk14_0 : set, ∀o_0_0_xboole_0 : set, ∀esk19_0 : set, ∀esk16_0 : set, ∀esk8_1 : setset, ∀esk12_0 : set, ∀esk20_1 : setset, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk6_0 : set, ∀esk5_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀v2_relat_1 : setprop, ∀esk13_1 : setset, ∀v1_relat_1 : setprop, ∀v1_subset_1 : setsetprop, ∀k1_xboole_0 : set, ∀esk22_2 : setsetset, ∀k1_mcart_1 : setsetsetsetset, ∀k3_mcart_1 : setsetsetsetset, ∀k2_tarski : setsetset, ∀k1_tarski : setset, ∀k3_zfmisc_1 : setsetsetset, ∀k9_mcart_1 : setsetsetsetsetsetset, ∀v1_xboole_0 : setprop, ∀a_6_0_domain_1 : setsetsetsetsetsetset, ∀r2_hidden : setsetprop, ∀m1_subset_1 : setsetprop, ∀k1_zfmisc_1 : setset, ∀k4_domain_1 : setsetsetsetsetsetset, ∀esk9_7 : setsetsetsetsetsetsetset, ∀esk10_7 : setsetsetsetsetsetsetset, ∀esk11_7 : setsetsetsetsetsetsetset, (∀X3 X7 X5 X1 X6 X2 X4, ((k4_domain_1 X2 X3 X4 (esk9_7 X1 X2 X3 X4 X5 X6 X7) (esk10_7 X1 X2 X3 X4 X5 X6 X7) (esk11_7 X1 X2 X3 X4 X5 X6 X7)) = X1False)(v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(r2_hidden (esk11_7 X1 X2 X3 X4 X5 X6 X7) X7False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(r2_hidden (esk10_7 X1 X2 X3 X4 X5 X6 X7) X6False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(r2_hidden (esk9_7 X1 X2 X3 X4 X5 X6 X7) X5False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(m1_subset_1 (esk11_7 X1 X2 X3 X4 X5 X6 X7) X4False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(m1_subset_1 (esk10_7 X1 X2 X3 X4 X5 X6 X7) X3False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X3 X7 X5 X1 X6 X2 X4, (v1_xboole_0 X4False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(m1_subset_1 (esk9_7 X1 X2 X3 X4 X5 X6 X7) X2False)m1_subset_1 X7 (k1_zfmisc_1 X4)m1_subset_1 X6 (k1_zfmisc_1 X3)m1_subset_1 X5 (k1_zfmisc_1 X2)r2_hidden X1 (a_6_0_domain_1 X2 X3 X4 X5 X6 X7)False)(∀X4 X7 X10 X9 X8 X1 X3 X5 X2 X6, (v1_xboole_0 X6False)(v1_xboole_0 X4False)(v1_xboole_0 X2False)(r2_hidden X7 (a_6_0_domain_1 X2 X4 X6 X8 X9 X10)False)X7 = (k4_domain_1 X2 X4 X6 X1 X3 X5)m1_subset_1 X5 X6m1_subset_1 X3 X4m1_subset_1 X1 X2r2_hidden X5 X10r2_hidden X3 X9r2_hidden X1 X8m1_subset_1 X10 (k1_zfmisc_1 X6)m1_subset_1 X9 (k1_zfmisc_1 X4)m1_subset_1 X8 (k1_zfmisc_1 X2)False)(∀X1 X2 X3 X4 X5 X6, (m1_subset_1 (k9_mcart_1 X2 X4 X6 X1 X3 X5) (k1_zfmisc_1 (k3_zfmisc_1 X2 X4 X6))False)m1_subset_1 X5 (k1_zfmisc_1 X6)m1_subset_1 X3 (k1_zfmisc_1 X4)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X2 X6 X5 X4 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k4_domain_1 X1 X2 X3 X4 X5 X6) (k3_zfmisc_1 X1 X2 X3)False)m1_subset_1 X6 X3m1_subset_1 X5 X2m1_subset_1 X4 X1False)(∀X2 X6 X5 X4 X1 X3, ((k4_domain_1 X1 X2 X3 X4 X5 X6) = (k2_tarski (k2_tarski (k2_tarski (k2_tarski X4 X5) (k1_tarski X4)) X6) (k1_tarski (k2_tarski (k2_tarski X4 X5) (k1_tarski X4))))False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X6 X3m1_subset_1 X5 X2m1_subset_1 X4 X1False)(∀X1 X2 X3 X4 X5 X6, ((k9_mcart_1 X2 X4 X6 X1 X3 X5) = (k3_zfmisc_1 X1 X3 X5)False)m1_subset_1 X5 (k1_zfmisc_1 X6)m1_subset_1 X3 (k1_zfmisc_1 X4)m1_subset_1 X1 (k1_zfmisc_1 X2)False)(∀X3 X4 X5 X6 X1 X2, (r2_hidden X1 X2False)r2_hidden (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X4) (k1_tarski (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)))) (k3_zfmisc_1 X2 X5 X6)False)(∀X3 X4 X5 X6 X1 X2, (r2_hidden X1 X2False)r2_hidden (k2_tarski (k2_tarski (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)) X4) (k1_tarski (k2_tarski (k2_tarski X3 X1) (k1_tarski X3)))) (k3_zfmisc_1 X5 X2 X6)False)(∀X3 X4 X5 X6 X1 X2, (r2_hidden X1 X2False)r2_hidden (k2_tarski (k2_tarski (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)) X1) (k1_tarski (k2_tarski (k2_tarski X3 X4) (k1_tarski X3)))) (k3_zfmisc_1 X5 X6 X2)False)(∀X1, ((k2_tarski (k2_tarski (k2_tarski (k2_tarski (k1_xtuple_0 (k1_xtuple_0 X1)) (k2_xtuple_0 (k1_xtuple_0 X1))) (k1_tarski (k1_xtuple_0 (k1_xtuple_0 X1)))) (k2_xtuple_0 X1)) (k1_tarski (k2_tarski (k2_tarski (k1_xtuple_0 (k1_xtuple_0 X1)) (k2_xtuple_0 (k1_xtuple_0 X1))) (k1_tarski (k1_xtuple_0 (k1_xtuple_0 X1)))))) = X1False)v2_xtuple_0 X1False)(∀X6 X3 X1 X4 X2 X5 X7, (v1_xboole_0 X7False)(v1_xboole_0 X6False)(v1_xboole_0 X5False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(r2_hidden (k3_mcart_1 X1 X2 X3 X4) X5False)m1_subset_1 X7 (k1_zfmisc_1 X2)m1_subset_1 X6 (k1_zfmisc_1 X1)m1_subset_1 X5 (k1_zfmisc_1 X3)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)r2_hidden X4 (k3_zfmisc_1 X6 X7 X5)False)(∀X6 X3 X1 X4 X2 X5 X7, (v1_xboole_0 X7False)(v1_xboole_0 X6False)(v1_xboole_0 X5False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(r2_hidden (k2_mcart_1 X1 X2 X3 X4) X5False)m1_subset_1 X7 (k1_zfmisc_1 X3)m1_subset_1 X6 (k1_zfmisc_1 X1)m1_subset_1 X5 (k1_zfmisc_1 X2)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)r2_hidden X4 (k3_zfmisc_1 X6 X5 X7)False)(∀X6 X3 X1 X4 X2 X5 X7, (v1_xboole_0 X7False)(v1_xboole_0 X6False)(v1_xboole_0 X5False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(r2_hidden (k1_mcart_1 X1 X2 X3 X4) X5False)m1_subset_1 X7 (k1_zfmisc_1 X3)m1_subset_1 X6 (k1_zfmisc_1 X2)m1_subset_1 X5 (k1_zfmisc_1 X1)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)r2_hidden X4 (k3_zfmisc_1 X5 X6 X7)False)(∀X1 X2 X3 X4 X5 X6, (r2_hidden (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)) X5) (k1_tarski (k2_tarski (k2_tarski X1 X3) (k1_tarski X1)))) (k3_zfmisc_1 X2 X4 X6)False)r2_hidden X5 X6r2_hidden X3 X4r2_hidden X1 X2False)(∀X2 X4 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k3_mcart_1 X1 X2 X3 X4) X3False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k2_mcart_1 X1 X2 X3 X4) X2False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(m1_subset_1 (k1_mcart_1 X1 X2 X3 X4) X1False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, ((k2_mcart_1 X1 X2 X3 X4) = (k2_xtuple_0 (k1_xtuple_0 X4))False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, ((k1_mcart_1 X1 X2 X3 X4) = (k1_xtuple_0 (k1_xtuple_0 X4))False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, ((k3_mcart_1 X1 X2 X3 X4) = (k2_xtuple_0 X4)False)(v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X4 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)(v2_xtuple_0 X4False)m1_subset_1 X4 (k3_zfmisc_1 X1 X2 X3)False)(∀X2 X1 X3, (v1_xboole_0 X3False)(v1_xboole_0 X2False)(v1_xboole_0 X1False)v1_xboole_0 (k3_zfmisc_1 X1 X2 X3)False)(∀X1 X3 X2, r2_hidden X3 X2r2_hidden X1 X2r2_hidden X1 (esk22_2 X3 X2)False)(∀X1, ((k2_tarski (k2_tarski (k1_xtuple_0 X1) (k2_xtuple_0 X1)) (k1_tarski (k1_xtuple_0 X1))) = X1False)v1_xtuple_0 X1False)(∀X2 X1 X3, (X3 = k1_xboole_0False)(X2 = k1_xboole_0False)(X1 = k1_xboole_0False)(k3_zfmisc_1 X1 X2 X3) = k1_xboole_0False)(∀X2 X1, (r1_tarski X1 X2False)r2_hidden (esk7_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, (r2_hidden (esk22_2 X1 X2) X2False)r2_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)(∀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)(∀X3 X2 X1, ((k3_zfmisc_1 X1 X2 X3) = k1_xboole_0False)X1 = k1_xboole_0False)(∀X3 X2 X1, ((k3_zfmisc_1 X2 X1 X3) = k1_xboole_0False)X1 = k1_xboole_0False)(∀X3 X2 X1, ((k3_zfmisc_1 X2 X3 X1) = k1_xboole_0False)X1 = k1_xboole_0False)(∀X1 X2, (r1_tarski X1 X2False)(r2_hidden (esk7_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_relat_1 X2False)v1_relat_1 X1m1_subset_1 X2 (k1_zfmisc_1 X1)False)(∀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 (esk21_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 (esk21_1 X1) X1False)False)(∀X1, (v1_xboole_0 X1False)v1_xboole_0 (esk13_1 X1)False)(∀X1, (v2_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀X1, (v3_relat_1 X1False)v1_xboole_0 X1v1_relat_1 X1False)(∀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)(∀X1, (v1_xtuple_0 X1False)v2_xtuple_0 X1False)(∀X1, (v1_relat_1 X1False)v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)((a_6_0_domain_1 esk1_0 esk2_0 esk3_0 esk4_0 esk5_0 esk6_0) = (k9_mcart_1 esk1_0 esk2_0 esk3_0 esk4_0 esk5_0 esk6_0)False)(∀X1 X2, v1_xboole_0 (k2_tarski X1 X2)False)(∀X1, v1_subset_1 (esk20_1 X1) X1False)(∀X1, v1_xboole_0 (k1_tarski X1)False)(∀X1, v1_xboole_0 (k1_zfmisc_1 X1)False)(v1_xboole_0 esk18_0False)(v1_xboole_0 esk12_0False)(v1_xboole_0 esk3_0False)(v1_xboole_0 esk2_0False)(v1_xboole_0 esk1_0False)(∀X2 X3 X1, ((k2_xtuple_0 (k1_xtuple_0 (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3) (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)))))) = X2False)False)(∀X1 X3 X2, ((k1_xtuple_0 (k1_xtuple_0 (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3) (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)))))) = X1False)False)(∀X3 X1 X2, ((k2_xtuple_0 (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3) (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))))) = X3False)False)(∀X3 X2 X1, (v2_xtuple_0 (k2_tarski (k2_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)) X3) (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))))False)False)(∀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_relat_1 (k1_tarski (k2_tarski (k2_tarski X1 X2) (k1_tarski X1)))False)False)(∀X2 X1, ((k2_xtuple_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) = X2False)False)(∀X1 X2, ((k1_xtuple_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))) = X1False)False)(∀X2 X1, (v1_xtuple_0 (k2_tarski (k2_tarski X1 X2) (k1_tarski X1))False)False)(∀X2 X1, ((k2_tarski X1 X2) = (k2_tarski X2 X1)False)False)(∀X1, (m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk17_1 X1) (k1_zfmisc_1 X1)False)False)(∀X1, (m1_subset_1 (esk8_1 X1) X1False)False)((m1_subset_1 esk6_0 (k1_zfmisc_1 esk3_0)False)False)((m1_subset_1 esk5_0 (k1_zfmisc_1 esk2_0)False)False)((m1_subset_1 esk4_0 (k1_zfmisc_1 esk1_0)False)False)(∀X1, (r1_tarski X1 X1False)False)(∀X1, (v1_xboole_0 (esk17_1 X1)False)False)((v2_relat_1 esk16_0False)False)((v1_xtuple_0 esk15_0False)False)((v1_relat_1 esk16_0False)False)((v1_relat_1 esk12_0False)False)((v2_xtuple_0 esk19_0False)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.