Theorem. (t2_bciideal)
∀l2_bcialg_1 : setprop, ∀v3_bcialg_1 : setprop, ∀m1_subset_1 : setsetprop, ∀u1_struct_0 : setset, ∀l1_bcialg_1 : setprop, ∀k5_binop_1 : setsetsetsetset, ∀u1_bcialg_1 : setset, ∀v1_funct_2 : setsetsetprop, ∀esk16_1 : setset, ∀v5_bcialg_2 : setsetprop, ∀v7_struct_0 : setprop, ∀esk19_1 : setset, ∀l1_struct_0 : setprop, ∀esk18_1 : setset, ∀esk14_1 : setset, ∀v8_struct_0 : setprop, ∀v1_finset_1 : setprop, ∀v1_funct_1 : setprop, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk2_0 : set, ∀esk5_0 : set, ∀esk4_0 : set, ∀esk17_0 : set, ∀esk13_1 : setset, ∀o_0_0_xboole_0 : set, ∀esk12_0 : set, ∀esk11_0 : set, ∀esk10_0 : set, ∀esk9_0 : set, ∀v1_zfmisc_1 : setprop, ∀k1_xboole_0 : set, ∀np__1 : set, ∀v13_struct_0 : setsetprop, ∀l2_struct_0 : setprop, ∀esk15_1 : setset, ∀v9_struct_0 : setsetprop, ∀r1_tarski : setsetprop, ∀esk20_1 : setset, ∀v10_bcialg_1 : setsetprop, ∀v1_bcialg_2 : setsetprop, ∀v1_xboole_0 : setprop, ∀r2_hidden : setsetprop, ∀k2_zfmisc_1 : setsetset, ∀k1_zfmisc_1 : setset, ∀r1_bcialg_1 : setsetsetprop, ∀esk7_1 : setset, ∀esk8_1 : setset, ∀esk6_1 : setset, ∀v4_bcialg_1 : setprop, ∀v2_struct_0 : setprop, ∀epred1_1 : setprop, ∀v7_bcialg_1 : setprop, ∀v5_bcialg_1 : setprop, ∀esk23_1 : setset, ∀k1_bcialg_1 : setsetsetset, ∀esk22_1 : setset, ∀esk21_1 : setset, ∀k4_struct_0 : setset, (∀X1, (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1))) (esk22_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1)) (k1_bcialg_1 X1 (esk21_1 X1) (esk23_1 X1))) (k1_bcialg_1 X1 (esk23_1 X1) (esk22_1 X1))) = (k4_struct_0 X1)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1))) (esk22_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1)) (k1_bcialg_1 X1 (esk21_1 X1) (esk23_1 X1))) (k1_bcialg_1 X1 (esk23_1 X1) (esk22_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1))) (esk22_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1)) (k1_bcialg_1 X1 (esk21_1 X1) (esk23_1 X1))) (k1_bcialg_1 X1 (esk23_1 X1) (esk22_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1))) (esk22_1 X1)) = (k4_struct_0 X1)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk21_1 X1) (esk22_1 X1)) (k1_bcialg_1 X1 (esk21_1 X1) (esk23_1 X1))) (k1_bcialg_1 X1 (esk23_1 X1) (esk22_1 X1))) = (k4_struct_0 X1)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v2_struct_0 X1False)(v3_bcialg_1 X1False)(k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 (esk6_1 X1) (esk7_1 X1)) (k1_bcialg_1 X1 (esk8_1 X1) (esk7_1 X1))) (k1_bcialg_1 X1 (esk6_1 X1) (esk8_1 X1))) = (k4_struct_0 X1)l2_bcialg_1 X1False)(∀X4 X3 X2 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X2 X4)) (k1_bcialg_1 X1 X4 X3)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1epred1_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X3 X2 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X4 X3)) (k1_bcialg_1 X1 X2 X4)) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X4 X2 X3 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 (k1_bcialg_1 X1 X2 X3)) X3) = (k4_struct_0 X1)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1epred1_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X4 X1, (v2_struct_0 X1False)(r1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X2 X4)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1r1_bcialg_1 X1 X4 X3m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X4 X2 X1, (v2_struct_0 X1False)(r1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) (k1_bcialg_1 X1 X4 X3)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1r1_bcialg_1 X1 X2 X4m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X4 X1, ((k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X3) X4) = (k1_bcialg_1 X1 (k1_bcialg_1 X1 X2 X4) X3)False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X4 (u1_struct_0 X1)m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, ((k5_binop_1 (u1_struct_0 X1) (u1_bcialg_1 X1) X2 X3) = (k1_bcialg_1 X1 X2 X3)False)l1_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (m1_subset_1 (u1_bcialg_1 X1) (k1_zfmisc_1 (k2_zfmisc_1 (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1)) (u1_struct_0 X1)))False)l1_bcialg_1 X1False)(∀X3 X2 X1, (v2_struct_0 X1False)(r1_bcialg_1 X1 X2 X3False)(k1_bcialg_1 X1 X2 X3) = (k4_struct_0 X1)l2_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X3 X2 X1, ((k1_bcialg_1 X1 X2 X3) = (k4_struct_0 X1)False)(v2_struct_0 X1False)l2_bcialg_1 X1r1_bcialg_1 X1 X2 X3m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X3 X1, (m1_subset_1 (k1_bcialg_1 X1 X2 X3) (u1_struct_0 X1)False)l1_bcialg_1 X1m1_subset_1 X3 (u1_struct_0 X1)m1_subset_1 X2 (u1_struct_0 X1)False)(∀X2 X1, ((k1_bcialg_1 X1 X2 (k4_struct_0 X1)) = X2False)(v2_struct_0 X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1m1_subset_1 X2 (u1_struct_0 X1)False)(∀X1, (v1_funct_2 (u1_bcialg_1 X1) (k2_zfmisc_1 (u1_struct_0 X1) (u1_struct_0 X1)) (u1_struct_0 X1)False)l1_bcialg_1 X1False)(∀X2 X1 X3, (m1_subset_1 X1 X3False)r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk16_1 X1) (u1_struct_0 X1)False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X2 X1 X3, v1_xboole_0 X3r2_hidden X1 X2m1_subset_1 X2 (k1_zfmisc_1 X3)False)(∀X1, (v2_struct_0 X1False)(v5_bcialg_2 (k4_struct_0 X1) X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v1_bcialg_2 (esk16_1 X1) X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v1_bcialg_2 (k4_struct_0 X1) X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v10_bcialg_1 (k4_struct_0 X1) X1False)v3_bcialg_1 X1v4_bcialg_1 X1v5_bcialg_1 X1v7_bcialg_1 X1l2_bcialg_1 X1False)(∀X1, (m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (m1_subset_1 (esk22_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (m1_subset_1 (esk21_1 X1) (u1_struct_0 X1)False)v2_struct_0 X1v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk22_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (l2_bcialg_1 X1False)(m1_subset_1 (esk21_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk22_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v4_bcialg_1 X1False)(m1_subset_1 (esk21_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk23_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk22_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v3_bcialg_1 X1False)(m1_subset_1 (esk21_1 X1) (u1_struct_0 X1)False)v5_bcialg_1 X1v7_bcialg_1 X1epred1_1 X1False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk19_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk20_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(m1_subset_1 (esk18_1 X1) (k1_zfmisc_1 (u1_struct_0 X1))False)l1_struct_0 X1False)(∀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, (v7_struct_0 X1False)l2_struct_0 X1v9_struct_0 (esk15_1 X1) X1False)(∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2)False)r1_tarski X1 X2False)(∀X1, (v2_struct_0 X1False)(v3_bcialg_1 X1False)(m1_subset_1 (esk8_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v3_bcialg_1 X1False)(m1_subset_1 (esk7_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1, (v2_struct_0 X1False)(v3_bcialg_1 X1False)(m1_subset_1 (esk6_1 X1) (u1_struct_0 X1)False)l2_bcialg_1 X1False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X1, (v7_struct_0 X1False)(m1_subset_1 (esk15_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X1, v2_struct_0 X1l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (m1_subset_1 (esk14_1 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (m1_subset_1 (k4_struct_0 X1) (u1_struct_0 X1)False)l2_struct_0 X1False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 np__1False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v13_struct_0 X1 k1_xboole_0False)(∀X1, (v2_struct_0 X1False)(v13_struct_0 X1 np__1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v1_finset_1 (u1_struct_0 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (esk19_1 X1)False)(∀X1, (v7_struct_0 X1False)l1_struct_0 X1v1_zfmisc_1 (u1_struct_0 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk20_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (esk18_1 X1)False)(∀X1, (v2_struct_0 X1False)l1_struct_0 X1v1_xboole_0 (u1_struct_0 X1)False)(∀X1, (v9_struct_0 (esk14_1 X1) X1False)l2_struct_0 X1False)(∀X1, (v9_struct_0 (k4_struct_0 X1) X1False)l2_struct_0 X1False)(∀X1, (v13_struct_0 X1 k1_xboole_0False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_finset_1 (u1_struct_0 X1)False)l1_struct_0 X1v8_struct_0 X1False)(∀X1, (v1_zfmisc_1 (u1_struct_0 X1)False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v1_xboole_0 (u1_struct_0 X1)False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v2_struct_0 X1False)(v1_zfmisc_1 (esk18_1 X1)False)l1_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)l1_struct_0 X1v7_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v8_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v7_struct_0 X1False)v2_struct_0 X1l1_struct_0 X1False)(∀X1, (v1_funct_1 (u1_bcialg_1 X1)False)l1_bcialg_1 X1False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (v2_struct_0 X1False)(epred1_1 X1False)l2_bcialg_1 X1False)(∀X1, (l2_struct_0 X1False)l2_bcialg_1 X1False)(∀X1, (l1_bcialg_1 X1False)l2_bcialg_1 X1False)(∀X1, (l1_struct_0 X1False)l2_struct_0 X1False)(∀X1, (l1_struct_0 X1False)l1_bcialg_1 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(r1_bcialg_1 esk1_0 (k1_bcialg_1 esk1_0 (k1_bcialg_1 esk1_0 esk2_0 (k1_bcialg_1 esk1_0 esk3_0 esk4_0)) (k1_bcialg_1 esk1_0 esk2_0 (k1_bcialg_1 esk1_0 esk3_0 esk5_0))) (k1_bcialg_1 esk1_0 esk4_0 esk5_0)False)(v1_xboole_0 np__1False)(v2_struct_0 esk17_0False)(v2_struct_0 esk1_0False)(∀X1, (m1_subset_1 (esk13_1 X1) X1False)False)((m1_subset_1 esk5_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk4_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk3_0 (u1_struct_0 esk1_0)False)False)((m1_subset_1 esk2_0 (u1_struct_0 esk1_0)False)False)(∀X1, (r1_tarski X1 X1False)False)((v1_xboole_0 o_0_0_xboole_0False)False)((l2_struct_0 esk17_0False)False)((l2_struct_0 esk12_0False)False)((l1_bcialg_1 esk9_0False)False)((v7_struct_0 esk17_0False)False)((l1_struct_0 esk10_0False)False)((l2_bcialg_1 esk11_0False)False)((l2_bcialg_1 esk1_0False)False)((v7_bcialg_1 esk1_0False)False)((v5_bcialg_1 esk1_0False)False)((v4_bcialg_1 esk1_0False)False)((v3_bcialg_1 esk1_0False)False)((o_0_0_xboole_0 = k1_xboole_0False)False)False
Proof:
The rest of the proof is missing.