Theorem. (l13_projred1)
∀r2_zfmisc_1 : setsetsetsetprop, ∀esk7_0 : set, ∀esk1_0 : set, ∀esk23_3 : setsetsetset, ∀esk34_1 : setset, ∀esk35_1 : setset, ∀esk30_1 : setset, ∀esk33_1 : setset, ∀esk29_1 : setset, ∀esk28_1 : setset, ∀esk27_1 : setset, ∀esk26_1 : setset, ∀esk12_1 : setset, ∀esk10_1 : setset, ∀esk9_1 : setset, ∀r2_hidden : setsetprop, ∀esk31_1 : setset, ∀v1_funct_1 : setprop, ∀v3_funct_1 : setprop, ∀v1_zfmisc_1 : setprop, ∀esk20_0 : set, ∀esk2_0 : set, ∀esk5_0 : set, ∀esk4_0 : set, ∀esk3_0 : set, ∀esk6_0 : set, ∀esk19_0 : set, ∀esk16_0 : set, ∀esk18_0 : set, ∀esk17_1 : setset, ∀esk8_0 : set, ∀esk21_0 : set, ∀k1_xboole_0 : set, ∀v2_funct_1 : setprop, ∀v4_funct_1 : setprop, ∀v1_relat_1 : setprop, ∀v1_xboole_0 : setprop, ∀esk11_1 : setset, ∀esk32_1 : setset, ∀esk15_1 : setset, ∀esk14_1 : setset, ∀esk13_3 : setsetsetset, ∀esk22_3 : setsetsetset, ∀v6_incsp_1 : setprop, ∀v2_incproj : setprop, ∀l1_incsp_1 : setprop, ∀v3_incproj : setprop, ∀v1_incproj : setprop, ∀esk24_4 : setsetsetsetset, ∀r1_incsp_1 : setsetsetprop, ∀esk25_10 : setsetsetsetsetsetsetsetsetsetset, ∀epred1_1 : setprop, ∀u2_incsp_1 : setset, ∀m1_subset_1 : setsetprop, ∀u1_incsp_1 : setset, ∀v4_incproj : setprop, (∀X1 X6 X10 X3 X5 X4 X2 X11 X9 X7 X8, (X7 = X8False)(r1_incsp_1 X1 X6 X10False)(r1_incsp_1 X1 X6 X9False)(r1_incsp_1 X1 (esk25_10 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10) X9False)v4_incproj X1epred1_1 X1r1_incsp_1 X1 X6 X8r1_incsp_1 X1 X6 X7r1_incsp_1 X1 X5 X10r1_incsp_1 X1 X5 X8r1_incsp_1 X1 X4 X9r1_incsp_1 X1 X4 X8r1_incsp_1 X1 X3 X10r1_incsp_1 X1 X3 X7r1_incsp_1 X1 X2 X9r1_incsp_1 X1 X2 X7m1_subset_1 X11 (u1_incsp_1 X1)m1_subset_1 X10 (u2_incsp_1 X1)m1_subset_1 X9 (u2_incsp_1 X1)m1_subset_1 X8 (u2_incsp_1 X1)m1_subset_1 X7 (u2_incsp_1 X1)m1_subset_1 X6 (u1_incsp_1 X1)m1_subset_1 X5 (u1_incsp_1 X1)m1_subset_1 X4 (u1_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X1 X6 X10 X3 X5 X4 X2 X11 X9 X7 X8, (X7 = X8False)(r1_incsp_1 X1 X6 X10False)(r1_incsp_1 X1 X6 X9False)(r1_incsp_1 X1 (esk25_10 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10) X10False)v4_incproj X1epred1_1 X1r1_incsp_1 X1 X6 X8r1_incsp_1 X1 X6 X7r1_incsp_1 X1 X5 X10r1_incsp_1 X1 X5 X8r1_incsp_1 X1 X4 X9r1_incsp_1 X1 X4 X8r1_incsp_1 X1 X3 X10r1_incsp_1 X1 X3 X7r1_incsp_1 X1 X2 X9r1_incsp_1 X1 X2 X7m1_subset_1 X11 (u1_incsp_1 X1)m1_subset_1 X10 (u2_incsp_1 X1)m1_subset_1 X9 (u2_incsp_1 X1)m1_subset_1 X8 (u2_incsp_1 X1)m1_subset_1 X7 (u2_incsp_1 X1)m1_subset_1 X6 (u1_incsp_1 X1)m1_subset_1 X5 (u1_incsp_1 X1)m1_subset_1 X4 (u1_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X1 X6 X10 X2 X4 X5 X3 X11 X9 X7 X8, (X7 = X8False)(r1_incsp_1 X1 X6 X10False)(r1_incsp_1 X1 X6 X9False)(m1_subset_1 (esk25_10 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10) (u1_incsp_1 X1)False)v4_incproj X1epred1_1 X1r1_incsp_1 X1 X6 X8r1_incsp_1 X1 X6 X7r1_incsp_1 X1 X5 X10r1_incsp_1 X1 X5 X8r1_incsp_1 X1 X4 X9r1_incsp_1 X1 X4 X8r1_incsp_1 X1 X3 X10r1_incsp_1 X1 X3 X7r1_incsp_1 X1 X2 X9r1_incsp_1 X1 X2 X7m1_subset_1 X11 (u1_incsp_1 X1)m1_subset_1 X10 (u2_incsp_1 X1)m1_subset_1 X9 (u2_incsp_1 X1)m1_subset_1 X8 (u2_incsp_1 X1)m1_subset_1 X7 (u2_incsp_1 X1)m1_subset_1 X6 (u1_incsp_1 X1)m1_subset_1 X5 (u1_incsp_1 X1)m1_subset_1 X4 (u1_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X3 X1 X2 X4, r2_zfmisc_1 X1 X2 X3 X4m1_subset_1 X4 (u1_incsp_1 esk1_0)m1_subset_1 X3 (u1_incsp_1 esk1_0)m1_subset_1 X2 (u1_incsp_1 esk1_0)m1_subset_1 X1 (u1_incsp_1 esk1_0)r1_incsp_1 esk1_0 X4 esk7_0r1_incsp_1 esk1_0 X3 esk7_0r1_incsp_1 esk1_0 X2 esk7_0r1_incsp_1 esk1_0 X1 esk7_0False)(∀X2 X3 X4 X1, (r1_incsp_1 X1 (esk24_4 X1 X2 X3 X4) X4False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X4 (u2_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X2 X3 X4 X1, (m1_subset_1 (esk24_4 X1 X2 X3 X4) (u1_incsp_1 X1)False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X4 (u2_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X2 X3 X4 X1, (esk24_4 X1 X2 X3 X4) = X2v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X4 (u2_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X2 X3 X4 X1, (esk24_4 X1 X2 X3 X4) = X3v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X4 (u2_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X3 X2 X1 X4 X5, (X4 = X5False)(X2 = X3False)v1_incproj X1l1_incsp_1 X1r1_incsp_1 X1 X3 X5r1_incsp_1 X1 X3 X4r1_incsp_1 X1 X2 X5r1_incsp_1 X1 X2 X4m1_subset_1 X5 (u2_incsp_1 X1)m1_subset_1 X4 (u2_incsp_1 X1)m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X3 X4 X1 X2, X1 = X2r2_zfmisc_1 X1 X2 X3 X4False)(∀X3 X4 X1 X2, X1 = X2r2_zfmisc_1 X1 X3 X2 X4False)(∀X3 X4 X1 X2, X1 = X2r2_zfmisc_1 X1 X3 X4 X2False)(∀X4 X3 X1 X2, X1 = X2r2_zfmisc_1 X3 X1 X2 X4False)(∀X4 X3 X1 X2, X1 = X2r2_zfmisc_1 X3 X1 X4 X2False)(∀X4 X3 X1 X2, X1 = X2r2_zfmisc_1 X3 X4 X1 X2False)(∀X1 X2 X3, (X2 = X3False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)r1_incsp_1 X1 (esk23_3 X1 X2 X3) X2False)(∀X1 X2 X3, (X2 = X3False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)r1_incsp_1 X1 (esk22_3 X1 X2 X3) X3False)(∀X1 X2 X3, (X2 = X3False)(r1_incsp_1 X1 (esk23_3 X1 X2 X3) X3False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)False)(∀X1 X2 X3, (X2 = X3False)(r1_incsp_1 X1 (esk22_3 X1 X2 X3) X2False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)False)(∀X2 X1 X3 X4, (X3 = X4False)(X2 = X4False)(X2 = X3False)(X1 = X4False)(X1 = X3False)(X1 = X2False)(r2_zfmisc_1 X1 X2 X3 X4False)False)(∀X3 X2 X1, (r1_incsp_1 X1 X2 (esk13_3 X1 X2 X3)False)v6_incsp_1 X1l1_incsp_1 X1m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X3 X2 X1, (r1_incsp_1 X1 X2 (esk13_3 X1 X3 X2)False)v6_incsp_1 X1l1_incsp_1 X1m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X1 X2 X3, (X2 = X3False)(m1_subset_1 (esk23_3 X1 X2 X3) (u1_incsp_1 X1)False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)False)(∀X1 X2 X3, (X2 = X3False)(m1_subset_1 (esk22_3 X1 X2 X3) (u1_incsp_1 X1)False)v6_incsp_1 X1v1_incproj X1v2_incproj X1v3_incproj X1v4_incproj X1l1_incsp_1 X1m1_subset_1 X3 (u2_incsp_1 X1)m1_subset_1 X2 (u2_incsp_1 X1)False)(∀X1 X2, (v6_incsp_1 X2False)l1_incsp_1 X2m1_subset_1 X1 (u2_incsp_1 X2)r1_incsp_1 X2 (esk14_1 X2) X1r1_incsp_1 X2 (esk15_1 X2) X1False)(∀X1 X2, (v4_incproj X2False)epred1_1 X2m1_subset_1 X1 (u1_incsp_1 X2)r1_incsp_1 X2 X1 (esk34_1 X2)r1_incsp_1 X2 X1 (esk35_1 X2)False)(∀X3 X2 X1, (m1_subset_1 (esk13_3 X1 X2 X3) (u2_incsp_1 X1)False)v6_incsp_1 X1l1_incsp_1 X1m1_subset_1 X3 (u1_incsp_1 X1)m1_subset_1 X2 (u1_incsp_1 X1)False)(∀X1, (v4_incproj X1False)epred1_1 X1r1_incsp_1 X1 (esk30_1 X1) (esk35_1 X1)False)(∀X1, (v4_incproj X1False)epred1_1 X1r1_incsp_1 X1 (esk30_1 X1) (esk34_1 X1)False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk30_1 X1) (esk33_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk30_1 X1) (esk32_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk29_1 X1) (esk35_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk29_1 X1) (esk33_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk28_1 X1) (esk34_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk28_1 X1) (esk33_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk27_1 X1) (esk35_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk27_1 X1) (esk32_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk26_1 X1) (esk34_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(r1_incsp_1 X1 (esk26_1 X1) (esk32_1 X1)False)epred1_1 X1False)(∀X1, (v1_incproj X1False)(r1_incsp_1 X1 (esk10_1 X1) (esk12_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(r1_incsp_1 X1 (esk10_1 X1) (esk11_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(r1_incsp_1 X1 (esk9_1 X1) (esk12_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(r1_incsp_1 X1 (esk9_1 X1) (esk11_1 X1)False)l1_incsp_1 X1False)(∀X2 X1, r2_hidden X2 X1r2_hidden X1 X2False)(∀X1 X2, (v1_xboole_0 X2False)(r2_hidden X1 X2False)m1_subset_1 X1 X2False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk35_1 X1) (u2_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk34_1 X1) (u2_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk33_1 X1) (u2_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk32_1 X1) (u2_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk31_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk30_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk29_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk28_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk27_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v4_incproj X1False)(m1_subset_1 (esk26_1 X1) (u1_incsp_1 X1)False)epred1_1 X1False)(∀X1, (v1_incproj X1False)(m1_subset_1 (esk12_1 X1) (u2_incsp_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(m1_subset_1 (esk11_1 X1) (u2_incsp_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(m1_subset_1 (esk10_1 X1) (u1_incsp_1 X1)False)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(m1_subset_1 (esk9_1 X1) (u1_incsp_1 X1)False)l1_incsp_1 X1False)(∀X1, (v6_incsp_1 X1False)(m1_subset_1 (esk15_1 X1) (u1_incsp_1 X1)False)l1_incsp_1 X1False)(∀X1, (v6_incsp_1 X1False)(m1_subset_1 (esk14_1 X1) (u1_incsp_1 X1)False)l1_incsp_1 X1False)(∀X2 X1, (m1_subset_1 X1 X2False)r2_hidden X1 X2False)(∀X2 X1, (v1_relat_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X2 X1, (v1_funct_1 X1False)v4_funct_1 X2m1_subset_1 X1 X2False)(∀X1 X2, v1_xboole_0 X2r2_hidden X1 X2False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_funct_1 X1v1_relat_1 X1v1_zfmisc_1 X1False)(∀X1, (v3_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v2_funct_1 X1False)v1_xboole_0 X1v1_funct_1 X1v1_relat_1 X1False)(∀X1, (v4_incproj X1False)(esk33_1 X1) = (esk32_1 X1)epred1_1 X1False)(∀X1, (v1_incproj X1False)(esk12_1 X1) = (esk11_1 X1)l1_incsp_1 X1False)(∀X1, (v1_incproj X1False)(esk10_1 X1) = (esk9_1 X1)l1_incsp_1 X1False)(∀X1, l1_incsp_1 X1v1_xboole_0 (u2_incsp_1 X1)False)(∀X1, l1_incsp_1 X1v1_xboole_0 (u1_incsp_1 X1)False)(∀X2 X1, (X1 = X2False)v1_xboole_0 X2v1_xboole_0 X1False)(∀X1, (epred1_1 X1False)l1_incsp_1 X1False)(∀X1, (v4_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (v1_funct_1 X1False)v1_xboole_0 X1False)(∀X1, (X1 = k1_xboole_0False)v1_xboole_0 X1False)(v3_funct_1 esk20_0False)(v1_xboole_0 esk21_0False)((r2_zfmisc_1 esk2_0 esk3_0 esk4_0 esk5_0False)False)((r1_incsp_1 esk1_0 esk8_0 esk7_0False)False)((r1_incsp_1 esk1_0 esk8_0 esk6_0False)False)((r1_incsp_1 esk1_0 esk5_0 esk6_0False)False)((r1_incsp_1 esk1_0 esk4_0 esk6_0False)False)((r1_incsp_1 esk1_0 esk3_0 esk6_0False)False)((r1_incsp_1 esk1_0 esk2_0 esk6_0False)False)(∀X1, (m1_subset_1 (esk17_1 X1) X1False)False)((m1_subset_1 esk8_0 (u1_incsp_1 esk1_0)False)False)((m1_subset_1 esk7_0 (u2_incsp_1 esk1_0)False)False)((m1_subset_1 esk6_0 (u2_incsp_1 esk1_0)False)False)((m1_subset_1 esk5_0 (u1_incsp_1 esk1_0)False)False)((m1_subset_1 esk4_0 (u1_incsp_1 esk1_0)False)False)((m1_subset_1 esk3_0 (u1_incsp_1 esk1_0)False)False)((m1_subset_1 esk2_0 (u1_incsp_1 esk1_0)False)False)((v4_funct_1 esk21_0False)False)((v2_funct_1 esk19_0False)False)((v1_relat_1 esk20_0False)False)((v1_relat_1 esk19_0False)False)((v1_relat_1 esk18_0False)False)((v1_funct_1 esk20_0False)False)((v1_funct_1 esk19_0False)False)((v1_funct_1 esk18_0False)False)((l1_incsp_1 esk16_0False)False)((l1_incsp_1 esk1_0False)False)((v4_incproj esk1_0False)False)((v3_incproj esk1_0False)False)((v2_incproj esk1_0False)False)((v1_incproj esk1_0False)False)((v6_incsp_1 esk1_0False)False)False
Proof:
The rest of the proof is missing.