Theorem. (
t22_substlat)
∀esk10_5 : set → set → set → set → set → set, ∀esk9_5 : set → set → set → set → set → set, ∀a_4_0_substlat : set → set → set → set → set, ∀r1_tarski : set → set → prop, ∀esk6_3 : set → set → set → set, ∀v1_xboole_0 : set → prop, ∀k1_finsub_1 : set → set → set → set, ∀esk27_2 : set → set → set, ∀k1_zfmisc_1 : set → set, ∀v5_finset_1 : set → prop, ∀v4_funct_1 : set → prop, ∀v1_zfmisc_1 : set → prop, ∀esk21_1 : set → set, ∀v2_funct_1 : set → prop, ∀v1_finsub_1 : set → prop, ∀v3_finsub_1 : set → prop, ∀k1_xboole_0 : set, ∀esk20_0 : set, ∀esk23_0 : set, ∀esk19_0 : set, ∀esk12_0 : set, ∀esk13_0 : set, ∀o_0_0_xboole_0 : set, ∀esk14_0 : set, ∀esk16_0 : set, ∀esk8_1 : set → set, ∀esk17_2 : set → set → set, ∀esk18_0 : set, ∀esk22_0 : set, ∀esk24_0 : set, ∀esk1_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk5_0 : set, ∀esk2_0 : set, ∀v2_finset_1 : set → prop, ∀v3_funct_1 : set → prop, ∀esk15_1 : set → set, ∀v1_funct_1 : set → prop, ∀v1_relat_1 : set → prop, ∀v4_finsub_1 : set → prop, ∀v1_finset_1 : set → prop, ∀esk7_2 : set → set → set, ∀esk11_4 : set → set → set → set → set, ∀r1_partfun1 : set → set → prop, ∀m1_subset_1 : set → set → prop, ∀k5_finsub_1 : set → set, ∀k4_partfun1 : set → set → set, ∀k4_substlat : set → set → set → set → set, ∀r2_hidden : set → set → prop, ∀k2_xboole_0 : set → set → set, ∀esk25_5 : set → set → set → set → set → set, ∀esk26_5 : set → set → set → set → set → set, (∀X4 X1 X3 X2 X5, ((k2_xboole_0 (esk25_5 X2 X3 X4 X5 X1) (esk26_5 X2 X3 X4 X5 X1)) = X1 → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (k4_substlat X2 X3 X4 X5) → False) → (∀X4 X1 X3 X2 X5, ((k2_xboole_0 (esk9_5 X1 X2 X3 X4 X5) (esk10_5 X1 X2 X3 X4 X5)) = X1 → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X4 X1 X3 X2 X5, (r1_partfun1 (esk9_5 X1 X2 X3 X4 X5) (esk10_5 X1 X2 X3 X4 X5) → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X4 X1 X3 X2 X5, (m1_subset_1 (esk10_5 X1 X2 X3 X4 X5) (k4_partfun1 X2 X3) → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X4 X1 X3 X2 X5, (m1_subset_1 (esk9_5 X1 X2 X3 X4 X5) (k4_partfun1 X2 X3) → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X3 X5 X2 X1 X4, (r2_hidden (esk26_5 X1 X2 X3 X4 X5) X4 → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X1 X2)) → m1_subset_1 X3 (k5_finsub_1 (k4_partfun1 X1 X2)) → r2_hidden X5 (k4_substlat X1 X2 X3 X4) → False) → (∀X3 X5 X2 X1 X4, (r2_hidden (esk25_5 X1 X2 X3 X4 X5) X3 → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X1 X2)) → m1_subset_1 X3 (k5_finsub_1 (k4_partfun1 X1 X2)) → r2_hidden X5 (k4_substlat X1 X2 X3 X4) → False) → (∀X4 X1 X3 X2 X5, (r2_hidden (esk10_5 X1 X2 X3 X4 X5) X5 → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X4 X1 X3 X2 X5, (r2_hidden (esk9_5 X1 X2 X3 X4 X5) X4 → False) → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → r2_hidden X1 (a_4_0_substlat X2 X3 X4 X5) → False) → (∀X5 X2 X3 X1 X4, (r1_tarski (k4_substlat X2 X3 X5 X1) (k4_substlat X2 X3 X5 X4) → False) → r1_tarski X1 X4 → m1_subset_1 X5 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X1 (k5_finsub_1 (k4_partfun1 X2 X3)) → False) → (∀X1 X2 X3 X4, (r1_tarski X3 X4 → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X1 X2)) → m1_subset_1 X3 (k5_finsub_1 (k4_partfun1 X1 X2)) → r2_hidden (esk11_4 X1 X2 X3 X4) X4 → False) → (∀X4 X1 X3 X6 X7 X2 X5, (r2_hidden X5 (a_4_0_substlat X2 X3 X6 X7) → False) → X5 = (k2_xboole_0 X1 X4) → r2_hidden X4 X7 → r2_hidden X1 X6 → r1_partfun1 X1 X4 → m1_subset_1 X4 (k4_partfun1 X2 X3) → m1_subset_1 X1 (k4_partfun1 X2 X3) → m1_subset_1 X7 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X6 (k5_finsub_1 (k4_partfun1 X2 X3)) → False) → (∀X4 X1 X2 X3, (m1_subset_1 (k4_substlat X2 X3 X1 X4) (k5_finsub_1 (k4_partfun1 X2 X3)) → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X1 (k5_finsub_1 (k4_partfun1 X2 X3)) → False) → (∀X2 X1 X3 X4, (r1_tarski X3 X4 → False) → (r2_hidden (esk11_4 X1 X2 X3 X4) X3 → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X1 X2)) → m1_subset_1 X3 (k5_finsub_1 (k4_partfun1 X1 X2)) → False) → (∀X4 X1 X2 X3, ((k4_substlat X2 X3 X1 X4) = (a_4_0_substlat X2 X3 X1 X4) → False) → m1_subset_1 X4 (k5_finsub_1 (k4_partfun1 X2 X3)) → m1_subset_1 X1 (k5_finsub_1 (k4_partfun1 X2 X3)) → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk6_3 X1 X2 X3) X3 → r2_hidden (esk6_3 X1 X2 X3) X1 → False) → (∀X2 X3 X1, (X3 = (k2_xboole_0 X1 X2) → False) → r2_hidden (esk6_3 X1 X2 X3) X3 → r2_hidden (esk6_3 X1 X2 X3) X2 → False) → (∀X1 X3 X2, (X3 = (k2_xboole_0 X1 X2) → False) → (r2_hidden (esk6_3 X1 X2 X3) X3 → False) → (r2_hidden (esk6_3 X1 X2 X3) X2 → False) → (r2_hidden (esk6_3 X1 X2 X3) X1 → False) → False) → (∀X1 X2, (X2 = (k5_finsub_1 X1) → False) → v4_finsub_1 X2 → v1_finset_1 (esk7_2 X1 X2) → r2_hidden (esk7_2 X1 X2) X2 → r1_tarski (esk7_2 X1 X2) X1 → False) → (∀X3 X2 X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (k1_finsub_1 X1 X2 X3) X1 → False) → v4_finsub_1 X1 → m1_subset_1 X3 X1 → m1_subset_1 X2 X1 → False) → (∀X3 X2 X1, ((k1_finsub_1 X1 X2 X3) = (k1_finsub_1 X1 X3 X2) → False) → (v1_xboole_0 X1 → False) → v4_finsub_1 X1 → m1_subset_1 X3 X1 → m1_subset_1 X2 X1 → False) → (∀X3 X2 X1, ((k1_finsub_1 X1 X2 X3) = (k2_xboole_0 X2 X3) → False) → (v1_xboole_0 X1 → False) → v4_finsub_1 X1 → m1_subset_1 X3 X1 → m1_subset_1 X2 X1 → False) → (∀X3 X1 X2, ((k1_finsub_1 X1 X2 X2) = X2 → False) → (v1_xboole_0 X1 → False) → v4_finsub_1 X1 → m1_subset_1 X3 X1 → m1_subset_1 X2 X1 → False) → (∀X1 X3 X2, r2_hidden X3 X2 → r2_hidden X1 X2 → r2_hidden X1 (esk27_2 X3 X2) → False) → (∀X3 X1 X2, (r1_partfun1 X1 X2 → False) → v1_funct_1 X3 → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X3 → v1_relat_1 X2 → v1_relat_1 X1 → r1_tarski X2 X3 → r1_tarski X1 X3 → False) → (∀X1 X2, (X2 = (k5_finsub_1 X1) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → (r1_tarski (esk7_2 X1 X2) X1 → False) → v4_finsub_1 X2 → False) → (∀X3 X2 X1, (r1_tarski (k2_xboole_0 X1 X3) X2 → False) → r1_tarski X3 X2 → r1_tarski X1 X2 → False) → (∀X1 X2, (X2 = (k5_finsub_1 X1) → False) → (v1_finset_1 (esk7_2 X1 X2) → False) → (r2_hidden (esk7_2 X1 X2) X2 → False) → v4_finsub_1 X2 → False) → (∀X3 X2 X1 X4, (r2_hidden X1 X4 → False) → (r2_hidden X1 X3 → False) → X2 = (k2_xboole_0 X3 X4) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (r1_partfun1 X2 X1 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_relat_1 X1 → r1_partfun1 X1 X2 → False) → (∀X2 X1, (r2_hidden (esk27_2 X1 X2) X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X2 X4) → r2_hidden X1 X2 → False) → (∀X2 X4 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k2_xboole_0 X4 X2) → r2_hidden X1 X2 → False) → (∀X2 X1 X3, (r2_hidden X1 X3 → False) → X3 = (k5_finsub_1 X2) → v1_finset_1 X1 → v4_finsub_1 X3 → r1_tarski X1 X2 → False) → (∀X3 X1 X2, (r1_tarski X1 X2 → False) → X3 = (k5_finsub_1 X2) → v4_finsub_1 X3 → r2_hidden X1 X3 → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X1 X2) → False) → (∀X2 X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (k2_xboole_0 X2 X1) → False) → (∀X1 X2, (v1_funct_1 X2 → False) → v1_funct_1 X1 → v1_relat_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (X1 = X2 → False) → r1_tarski X2 X1 → r1_tarski X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v5_finset_1 (k2_xboole_0 X1 X2) → False) → v5_finset_1 X2 → v5_finset_1 X1 → False) → (∀X2 X1, (v1_finset_1 (k2_xboole_0 X1 X2) → False) → v1_finset_1 X2 → v1_finset_1 X1 → False) → (∀X1 X2, (v4_funct_1 X2 → False) → v4_funct_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v5_finset_1 X2 → False) → v5_finset_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X1 X2, (v1_finset_1 X2 → False) → v1_finset_1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X2 X1, (r1_partfun1 X1 X1 → False) → v1_funct_1 X2 → v1_funct_1 X1 → v1_relat_1 X2 → v1_relat_1 X1 → False) → (∀X2 X3 X1, (v1_finset_1 X1 → False) → X2 = (k5_finsub_1 X3) → v4_finsub_1 X2 → r2_hidden X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X2 X1, (v1_finset_1 X1 → False) → m1_subset_1 X1 (k5_finsub_1 X2) → False) → (∀X2 X1, (v1_relat_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X2 X1, (v1_funct_1 X1 → False) → v4_funct_1 X2 → m1_subset_1 X1 X2 → False) → (∀X1 X2, (v1_finset_1 X2 → False) → v5_finset_1 X1 → m1_subset_1 X2 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (m1_subset_1 (esk21_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (m1_subset_1 (esk15_1 X1) (k1_zfmisc_1 X1) → False) → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_funct_1 X1 → v1_relat_1 X1 → v1_zfmisc_1 X1 → False) → (∀X1, (v3_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v2_funct_1 X1 → False) → v1_xboole_0 X1 → v1_funct_1 X1 → v1_relat_1 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → v1_zfmisc_1 (esk21_1 X1) → False) → (∀X1, (v1_xboole_0 X1 → False) → v1_xboole_0 (esk15_1 X1) → False) → (∀X1, (v2_finset_1 X1 → False) → v1_xboole_0 X1 → v1_relat_1 X1 → False) → (∀X1, (v4_finsub_1 X1 → False) → v1_finsub_1 X1 → v3_finsub_1 X1 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → X1 = X2 → False) → (∀X1, (v5_finset_1 (k1_zfmisc_1 X1) → False) → v1_finset_1 X1 → False) → (∀X1, (v1_finset_1 (k1_zfmisc_1 X1) → False) → v1_finset_1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v1_zfmisc_1 X1 → False) → (v1_finset_1 (esk21_1 X1) → False) → False) → (∀X1, (v1_xboole_0 X1 → False) → (v1_finset_1 (esk15_1 X1) → False) → False) → (∀X1, (v4_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_finset_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v1_funct_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_finsub_1 X1 → False) → v4_finsub_1 X1 → False) → (∀X1, (v1_finsub_1 X1 → False) → v4_finsub_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_zfmisc_1 X1 → False) → (∀X1, (v1_finset_1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → ((k1_finsub_1 (k5_finsub_1 (k4_partfun1 esk1_0 esk2_0)) (k4_substlat esk1_0 esk2_0 esk3_0 esk4_0) (k4_substlat esk1_0 esk2_0 esk3_0 esk5_0)) = (k4_substlat esk1_0 esk2_0 esk3_0 (k1_finsub_1 (k5_finsub_1 (k4_partfun1 esk1_0 esk2_0)) esk4_0 esk5_0)) → False) → (∀X1 X2, v1_xboole_0 (k4_partfun1 X1 X2) → False) → (∀X1, v1_xboole_0 (k5_finsub_1 X1) → False) → (v3_funct_1 esk20_0 → False) → (v1_xboole_0 esk24_0 → False) → (v1_xboole_0 esk23_0 → False) → (v1_xboole_0 esk22_0 → False) → (v1_xboole_0 esk19_0 → False) → (v1_xboole_0 esk18_0 → False) → (v1_xboole_0 esk12_0 → False) → (∀X1 X2, (m1_subset_1 (esk17_2 X1 X2) (k4_partfun1 X1 X2) → False) → False) → ((m1_subset_1 esk5_0 (k5_finsub_1 (k4_partfun1 esk1_0 esk2_0)) → False) → False) → ((m1_subset_1 esk4_0 (k5_finsub_1 (k4_partfun1 esk1_0 esk2_0)) → False) → False) → ((m1_subset_1 esk3_0 (k5_finsub_1 (k4_partfun1 esk1_0 esk2_0)) → False) → False) → (∀X1 X2, (r1_tarski X1 (k2_xboole_0 X1 X2) → False) → False) → (∀X1 X2, (v4_funct_1 (k4_partfun1 X1 X2) → False) → False) → (∀X1 X2, (v1_relat_1 (esk17_2 X1 X2) → False) → False) → (∀X1 X2, (v1_funct_1 (esk17_2 X1 X2) → False) → False) → (∀X1 X2, (v1_finset_1 (esk17_2 X1 X2) → False) → False) → (∀X2 X1, ((k2_xboole_0 X1 X2) = (k2_xboole_0 X2 X1) → False) → False) → (∀X1, (m1_subset_1 (esk8_1 X1) X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 X1) = X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → (∀X1, ((k2_xboole_0 X1 k1_xboole_0) = X1 → False) → False) → (∀X1, (v4_finsub_1 (k1_zfmisc_1 X1) → False) → False) → (∀X1, (v4_finsub_1 (k5_finsub_1 X1) → False) → False) → (∀X1, (v4_finsub_1 (k5_finsub_1 X1) → False) → False) → ((v2_finset_1 esk24_0 → False) → False) → ((v4_funct_1 esk22_0 → False) → False) → ((v5_finset_1 esk23_0 → False) → False) → ((v2_funct_1 esk16_0 → False) → False) → ((v1_relat_1 esk24_0 → False) → False) → ((v1_relat_1 esk20_0 → False) → False) → ((v1_relat_1 esk19_0 → False) → False) → ((v1_relat_1 esk16_0 → False) → False) → ((v1_relat_1 esk13_0 → False) → False) → ((v1_funct_1 esk24_0 → False) → False) → ((v1_funct_1 esk20_0 → False) → False) → ((v1_funct_1 esk19_0 → False) → False) → ((v1_funct_1 esk16_0 → False) → False) → ((v1_funct_1 esk13_0 → False) → False) → ((v1_finset_1 esk23_0 → False) → False) → ((v1_finset_1 esk19_0 → False) → False) → ((v1_finset_1 esk12_0 → False) → False) → ((v1_xboole_0 esk14_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False